Course Title  Lead Instructors  ECTS credits  Course Code 

Pedagogy of Higher Education
The course offers an introduction to facilitating learning in higher education for PhD students who are asked to act as teaching assistants or supervisors. The course content focuses on aligning learning outcomes with learning activities and assessment strategies. Constructive alignment in the course is defined at high resolution such that learning outcomes for a course are elaborated into separate activities and assignments for students. In other words, learning outcomes need to be articulated at every level of learning activities from course to assignment.
The course also rests on the approach that learning is promoted by feedback. The assessment design that participants in the course design will therefore be required to reflect significant and effective use of continuous formative assessment. Such formative assessment requires strategic learning activities and assignments, and the course therefore comes with an emphasis on communicationtolearn activities including peer learning. Skoltech is an English medium instruction environment, and the course contains discussion topics to highlight ways of addressing the potential effects of language and culture barriers for high quality student learning. All topics in the course are applied by participants on their own teaching and learning experiences and are meant to be used as they prepare and plan for their teaching assistantships or their supervisory activities to come. All participants will have a task to produce a reflection on their future actions to evolve as facilitators and meet the requirements of the scholarship of teaching and learning. 
Magnus Gustaffson  3  PE03025 
Course Title  Lead Instructors  ECTS credits  Course Code 

Academic Communication: Preparatory English for Phd Exam (Term 1B2)
Efficient professional communication is the key to Academic success. The course is designed for PhD students who want to maximize their academic potential by boosting their ability to write research papers, present in front of multidisciplinary audiences, participate in scholarly discussions and engage in other forms of academic communication.
The main goal of the course is to enable PhD students to produce clear, correct, concise and coherent texts acceptable for the international professional community. The course is designed for a multidisciplinary audience. The course serves as a preparation for the qualification language exam, which is a prerequisite for the Thesis defense. 
Elizaveta Tikhomirova  1.5  PE03029 
Academic Writing Essentials (Term 1B2)
Academic writing skills are necessary for effective research, innovation, and educational activities in a multinational setting. The aim of the course is to provide guidelines and strategies for writing academic texts, focusing on relevant aspects of grammar, vocabulary, and style. The course includes analysis and practice of various forms of scientific and technical writing, and builds writing skills from sentences to paragraph structure, from summary to abstract, and lays the foundations for writing scientific papers and Master Thesis.
Modern science is, for most purposes, a collective collaborative effort, so the course is designed to promote individual and group responsibility by providing mutually related and timedependent tasks, such as peer review. The course is writingintensive with ample opportunity to practice editing and peerreviewing. 
Elizaveta Tikhomirova  1.5  MO03002 
Advanced Molecular Biology Laboratory Practice
This course offers students the opportunity to work individually on laboratory projects assigned by the course instructor. During the term students are expected to have at least one entire working day in the lab, although additional days may be required. Final grades are determined by the students' final presentations, which describe their project/goals along with the results/progress accomplished. Participation in the course requires approval from the students' own advisors, as well as the instructors of the course

Konstantin Severinov  6  MA06046 
Affine Lie Algebras and Conformal Field Theory (Term 56)
The course will be devoted to conformal theories (more precisely, their chiral parts – vertex algebras) with the symmetry of the affine Lie algebra and the theories that are obtained from them by basic constructions. The basic examples are WessZuminoWitten theory, coset theories, DrinfeldSokolov reductions. In general, we will discuss the mathematical aspects associated with the theory of representations and geometries. The course is supposed to be relatively advanced, see Course Prerequisites below.

Mikhail Bershtein  3  MA06321 
Applied Mathematics for Integrated Energy Systems
In this Ph.D. level 3 creditcourse (also accessible for motivated M.Sc. students) we discuss how modern Applied Mathematics, and specifically Optimization, Inference and Learning (OIL), methodology is expected to reshape future technologies acting across interdependent energy, i.e. power, natural gas and heating/cooling, infrastructures at both transmission and distribution, i.e. district/metropolitan/distribution, levels. The course will consist of 6 lectures and in independent studies done by students and resulted in an oral presentation and written report.
The course will start with description of the hierarchy of deterministic and stochastic planning and operational problems emerging in the context of physical flows over networks associated with the laws of electricity, gas, fluid and heatmechanics. Then we proceed to illustrate development and challenges of the OIL methodology on examples of: a) Graphical Models approach applied to a broad spectrum of the energy flow problems, including online reconstruction of the grid(s) topology from measurements; b) Direct and inverse dynamical problems for timely delivery of services in the district heating/cooling systems; c) Ensemble Control of the phasespace cycling energy loads via Markov Decision Process (MDP) and related reinforcement learning approaches. 
Michael Chertkov  3  MA03323 
Applied Methods of Analysis (Term 12) The course is addressed to undergraduates of the first year and contains applications of various mathematical methods for solving problems of mathematical physics. The course assumes familiarity with various sections of theoretical physics (classical mechanics, field theory, quantum mechanics, statistical physics, hydrodynamics, elasticity theory) on the example of solving specific problems. The main purpose of the course is to encourage undergraduates to independent research work. For this reason, the main element of the course is an independent solution to the problem, requiring the study of additional material. 
Sergei Khoroshkin  3  MA06317 
Bayesian Methods of Machine Learning
The course addresses Bayesian methods for solving various machine learning and data analysis problems (classification, regression, dimension reduction, topic modeling, etc.).
The course starts with an overview of canonical machine learning (ML) applications and problems, learning scenarios, etc. and then introduces foundations of Bayesian approach to solve these problems. Bayesian approach allows one to take into account subject domain knowledge and/or user’s preferences through a prior distribution when constructing the model. Besides, it offers an efficient framework for model selection. We discuss which prior distributions types are usually used, limit properties of a posterior distribution, and provide some illustrations of the Bayesian approach. The practical applicability of Bayesian methods in the last 20 years has been greatly enhanced through the development of a range of approximate inference algorithms such as variational Bayes and expectation propagation, as well as posterior simulation methods based on the Markov chain Monte Carlo approach. As a result Bayesian methods have grown from a specialist niche to become mainstream. Therefore, we devoted a second part of the course to approximation tools, vitally important for Bayesian inference, and provide examples how to use Bayesian approaches to automatically select features, tune the regularization parameter in regression and classification, etc. The last part of the course is devoted to advanced Bayesian methods, namely, Gaussian Processes and deep Bayesian neural networks, which have become widespread in the last 58 years. We discuss deep Bayesian framework and then illustrate its applications through construction of deep variational autoencoders, approaches to variational dropout, Wasserstein Generative Adversarial Networks, deep Kalman filter, etc. Home assignments include solution of applied problems, development of modifications of Bayesian ML algorithms, and some theoretical exercises. 
Evgeny Burnaev  6  MA06129 
Cancer Biology
The course is dedicated to basics of clinical and molecular cancer biology with emphasis on innovative drugs and technologies for cancer treatment and diagnostics.
the main themes to be discussed: 1What is cancer? Classification, staging, grading. The hallmarks of cancer Mutations, oncogenes, tumor suppressors. Genomic instability Epigenetics in cancer initiation and progression (miRNA, siRNA, lncRNA, methylation, histones modification, etc.) Cell cycle and growth and it’s deregulation in cancer Tumor energy metabolism (the Warburg effect), Cell death and it’s deregulation in cancer (necrosis, apoptosis, autophagy) Cell differentiation and dedifferentiation in cancer, EMT, Metastasis, Cancer stem cells hypothesis Tumor stroma and heterogeneity, neoangiogenesis. The “seed and soil hypothesis” – premetastatic niche Extracellular vesicles for communication between cells, Cancer diagnostics, tumor markers Liquid biopsy, Conventional treatment trajectories for patients Biological factors in Cancer (inflammation, viruses, bacteria, microbiome) Target therapy, Immune checkpoint inhibitors Emerging therapeutic modalities, CarT, dendritic cells, viruses Invited medical oncologists will give talks on the usolved questions in the field. 
Vera Rybko  3  MA03088 
Classical Integrable Systems (Term 56)
Course description: A selfcontained introduction to the theory of soliton equations with an emphasis on their algebraicgeometrical integration theory. Topics include:
1. General features of the soliton systems. 2. Algebraicgeometrical integration theory. 3. Hamiltonian theory of soliton equations. 4. Perturbation theory of soliton equations and its applications to Topological Quantum 
Igor Krichever, Anton Zabrodin 
3  MA06179 
Computational Materials Science Seminar (Term 14)
This is the main research seminar at Skoltech for Computational Materials scientists. All students of Computational Materials Science subtrack of Materials Science MSc program should attend this seminar. Topics include materials modeling (at atomistic scale), theoretical and computational chemistry, theoretical and computational physics of materials, underlying mathematical methods and algorithms etc. Invited lectures are top scientists in their research field.
Please see the seminar webpage at https://www.skoltech.ru/en/cms/ 
Dmitry Aksenov  0.75  MO03005 
Condensed Matter Spectroscopy and Physics of Nanostructures (Term 1B4)
The first part of this course covers major topics of the modern optical spectroscopy of solid state systems, including nanomaterials and novel topological materials. The introductory part of the course outlines the basic classical and quantum theory of electromagnetic response, and basics of the solid state spectroscopy. Then the major research directions in the modern condensed matter spectroscopy are considered, such as spectroscopy of graphene, topological materials, and transition metal dichalcogenides.
The second part of the course describes the physics of lowdimensional electron systems and nanostructures. Twodimensional electron and electronhole systems, lowdimensional disordered systems, quantum Hall effect, carbon nanostructures, photonic crystals and optical microcavities will be considered. 
Alexey Sokolik  1.5  MA06313 
Differential and Symplectic Geometry (Term 12)  Maxim Kazaryan, Sergei Lando 
3  MA06175 
Efficient Algorithms and Data Structures (Term 1B2)
Design and analysis of algorithms and data structures is a core part of Computer Science and is of fundamental importance to all application areas. The goal of this course is to provide a representative sample of advanced algorithmic notions and techniques that constitute a modern “toolbox” for solving reallife problems. We will mainly deal with basic discrete objects – sets, trees, graphs, strings, … – and present efficient data structures and algorithms for solving various basic problems on these objects. Therefore, this course can be viewed as a basis for more specialized subjects. Lecture part of the course will focus on principles and ideas as well as on their mathematical justification. The practical part will be devoted to programming exercises and developing practical problem solving skills.

Gregory Kucherov  3  MA06270 
Energy Colloquium
The Energy Colloquium educates the audience in the presentday research and applications within the broader field of Energy Science and Technology. The Colloquium consists of a series of presentations by invited academic and industry speakers. The presentations target a nonspecialist audience.
All Master and Ph.D. students within the Energy Program are encouraged to attend the Energy Colloquium during the entire period of their studies. Students can earn 1 credit, if he/she participates in the Energy Colloquium over the course of any 2 terms of the academic year. Students who passed one round can make next (for credit) over the course of their subsequent studies. 
Alexei Buchachenko  1  MA01092 
English Toolkit (Term 1B2)
The goal of the English Toolkit course is to activate Academic English skills required for successful education at Skoltech.
The students will practice Academic vocabulary and grammar, as well as boost their reading, writing and speaking skills. The blended format includes a weekly online workload plus an offline group tutorial providing a flexible and individualised learning trajectory. Realtime feedback in online exercises will be complimented by tutor feedback for the writing and speaking assignments. 
Elizaveta Tikhomirova  1.5  MO03001 
English. Candidate Examinations
This is a metacourse which allows PhD students to register for English Qualification Exam for the Russian PhD Degree. There will be no lectures or seminars, only the exam. The preparatory course is also available in course catalog (look for "Academic Communication for PhD students" course).
The Exam has two parts: Part 1 – Preexam activities (Assignments 1, 2a, 2b) 
Elizaveta Tikhomirova  3  PE03003 
Experimental Data Processing
The course introduces students to practically useful approaches of data processing for control and forecasting. The focus will be on identifying the hidden and implicit features and regularities of dynamical processes using experimental data. The course exposes data processing methods from multiple vantage points: standard data processing methods and their hidden capacity to solve difficult problems; statistical methods based on statespace models; methods of extracting the regularities of a process on the basis of identifying key parameters. The course addresses the problems in navigation, solar physics, geomagnetism, space weather and biomedical research and will be useful for broad range of interdisciplinary applications.

Tatiana Podladchikova  6  MA06238 
Fast and Efficient Solvers
Partial differential and integral equations play a key role in modelling of modern physical and engineering applications. Problems arising in these applications often require largescale computations, so fast and efficient methods have to be used. This course is devoted to modern algorithms that have nearlinear time complexity for largescale partial differential and integral equations. Course topics include fast multipole method and hierarchical lowrank matrices, highfrequency problems, multigrid and domain decomposition methods. Examples of applications include aircraft modelling, MRI, electronic structure computations and acoustics.

Ivan Oseledets  6  MA06227 
Fluid Mechanics
The course will be given one time only. This basic course represents the minimum of what every physicist, engineer and mathematician needs to know about fluids. The main goal is to develop physical intuition and learn the art of making fluidmechanical estimates, equally needed for theoreticians in biophysics and astrophysics, as well as for experimentalists and engineers in nanophysics and optics. We shall understand why exactly the wind blows, the aircraft do not fall out of the sky, and the water cannot be held in an upsidedown glass. The subjects will range from the very viscous flows produced by swimming bacteria and electrons in graphene to very turbulent flows in oil pipes and clouds and Millennium problem in mathematics. We shall also consider nonlinear wave phenomena with applications in acoustics, optics and cold atoms.

Gregory Falkovich  3  MA03280 
Foundations of Engineering Physics (Term 1B4)
The course is dedicated to basics of building interfaces ”experimentcomputer” in the modern scientific research. In most general configuration such interface comprises three stages:
1) “input” analog frontend feeding the electronic signals from sensors, transducers, 2) analogtodigit as well as digittoanalog conversion “bridges” and 3) logical channels conveying the ultimate digital information to a computer. The consideration of the three stages is made with emphases on the principle aspects of scientific measurements rather than detailed schematic/circuitry of the instrumentation. All stages of the measurement systems will be reviewed from the point of view of the fundamental imperatives of signal conditioning like impedance matching, optimal choice of the bandwidth solving the ubiquitous tradeoff “precision versus rate” of data acquisition and et al. As well important peculiarities of configuring the elements of the system – such as prefiltering, modulationdemodulation techniques, the choice of the type and bit width of ADCs/DACs – will also be thoroughly discussed. At all stages a short concomitant overview of the modern commercially available electronic equipment will be given in order to improve students’ ability to select a proper set of the electronic devices among a great variety of those available on the market. 
Yuri Romanovskiy  1.5  MA06213 
Geometric Representation Theory (Term 12)
Geometric representation theory applies algebraic geometry to the problems of
representation theory. Some of the most famous problems of representation theory were solved on this way during the last 40 years. The list includes the Langlands reciprocity for the general linear groups over the functional fields, the LanglandsShelstad fundamental Lemma, the proof of the KazhdanLusztig conjectures; the computation of the characters of the finite groups of Lie type. We will study representations of the affine Hecke algebras using the geometry of affine Grassmannians (Satake isomorphism) and Steinberg varieties of triples (DeligneLanglands conjecture). This is a course for master students knowing the basics of algebraic geometry, sheaf theory, homology and Ktheory. 
Mikhail Finkelberg  3  MA06271 
Hamiltonian Mechanics (Term 12)
This is the first among the base courses in the theoretical physics, aimed for the master
students. Matematical methods of modern theory of Hamiltonian systems are based on the concepts, The preliminary program of the course includes: 
Andrei Marshakov  3  MA06174 
Innovation Workshop
The Innovation Workshop (IW) is a unique onemonth, fulltime, intensive “boot camp” style MSlevel course that unites the entire Skoltech incoming class with Skoltech faculty and esteemed invited mentors to create a foundational experience in Entrepreneurship and Innovation (E&I) for all. IW is designed to instill a positive “cando” teamwork attitude in the Skoltech culture, as well as to cultivate the art of prototyping the entire end user need. IW students prototype quickly, under pressure, with help from others, and based on whatever resources are at hand. Experiential inquirybased learning leads IW student through the entire technology innovation cycle along the three pillars of innovation: (i) Impact (a.k.a. End User Need), (ii) Embedded Technology Prototype (provided and validated by good science), and (iii) End User Delivery (a.k.a. Business Model). This work is performed in crossdisciplinary teams operating under time pressure thus creating real life experience of complex innovation project. IW is less about knowledge and more about developing skills and attitudes necessary to lead successful life in innovation. It is also an opportunity for students to learn more about Skoltech’s basic values and meet the entire class and most of the faculty in an intensive relationshipbuilding setting.

Dmitry Kulish  6  MC06001 
Innovation and Intellectual Property Studies Doctoral Seminar (Term 14)
This course is a compulsory academic seminar series for all Ph.D. students in the Innovation and Intellectual Property Management Ph.D. Program. It consists of weekly research seminars that address the state of the art in research about the role of intellectual property in technological innovation. Specific topics and themes in the course will vary from year to year, but will typically include: theories of innovation; concepts and theories in IP management; practical issues in IP management; case studies in IP strategy; valuation of IP; Russian and international trends in intellectual property law; topics in technology entrepreneurship; product development and new technology; IP and design; patent analytics for innovation research; commercialization strategies of technology startups; organizational issues in technology innovation; conceptual issues at the interface of technology, science and business; public policy for technology, science and innovation; ethical and social issues related to IP and technological innovation; case studies in innovation management; philosophy of technology and philosophy of intellectual property; theory and methodology in IP management research; technology transfer and commercialization of university research; international collaboration and international trade in technology. As part of their seminar obligations, all students must prepare a formal written research paper on a topic that may or may not be directly related to their thesis research and make a presentation about the paper to the seminar group. The paper will be assessed.

Kelvin Willoughby  1.5  PC06009 
Introduction to "Life Sciences" program
Professors from the Life Science Center will tell about their labs and research projects. This course will help students to select a lab of their interest and a future research adviser.
The information about the Life Science labs is here: https://crei.skoltech.ru/cls/researchprojects/currentprojects/ As final project students should select a research topic from one of the labs, write a short text about a possible project and discuss it. It will be the first step for future thesis research or just training. The final schedule (what lecture reads which professor, and when) will be available by the end of the September. 
Mikhail Gelfand  3  MA03306 
Introduction to Advanced Manufacturing Technologies
The course provides an introduction to the field of Advanced Manufacturing and Digital Engineering Technologies and focuses on three main research and educational thrusts of the Center for Design, Manufacturing and Materials, namely the Advanced Manufacturing Technologies, Digital Engineering Technologies, and Mechanics and Physics of Advanced Manufacturing. The first thrust is focused on advanced technologies such as Industrial Robotics, Advanced Manufacturing of Composite Materials, Additive Technologies, Thermal Spray Coatings, and Materials Selection in Design. The second thrust is focused on digital engineering technologies related to simulationdriven product development, model based systems engineering, digital manufacturing, product lifecycle management, geometric modeling in ComputerAided Design, and numerical and optimization methods. Finally, the last thrust consists of fundamental disciplines required to understand the mechanics and physics of advance manufacturing processes, to develop mathematical models of these process to predict and improve the properties of the materials, structures, and engineering properties of the materials, structures, and engineering systems, as well as to develop digital twins of manufacturing processes and its individual components, what is commonly referred as simulationbased engineering science.
Professors from the Center for Design, Manufacturing and Materials will provide overviews of their laboratories and research projects. This course will help students to select a specialization and a future research adviser. The information about the Center for Design, Manufacturing and Materials and its laboratories can be found at: https://https://crei.skoltech.ru/cdmm As a final project students should select a research topic, write a short text about a possible project and discuss it. 
TBD  6  MA06296 
Introduction to Data Science
The course gives an introduction to the main topics of modern data analysis such as classification, regression, clustering, dimensionality reduction, reinforcement and sequence learning, scalable algorithms. Each topic is accompanied by a survey of key machine learning algorithms solving the problem and is illustrated with a set of realworld examples. The primary objective of the course is giving a broad overview of major machine learning techniques. Particular attention is paid to the modern data analysis libraries which allow solving efficiently the problems mentioned above.

Mikhail Belyayev, Maxim Panov 
3  MA03111 
Introduction to IoT
In the last decade the Internet of Things (IoT) paradigm has slowly but steadily and increasingly permeated what researchers and engineers study and build. The term “Internet of Things” doesn’t have a single definition and people today often use it to interchangeably refer to Wireless Sensor Network (WSN), MachinetoMachine (M2M), Web of Things (WoT) and other concepts. The focus of this course is to learn about these technologies that will be extending the Internet as we know it and use it today, to interconnect not only people and computers but also sensors and associated objects. The course will be divided into two strongly coupled parts. The first part of the course covers the IoT ‘pillar’ technologies, i.e. embedded systems, wireless sensor networks, semantic technologies, and theory behind them while the second part will have a special focus on IoT development, i.e. IoT apps, open platforms, sensors and actuators, software/middleware. Apart from covering the theory behind the IoT and “how to connect things to the Internet”, the course will therefore also engage the students to demonstrate the feasibility of simple IoT real applications and will challenge them to improve their applications through the use of cognitive technologies and cloud computing.

Andrey Somov  3  MA03233 
Introduction to Petroleum Engineering (Term 1B2)
The course is an introduction to Petroleum Engineering and gives an overview of Petroleum Engineering and its various components and their internal connection.
The course will address the story of oil from its origin to the end user. The objective is to provide an overview of the fundamental operations in exploration, drilling, production, processing, transportation, and refining of oil and gas. As additional topics it is planned to consider Permafrost Engineering and Flow Asuurance, which are actual for Russian Oil&Gas Industry. Within the framework of the course it is planned to invite speakers form industry. 
Evgeny Chuvilin  3  MA06064 
Introduction to The Quantum Field Theory (Term 12)
Introduction to basic notions of gauge theory: gauge invariance, SU(N) Lie algerbras and their representations, Yang Mills Largangian and its quantization, FaddeevPopov method, ghosts and unitarity, diagram technique, basics on perturbation theory, analysis of simplest Feynman diagramms, beta function in nonabelian YangMills theory, renormalization group, asymptotic freedom, Higgs mechanism, basic notions of QCD and electroweak interaction. Depending on progress: some advanced topics: anomalies, instantons.

Yaroslav Pugai  3  MA06273 
Introduction to The Theory of Disordered Systems (Term 12)
This course is mainly dealing with the quantum electronic properties of disordered materials. I start with a review of different types of disorder and general methods of their theoretical treatment. Then I give a detailed discussion of the two popular models of quenched disorder, widely used for description of quantum solid state systems: Anderson model and Lifshits model. I discuss the properties of the disordered systems in the insulating phase: the density of states, the tails in the optical absorption ( with the optimal fluctuation method) and different versions of hopping conductivity: the nearest neighbour hopping and the Mott's variable range hopping. I also take into account the longrange Coulomb correlations and derive the Coulomb gap in the density of states and the EfrosShklovskii law for the conductivity.
As to the vicinity of the metalinsulator transition, I give a qualitative discussion of the mechanism behind the transition, as well as the most powerful tools for probing the properties of the system near the transition: analysis of inverse participation ratios and the concept of multifractality of the wavefunctions. In the metallic phase I discuss the weak localization corrections, including magnetoresistance, inelastic phasebreaking mechanisms and interactioninduced anomalies in the density of states near the Fermi surface. At the end of the course I give a brief introduction to mesoscopics, including the Landauer formalism and quantization of the ballistic conductance. 
Alexey Ioselevich  3  MA06274 
LargeScale Optimization
This MSc level course is an applicationoriented introduction to numerical optimization. It will focus on modeling realworld engineering tasks as optimization problems and using stateoftheart optimization techniques to solve these problems. The course will start with the basics of convex analysis, then we go ahead to iterative optimization algorithms to solve convex optimization problems. The last part of the course focuses on realworld engineering applications and provides a student with the stateoftheart techniques to solve them.

Yury Maximov  3  MA03123 
Laser Spectroscopy (Term 1B4)  Alexander Makarov  1.5  MA06212 
Lie Groups and Lie Algebras, and Their Representations (Term 12)
We shall begin with the basics of the theory of Lie groups and Lie algebras. Then we shall provide an accessible introduction to the theory of finitedimensional representations of classical groups on the example of the unitary groups U(N).
Tentative plan: linear Lie groups and their Lie algebras; universal enveloping algebras; Haar measure on a linear Lie group; general facts about representations of compact groups and their characters; radial part of Haar measure; Weyl's formula for characters of the unitary groups; Weyl's unitary trick; classification and realization of representations; symmetric functions. 
Grigory Olshanski  3  MA06173 
Master Your English for Thesis (Term 57)
Writing is the key priority and the need of utmost importance for wouldbe scientists. Science demands not just writing, but good writing, that presupposes the skills to communicate ideas, theories and findings as efficiently and clearly as possible. Science lives and dies by how it is represented in print and a printed material is the final product of scientific endeavour. The primary goal of this course is to prepare master students for wiring, editing, and defending a Master Thesis.
This course is designed to explain how to write chapters of their Thesis through practical examples of good writing taken from the authentic linguistic environment. The course teaches how to overcome certain typical problems in writing a text of a thesis and abounds in useful linguistics assistance on its various parts. Feedback on students’ texts will constitute the major part of the course. 
Anastasiia Sharapkova  1.5  MO03003ls 
Master Your English for Thesis (Term 57)
The key to efficient professional communication is the ability to convey ideas clearly, coherently and correctly both orally and in writing.
The Course offers concise and practical guidelines for writing and defending a Master Thesis at Skoltech. The course focuses on the main parts of the Thesis in terms of structure, vocabulary and grammar, and their transformations for a presentation with slides. Students will develop a conscious approach to own writing and presentations through thorough analyses of the best authentic examples combined with intensive writing and editing practice. The ‘processforproduct’ approach teaches the students to write – use (peer) reviewer’s advice – revise/edit – repeat, and creates linguistic awareness needed to avoid the typical pitfalls. The Course is offered in two modules which gradually build on the necessary writing and presentation skills. 
Elizaveta Tikhomirova  1.5  MO03003 
Mathematics for Engineers
The aim of this is to recap the basic topics that you are expected to get at bachelor level. If you do not feel confident with basic matrix manipulations, integration and differentiation – you should definitely take this course; fluency in these is a must for an educated engineer. At the first day of studies you’ll take the preliminary exam to make final decision regarding taking this course.

Elena Gryazina  3  MA03282 
Molecular Biology (Term 1B2)
Molecular biology course is based on learning the principles of replication, recombination, DNA repair. Additionally, replication strategies of phages and viruses will be discussed. Mitosis and meiosis will be described in a context of DNA biosynthesis. Also, the principles of RNA biosynthesis, i.e. transcription and processing, as well as protein biosynthesis, i.e. translation, maturation and transport will be described.
The goal of the course is obtaining a comprehensive knowledge on the structure of DNA and processes of DNA replication, recombination and repair in bacteria and eukaryotes, as well as on replication of phages and viruses. To obtain a detailed knowledge on the processes of transcription, in bacteria and eukaryotes, on the regulation of transcription in bacteria and eukaryotes, on examples of complex networks of transcriptional regulation in bacteria and eukaryotes, on maturation of RNA in eukaryotes, on protein biosynthesis in bacteria and eukaryotes, on the transport of protein in bacteria and eukaryotes. Students activities include: 
Petr Sergiev  3  MA06034 
Molecular Spectroscopy (Term 1B4)  Vladimir Mironenko  1.5  MA06209 
Nanooptics
Nanooptics aims at the understanding of optical phenomena on the nanometer scale, i.e. near or beyond the diffraction limit of light. Typically, elements of nanooptics are scattered across the disciplines. Nanooptics is built on the foundation of optics, quantum optics, and spectroscopy. In the presence of an inhomogeneity in space the Rayleigh limit for the confinement of light is no longer strictly valid. In principle infinite confinement of light becomes possible, at least theoretically.
The course will cover basic theoretical concepts, multiphoton microscopy, interaction of light with nanoscale systems, optical interaction between nanosystems, and resonance phenomena, namely localized surface plasmons, surface plasmon polaritons, and microresonators. 
Vladimir Drachev  3  MA03153 
Pedagogical Experience
The main function of this course is to articulate Skoltech's expectations on Phdstudents who do their pedagogical TA assignment as Skoltech. The course describes the intended learning outcomes and how they are assessed.
The course also offers a forum for TA and allows Skoltech TAs to collect and discuss resources and issues relevant for their TA experience. The forum provides a peertopeer feedback opportunity but also enables instructors to participate in the conversation when asked to. The main bulk of the 81 hours of the course is spent in the actual courses in which the PhDstudents do their TAassignments. The assignments in the course itself require less than 10 hours of time. 
Magnus Gustaffson  3  PE03005 
Quantum Mechanics
The course will review the basic concepts of quantum mechanics. It is intended both for those who studied quantum mechanics previously and for those who did not. The purpose of the course is not only to introduce the main principles of quantum mechanics but to familiarize with them through active problem solving, which is the only practical way to study quantum mechanics. The course will cover the main topics such as onedimensional motion, perturbation theory, scattering theory, approximate methods in quantum mechanics, density matrix formalism.

Mikhail Skvortsov  3  MA03177 
Quantum Theory of Radiation and Quantum Optics (Term 1B4)  Yuri Lozovik  1.5  MA06314 
Research Methodology: Space Center Seminar (Term 14)  Anton Ivanov  3  PA03102es 
Research seminar "Modern Problems of Mathematical Physics" (Term 18)
Course "Modern problems of mathematical physics" is a student seminar, so participants are expected to give talks based on the modern research papers. Current topic of the seminar can vary from time to time: now it is devoted to the study of N=2 supersymmetric gauge theory and its links with random matrix models, complex curves, and integrable systems. Other topics that were already covered, or can be covered in the future, are: classical integrable equations, complex curves and their thetafunctions, quantum integrable models (quantummechanical and fieldtheoretical), models of statistical physics.

Andrei Marshakov  1.5  MA12268 
Research seminar "Modern Problems of Theoretical Physics" (Term 18)
Research seminar "Modern Problems of Theoretical Physics" is supposed to teach students to read, understand and represent to the audience recent advances in theoretical physics. Each student is supposed 1) to choose one of recent research papers from the list composed by the instructor in the beginning of each term, 2) read it carefully, 3) present the major results of the paper to his/her colleagues during the seminar talk, 4) answer the questions from the audience about the content of the paper. The papers in the list are selected, normally, from the condensed matter theory and related fields, like: physics quantum computing, statistical physics, etc. The papers to the list are usually chosen from most competitive physics journals, like Nature Physics, Science, Physical Review Letters, Physical Review X and others.

Mikhail Feigelman, Konstantin Tikhonov 
1.5  MA12319 
Research seminar "Strings and Cluster Varieties" (Term 18)
The course is directed to substantive work of the master and PhD students in order to understand recently found relations among supersymmetric gauge theories, refined topological strings, cluster varieties and integrable systems. The plan of wrk on the course consists of several introductive lectures on the various consistuents of the subject as well as student talks on recent original papers and results of their own investigation. The core topics include relation between cluster varieties and Painleve equations and approaches to the SeibergWitten theories with fundamental matter based on Toda systems and spin chains.

Andrei Marshakov  1.5  MA12176 
Scientific Computing
This is an introductory course to Scientific Computing with a focus on mathematical and algorithmic aspects of HighPerformance Computing (HPC) techniques and their areas of applications. The course has also a practical component, consisting of learning basic principles of HPC and applying the acquired knowledge and skills to solving industryrelevant problems in oil & gas, electrochemical energy storage, aerospace, food and pharmaceutics.
The practical aspects of use of a variety of computational techniques for solving scientific and engineering tasks will be taught during practical demonstrations and they will be integrated as much as possible with the corresponding theoretical materials given during the lectures. During the practical demonstrations the students will get access to the parallel cluster in Skoltech. All topics in the course will be covered at an advanced introductory level, with the goal that after passing the course the students will learn enough to start using scientific computing and HPC methods in their everyday research work. Once the students reached that level, they will learn more details and more advanced subjects in other courses in the overall Computational Science & Engineering program. Students should be comfortable with undergraduate mathematics, particularly with basics of calculus, linear algebra and probability theory. Some preliminary knowledge of Unixlike operative systems is a plus. Many of the examples used in lectures and assignments will require this background. Although the course will overview most popular pieces of commercial software used in HPC, all of the software used for practical tasks in this course is open source and freely available. 
Maxim Fedorov  6  MA06113 
Space Center Seminar (Term 14)
The seminar will cover current topics in the space domain: latest news, discoveries. Also planned that all PhD students and some Master students will present their research. External lecturers will be invited regularly to focus on the main applications of space technologies: science, telecommunication, navigation and remote sensing. Aspects of space technologies will also be discussed: structures, software, attitude determination and control systems, on board computers, communication system power supply systems and others. The seminar will be offered in English.

Anton Ivanov  0.25  MO01004 
Survey of Materials
Please see the course website for syllabus and other information: http://zhugayevych.me/edu/Materials/index.htm
The course teaches fundamentals of modern Materials Science (Part I of the course) and provides a survey of materials (Part II), covering all relevant Skoltech research areas and beyond, with brief explanation of structural, electronic, physical, chemical or other properties of materials relevant for their practical use, or from the point of view of utilizing their unique properties in applications. It is a core course in Materials Science educational track providing a reference knowledge base for the rest of materialspecific courses as well for student research. 
Andriy Zhugayevych  6  MA06063 
Theory of Phase Transitions (Term 12)
The role of longrange thermal fluctuations in the condensed matter
physics is considered. We give a theory of the second order transitions starting from the Landau expansion in the order parameter. As an introduction we consider the mean field theory, then we take into account fluctuations the role of which can be examined in the framework of the perturbation theory and the socalled renormgroup formalism. The peculiarities of a weak crystallization transition where fluctuations qualitatively change the nature of the phase transition in comparison with the mean field picture are treated on the same diagrammatic language. The theoretical approach based on the Landau expansion is utilized to examine thermal fluctuation effects far from phase transition points. We consider the longscale properties of smectics where fluctuations destroy the longrange order. The smectics are treated in the framework of the renormgroup approach. The same renormgroup technique is developed also for twodimensional ferromagnets where the effective coupling constant increases with increasing scale what drastically change longscale properties of the system. Longrange fluctuations are also relevant for membranes which are twodimensional objects immersed into a threedimensional fluid. Elastic modules of a membrane are logarithmically renormalized, the renormalization law can be found by using renormgroup methods. Of special interest is BerezinskiiKosterlitzThouless phase transition in superfluid, crystal or hexatic films which is related to appearing free point defects (vortices, dislocations or disclinations). The problem can be mapped into sineGordon model and then examined by renormgroup methods. We present some facts concerning critical dynamics and the socalled KPZ (KardarParisiZhang) problem. Then we consider peculiarities of the 2d hydrodynamics and passive scalar. 
Vladimir Lebedev  3  MA06138 
Course Title  Lead Instructors  ECTS credits  Course Code 

Academic Communication: Preparatory English for Phd Exam (Term 1B2)
Efficient professional communication is the key to Academic success. The course is designed for PhD students who want to maximize their academic potential by boosting their ability to write research papers, present in front of multidisciplinary audiences, participate in scholarly discussions and engage in other forms of academic communication.
The main goal of the course is to enable PhD students to produce clear, correct, concise and coherent texts acceptable for the international professional community. The course is designed for a multidisciplinary audience. The course serves as a preparation for the qualification language exam, which is a prerequisite for the Thesis defense. 
Elizaveta Tikhomirova  1.5  PE03029 
Academic Writing Essentials (Term 12)
Academic writing skills are necessary for effective research, innovation, and educational activities in a multinational setting. The aim of the course is to provide guidelines and strategies for writing academic texts, focusing on relevant aspects of grammar, vocabulary, and style. The course includes analysis and practice of various forms of scientific and technical writing, and builds writing skills from sentences to paragraph structure, from summary to abstract, and lays the foundations for writing scientific papers and Master Thesis.
Modern science is, for most purposes, a collective collaborative effort, so the course is designed to promote individual and group responsibility by providing mutually related and timedependent tasks, such as peer review. The course is writingintensive with ample opportunity to practice editing and peerreviewing. 
Elizaveta Tikhomirova  1.5  MO03002 
Advanced Manufacturing of Composite Materials
This course is developed to give students a broad background and hands on experience in manufacturing of advanced composite materials. Both materials and manufacturing methods are discussed. A brief introduction to advanced composite materials and processes is presented. The course is focused on the innovative nonautoclave technologies of thermosetting resin based/fiber reinforced advanced composites. Manufacturing is covered in terms of the major steps required to fabricate laminated composite parts. These will be described and discussed in details and worked out experimentally through conducting a set of lab projects. The following technologies and methods will be covered: Vacuum Infusion, Press Molding, Pultrusion, Filament Winding, and Mechanical Testing. Typical problems of materials, tooling, cure, and technological defects will be discussed.

Iskander Akhatov  6  MA06298 
Advanced Molecular Biology Laboratory Practice
This course offers students the opportunity to work individually on laboratory projects assigned by the course instructor. During the term students are expected to have at least one entire working day in the lab, although additional days may be required. Final grades are determined by the students' final presentations, which describe their project/goals along with the results/progress accomplished. Participation in the course requires approval from the students' own advisors, as well as the instructors of the course

Konstantin Severinov  6  MA06046 
Advanced PLM techniques: Digital Design and Optimization
This course is dedicated to the endtoend design methodology, based on the PLM approach. During the course students will develop small unmanned aerial vehicle with deployable wings.
The design includes: concept development, conceptual design, systems engineering, 3D physical simulation (CFD and FEM), parametric and topology optimization, final solid design. Educational process is focused on teamwork in this course. Siemens Teamcenter PLM platform is used as to provide interaction within students workgroup. The course provides students with a theoretical and practical basis for implementing projects devoted to the design of complex technical systems, such as unmanned aerial vehicles. 
Ighor Uzhinsky  6  MA06252 
Advanced Quantum Mechanics  Mikhail Feigelman  6  MA06207 
Advanced Solid State Physics
The course presents an overview of solidstate physics with emphasis on the quantum properties of solids. It covers quantum theory of electronic and lattice degrees of freedom, magnetism and superconductivity, including, in particular, stronglycorrelated electronic systems and hightemperature superconductivity. The course also includes a review of experimental techniques used in the modern solidstate physics research.
The course assumes basic preliminary knowledge of quantum mechanics and statistical physics. Secondquantization formalism is introduced and used throughout the course. 
Boris Fine  6  MA06068 
Aerosol Science and Technology
The course will introduce the basic phenomena of aerosol science, particle formation in the gas phase and their behavior, concepts and measurement techniques for the aerosol particles. Students will synthesize (carbon nanotubes, NaCl, metal and polymer) nanoparticles by two aerosol techniques: gastoparticle and liquidtoparticle conversions.
The student will perform the online measurements of number size distribution of aerosol synthesized nanoparticles by differential mobility analyzer (size range: 21000 nm). Students will become familiar with processes of the aerosol particle collection (filtration, electrostatic precipitation, thermophoretic precipitation). The produced samples of nanoparticles will be observed with means of transmission and scanning electron microscopies. 
Albert Nasibulin  3  MA03300 
Affine Lie Algebras and Conformal Field Theory (Term 56)
The course will be devoted to conformal theories (more precisely, their chiral parts – vertex algebras) with the symmetry of the affine Lie algebra and the theories that are obtained from them by basic constructions. The basic examples are WessZuminoWitten theory, coset theories, DrinfeldSokolov reductions. In general, we will discuss the mathematical aspects associated with the theory of representations and geometries. The course is supposed to be relatively advanced, see Course Prerequisites below.

Mikhail Bershtein  3  MA06321 
Applied Methods of Analysis (Term 12) The course is addressed to undergraduates of the first year and contains applications of various mathematical methods for solving problems of mathematical physics. The course assumes familiarity with various sections of theoretical physics (classical mechanics, field theory, quantum mechanics, statistical physics, hydrodynamics, elasticity theory) on the example of solving specific problems. The main purpose of the course is to encourage undergraduates to independent research work. For this reason, the main element of the course is an independent solution to the problem, requiring the study of additional material. 
Sergei Khoroshkin  3  MA06317 
Bioinformatics
This course is aimed for the first year master students with no prior knowledge in bioinformatics. The main course idea is to get students from different backgrounds acquainted with basic tools and algorithms in bioinformatics, such as basic phylogenetic analysis, algorithms behind sequence alignments, protein structure analysis, gene and genome annotation, as well as main databases storing sequence, protein and epigenetics data.
The knowledge obtained during this course can be immediately utilized in real biological and computational projects. 
Mikhail Gelfand  6  MA06307 
Biomedical Innovation and Entrepreneurship  Dmitry Kulish  3  MC03013 
Business Communication
Business Communication is an intensive hands on, practical course, designed to provide Skoltech students with the set of skills needed to effectively communicate with others – their classmates, working teams, professors and any audiences inside and outside of Skoltech. The course learning outcomes correspond directly with the Group 3 of Skoltech learning outcomes – “Relating to Others – Communication and Collaboration”. The course will show students the secrets and technologies to becoming confident when speaking in public – developing the skills they will be able to use throughout their career and their life. In a highly interactive, informative and supportive manner through inclass activities, games and simulations the course will enable students to: Speak with confidence and overcome their nervousness; Establish rapport with any audience; Present their message in a clear, concise, and engaging manner; Successfully manage impression they make onto audience; Create—and repurpose—presentations quickly and efficiently; Make successful and memorable pitch; Sharpen the story they want to tell; Use confidently body language and movement, strengthening their speech; Respond to questions and comments without getting flustered; Gain people’s attention, respect, and cooperation.

Maxim Kiselev  3  MC03014 
Cardiovascular integrative physiology
This course will give advanced understanding of normal physiology and pathophysiology of cardiovascular system. The course Transgenic model in drug discovery will be continuation of it and students attended IPCS will have advantage to be inrolled in TGMDD It will include following topics which will be studied in the form of lectures, seminars and students projects:
General anatomy and histology of the heart and blood vessels. The course also will include principles of regulation of blood pressure, Guton theory, Theory of vascular resistance. Genetic predisposition to hypertension. Genetic loci associated with essential hypertension and GWAS studies in humans. Mutagenesis screens for new genes involved in cardiovascular pathology. Modern methods in cardiac physiology, renal physiology, vascular biology. 
Yuri Kotelevtsev  3  MA03308 
Classical Integrable Systems (Term 56)
Course description: A selfcontained introduction to the theory of soliton equations with an emphasis on their algebraicgeometrical integration theory. Topics include:
1. General features of the soliton systems. 2. Algebraicgeometrical integration theory. 3. Hamiltonian theory of soliton equations. 4. Perturbation theory of soliton equations and its applications to Topological Quantum 
Igor Krichever, Anton Zabrodin 
3  MA06179 
Communication Technologies for Iot
This is a newly developed course that prepares students for the applying modern telecommunication technologies, both wired and wireless in the Internet of Things area.
The course combines lectures and labs related to hardware, transmission techniques, the mediumaccess control layer, networking, applications and standards for the IoT communication technologies. All technologies are considered with usecase based approach that shows their practical application in real industrial and research scenarios. 
Dmitry Lakontsev  3  MA03234 
Computational Chemistry and Materials Modeling
The course provides an overview of modern atomistic computer simulations used to model, understand, and predict properties of realistic materials. The emphasis is on practical techniques, algorithms and programs to bridge theory and applications, from the discovery of materials to their use in realworld technologies. This introductory course is intended for both theoreticians and experimentalists in modern Materials Science at academic level ranging from MSc students to PhD students and postdocs. For more information please see the course website at http://zhugayevych.me/edu/CC/index.htm

Andriy Zhugayevych  6  MA06008 
Computational Materials Science Seminar (Term 14)
This is the main research seminar at Skoltech for Computational Materials scientists. All students of Computational Materials Science subtrack of Materials Science MSc program should attend this seminar. Topics include materials modeling (at atomistic scale), theoretical and computational chemistry, theoretical and computational physics of materials, underlying mathematical methods and algorithms etc. Invited lectures are top scientists in their research field.
Please see the seminar webpage at https://www.skoltech.ru/en/cms/ 
Dmitry Aksenov  0.75  MO03005 
Condensed Matter Spectroscopy and Physics of Nanostructures (Term 1B4)
The first part of this course covers major topics of the modern optical spectroscopy of solid state systems, including nanomaterials and novel topological materials. The introductory part of the course outlines the basic classical and quantum theory of electromagnetic response, and basics of the solid state spectroscopy. Then the major research directions in the modern condensed matter spectroscopy are considered, such as spectroscopy of graphene, topological materials, and transition metal dichalcogenides.
The second part of the course describes the physics of lowdimensional electron systems and nanostructures. Twodimensional electron and electronhole systems, lowdimensional disordered systems, quantum Hall effect, carbon nanostructures, photonic crystals and optical microcavities will be considered. 
Alexey Sokolik  1.5  MA06313 
Continuum Mechanics
Continuum mechanics is a section of mechanics and theoretical physics, or rather the continuation of theoretical mechanics that deals with analysis of deformable bodies. However, mathematics in continuum mechanics represents the main constructive tool. Continuum mechanics allows to demonstrate the power of logic and mathematical thinking. Based on a few fundamental postulates and principles, using the mathematical apparatus can reveal nontrivial, and even striking results.
Foundation of continuum mechanics consists of: This course uses tensor representations in the Cartesian coordinate system of the observer. But it will one shown in detail how to to write the continuum mechanics equations in the arbitrary curvilinear coordinate system. This way the common link is not lost and the exposition becomes easier and clearer. 
Robert Nigmatulin  6  MA06181 
Control Systems Engineering
The course focuses on dynamic systems, and their control. Such systems evolve with time and have inputs, disturbance, and outputs. One can find examples of dynamic systems in everyday life, for examples, automobiles, aircrafts, cranes, electrical circuits, fluid flow.
You will analyze the response of these systems to input. Students will learn how to control system through feedback to ensure desirable dynamic properties (performance, stability). The practice will include work with an industrial, a humanoid, a mobile, and a telepresence robot. 
Dzmitry Tsetserukou  6  MA06083 
Convex Optimization and Applications
This course gives basic knowledge of contemporary numerical methods for solving largescale and hugescale convex optimization problems. Most of these problems go back to the Data Science. In particular, we plane to demonstrate the power of different variants of stochastic gradient descents for such problems. Course required high mathematical skills in probability theory and linear algebra.Required topics:
Foundations of Convex Analysis Black Box Convex Optimization. Lower bounds Mirror descent Fast Gradient Method. Universal method. Stochastic programming Coordinate descent 
An Huy Phan, Andrzej Cichocki 
3  MA03136 
Differential and Symplectic Geometry (Term 12)  Maxim Kazaryan, Sergei Lando 
3  MA06175 
Digital Signal Processing
Digital signal processing (DSP) refers to various techniques for improving the accuracy and reliability of digital communications. The goal, for students of this course, will be to learn the fundamentals of Digital Signal Processing from the ground up. Starting from the basic definition of a discretetime signal, we will work our way through Fourier analysis, filter design, sampling, signal statistics estimation theory, interpolation and quantization to build a DSP toolset complete enough to analyze a practical communication system in detail. We will also deal with modulation, synchronization and propagation channel modes. Handson examples and demonstration will be routinely used to close the gap between theory and practice.
The extra topics covered in this course are: – Fundamentals of random signal theory and analysis; – Modeling communication signals as random processes; – Baseband signal processing, signal synthesis and filter design for communication; – Statistical signal processing in communication; It is hoped that through learning this course students will be equipped with a clear picture of DSP as well as a necessary foundation for further study of advanced DSP topics in the future. 
Andrey Ivanov  6  MA06255 
Efficient Algorithms and Data Structures (Term 1B2)
Design and analysis of algorithms and data structures is a core part of Computer Science and is of fundamental importance to all application areas. The goal of this course is to provide a representative sample of advanced algorithmic notions and techniques that constitute a modern “toolbox” for solving reallife problems. We will mainly deal with basic discrete objects – sets, trees, graphs, strings, … – and present efficient data structures and algorithms for solving various basic problems on these objects. Therefore, this course can be viewed as a basis for more specialized subjects. Lecture part of the course will focus on principles and ideas as well as on their mathematical justification. The practical part will be devoted to programming exercises and developing practical problem solving skills.

Gregory Kucherov  3  MA06270 
Energy Colloquium
The Energy Colloquium educates the audience in the presentday research and applications within the broader field of Energy Science and Technology. The Colloquium consists of a series of presentations by invited academic and industry speakers. The presentations target a nonspecialist audience.
All Master and Ph.D. students within the Energy Program are encouraged to attend the Energy Colloquium during the entire period of their studies. Students can earn 1 credit, if he/she participates in the Energy Colloquium over the course of any 2 terms of the academic year. Students who passed one round can make next (for credit) over the course of their subsequent studies. 
Alexei Buchachenko  1  MA01092 
Energy Systems Physics and Engineering
Classical equilibrium thermodynamics is a theory of principles, which provides a framework to study means to produce motive power and useful heat, crucial for our everyday life. It is a pillar of any serious physics and engineering curriculum. This graduate course provides the students from possibly diverse backgrounds with the theoretical concepts that underlie the physics of energy conversion at the heart of heat engines operation, including chemical processes, and the specific knowledge of energy technologies in use nowadays. Covering some of the main realworld technologies for the generation of electric/mechanic, heating and cooling power: boilers, steam and organic Rankine cycles, gas turbines, internal combustion engines, heat pumps and chillers to name a few, students will learn to critically analyze and assess these technologies to improve their performance and imagine innovative and commercially viable solutions to energy problems, accounting for costs and environmental aspects like pollutants formation and their abatement.
Essential notions which are taught include: energy conversion; heat transfer; work; first and second principles; working fluids and thermoelastic coefficients; chemical reactions; thermodynamic cycles; motors and refrigerators: engines and heat pumps; sources of irreversibility; finitetime thermodynamics. Time permitting, notions of kinetic theory and statistical thermodynamics may be briefly introduced. The course is organized around the learning of essential concepts and an awareness development of current energy technologies. It is based both on "teaching with lecture" and "teaching with discussions" methods. In addition to home assignments and project, students will solve problems during tutorials and discuss their solutions. 
Henni Ouerdane  6  MA06001 
English Toolkit (Term 12)
The goal of the English Toolkit course is to activate Academic English skills required for successful education at Skoltech.
The students will practice Academic vocabulary and grammar, as well as boost their reading, writing and speaking skills. The blended format includes a weekly online workload plus an offline group tutorial providing a flexible and individualised learning trajectory. Realtime feedback in online exercises will be complimented by tutor feedback for the writing and speaking assignments. 
Elizaveta Tikhomirova  1.5  MO03001 
English. Candidate Examinations
This is a metacourse which allows PhD students to register for English Qualification Exam for the Russian PhD Degree. There will be no lectures or seminars, only the exam. The preparatory course is also available in course catalog (look for "Academic Communication for PhD students" course).
The Exam has two parts: Part 1 – Preexam activities (Assignments 1, 2a, 2b) 
Elizaveta Tikhomirova  3  PE03003 
Foundations of Engineering Physics (Term 1B4)
The course is dedicated to basics of building interfaces ”experimentcomputer” in the modern scientific research. In most general configuration such interface comprises three stages:
1) “input” analog frontend feeding the electronic signals from sensors, transducers, 2) analogtodigit as well as digittoanalog conversion “bridges” and 3) logical channels conveying the ultimate digital information to a computer. The consideration of the three stages is made with emphases on the principle aspects of scientific measurements rather than detailed schematic/circuitry of the instrumentation. All stages of the measurement systems will be reviewed from the point of view of the fundamental imperatives of signal conditioning like impedance matching, optimal choice of the bandwidth solving the ubiquitous tradeoff “precision versus rate” of data acquisition and et al. As well important peculiarities of configuring the elements of the system – such as prefiltering, modulationdemodulation techniques, the choice of the type and bit width of ADCs/DACs – will also be thoroughly discussed. At all stages a short concomitant overview of the modern commercially available electronic equipment will be given in order to improve students’ ability to select a proper set of the electronic devices among a great variety of those available on the market. 
Yuri Romanovskiy  1.5  MA06213 
Fundamentals of Photonics
This course is aimed for the first year master students, and provides an overview of the main physical principles of photonics and photonic devices. The emphasis is made on the demonstration that the light matter interaction in photonic devices can be modified by means of the modern technology. The course give the illustration how the basic physical laws help to get qualitative understanding of different branches of photonics such as light emission, transmission and detection. This introductory course is designed for both theoreticians and experimentalists.

Nikolay Gippius  6  MA06160 
Fundamentals of Power Systems
This course covers power systems analysis & operations, including fundamentals (balanced threephase power) steadystate analysis (power flow), state estimation, operation (optimal power flow), security (contingency analysis and security constrained optimal power flow), power system dynamics (frequency and voltage control) and challenges and trend of future power systems. After successfully completing this course, the student will be capable of analyzing the technical and economic operation of an electric energy system.

David Pozo  6  MA06007 
Gas Recovery and Gas Hydrates
Natural gases characterization of the gas and gascondensate fields. Traditional and nonconventional gas resources. Overview of technological complications (flow assurance) in gas production at different stages of field development.
Phase diagrams of hydrocarbon systems including water. General characteristics of phase transformations during reservoir development. A moisture content of natural gas. Gas hydrates: basic physical and chemical properties. Twophase and threephase equilibria. Gas hydrates as a technological complication in gas production. Thermodynamic (methanol and MEG) and lowdosage (kinetic and antiagglomerant) inhibitors. Permafrost at northern gas fields: general characteristic, ice content, thermophysical and mechanical properties of frozen and thawed rocks. Wells and well clusters. Thawing and reverse freezing of rocks around the producing well. Simulation of the thermal interaction of well and permafrost rocks. Thermal regime of the operating well. Gas gathering systems. Technological complications in the operation of infield systems. Gas hydrate control. Gas gathering systems at the late stages of field development (water accumulations, ice formation, sand, scales). The main technological processes of gas treatment in field conditions (general overview). Dehydration of lean gases. Adsorption method of dehydration. Adsorbents and their choice. Technological schemes of adsorption dehydration. Absorption method of dehydration.Glycols as absorbents.Technological schemes of absorption dehydration. Lowtemperature processes of gas treatment at gascondensate fields. Isoenthalpic and isoentropic processes. The lowtemperature separation technology and its modifications (application of ejectors, turboexpanders, gasdynamic separators and vortex tubes in process diagrams). Application of thermodynamic inhibitors (methanol, MEG) for hydrate control. Promising lowtemperature technological schemes for gas processing at field conditions. 
Vladimir Istomin  3  MA03291 
Geometric Modeling
Classification, principles and techniques of digital modelling of point sets are presented for points, curves, surfaces and solids. Specifically these include methods of modelling of point clouds, depth fields, parametric curves and surfaces, implicit surfaces and solids. Solid modelling includes such representations as Constructive Solid Geometry (CSG), Boundary Representation (BRep) with polygonal meshes and parametric surfaces, sweeping, spatial occupancy enumeration, and Function Representation (FRep).

Alexander Pasko  6  MA06297 
Geometric Representation Theory (Term 12)
Geometric representation theory applies algebraic geometry to the problems of
representation theory. Some of the most famous problems of representation theory were solved on this way during the last 40 years. The list includes the Langlands reciprocity for the general linear groups over the functional fields, the LanglandsShelstad fundamental Lemma, the proof of the KazhdanLusztig conjectures; the computation of the characters of the finite groups of Lie type. We will study representations of the affine Hecke algebras using the geometry of affine Grassmannians (Satake isomorphism) and Steinberg varieties of triples (DeligneLanglands conjecture). This is a course for master students knowing the basics of algebraic geometry, sheaf theory, homology and Ktheory. 
Mikhail Finkelberg  3  MA06271 
Hamiltonian Mechanics (Term 12)
This is the first among the base courses in the theoretical physics, aimed for the master
students. Matematical methods of modern theory of Hamiltonian systems are based on the concepts, The preliminary program of the course includes: 
Andrei Marshakov  3  MA06174 
History and Philosophy of Science. Candidate Examinations
The aim of this course is to give to Scoltech students and postgraduates some basic information about the main stages of the development of science from its birth in Ancient Greece through the Middle Ages and the Renaissance to Modern Times and to the great scientific revolutions of the XX century. Every man of culture especially a future scientist should know the impact of such great thinkers as Plato, Aristotle, Thomas Aquinas, Jean Buridan, Nicholas of Cusa, Copernicus, Galileo, Descartes, Newton, Boscovich, Darwin, Mendel, Bohr and Einstein (omitting many other brilliant names, that would be spoken about in the frames of the course) to the development of a scientific picture of the universe. Also there will be discussed the main topics and notions of the philosophy of science: demarcation between science and humanities, Popper’s theory of falsification, Kuhn’s theory of scientific revolutions, the concept of research programmes of Lakatos and methodological anarchism of Feyerabend. We'll also discuss Lombroso's theory of genius and folly, Spengler's morthology of culture and Wittgenstein's language games.

Ivan Lupandin  6  PE06026 
Hydrolic Fracture Simulation
Hydraulic Fracture Simulation
Prof. A.A. Osiptsov, Skoltech / Prof. D.I. Garagash, Dalhousie University, CA. Part I. Fluid Mechanics (A.A.Osiptsov). 1. Intro 2. Phenomenological models of multiphase flow 3. Proppant placement in a fracture 4. Numerical methods. Fingering. Interfacial instability. Particle migration 5. Particle bridging, transition to close packing, suspension rheology. 6. Flow in a porous medium. 7. Multiphase gasliquid flow in a well. Particle transport. Part II. Solid Mechanics (Prof. D.I. Garagash). Elements of elasticity and fracture mechanics: 
Andrei Osiptsov  6  MA06237 
Ideas to Impact
Technological innovation is critical to the survival and competitiveness of emerging and existing organizations. This course lays the foundation to undertake a robust analysis and design of opportunities for technologybased commercialization. We introduce tools and frameworks that help isolate and control the factors shaping the identification, evaluation and development of commercial opportunities. Throughout the course we use technology examples originating from problem sets found in engineering and scientific education to develop the skills necessary to connect technology and impact.
At the same time, through creativity lab students will be introduced to a variety of creative problem solving techniques and learn how to apply these techniques in the context of the development, evaluation and application of ideas and concepts with commercial potential; consider the evaluation of business ideas that translate existing business models into new national contexts. The course is designed to help students develop the ability to find, evaluate, and develop technological ideas into commercially viable product and process concepts, and build those concepts into viable business propositions. The material covered is research and theorybased but the course is practiceoriented with much of the term spent on shaping technologybased opportunities. A central objective of this subject is to equip students with an understanding of the main issues involved in the commercialization of technological advances at both strategic and operational levels. 
Zeljko Tekic  6  MC06002 
Innovation and Intellectual Property Studies Doctoral Seminar (Term 14)
This course is a compulsory academic seminar series for all Ph.D. students in the Innovation and Intellectual Property Management Ph.D. Program. It consists of weekly research seminars that address the state of the art in research about the role of intellectual property in technological innovation. Specific topics and themes in the course will vary from year to year, but will typically include: theories of innovation; concepts and theories in IP management; practical issues in IP management; case studies in IP strategy; valuation of IP; Russian and international trends in intellectual property law; topics in technology entrepreneurship; product development and new technology; IP and design; patent analytics for innovation research; commercialization strategies of technology startups; organizational issues in technology innovation; conceptual issues at the interface of technology, science and business; public policy for technology, science and innovation; ethical and social issues related to IP and technological innovation; case studies in innovation management; philosophy of technology and philosophy of intellectual property; theory and methodology in IP management research; technology transfer and commercialization of university research; international collaboration and international trade in technology. As part of their seminar obligations, all students must prepare a formal written research paper on a topic that may or may not be directly related to their thesis research and make a presentation about the paper to the seminar group. The paper will be assessed.

Kelvin Willoughby  1.5  PC06009 
Introduction to Blockchain
This course provide an overview of modern blockchain technology and its' practical applications (Cryptocurrency, Certification, Anchoring. Industrial examples.) We will start from basic cryptography and distributed data base systems and show how these tools are used in blockchain. The covered topics are the following:
) Introduction to cryptography, type of ciphers. Private and Public crypto systems 
Alexey Frolov  3  MA03272 
Introduction to Petroleum Engineering (Term 1B2)
The course is an introduction to Petroleum Engineering and gives an overview of Petroleum Engineering and its various components and their internal connection.
The course will address the story of oil from its origin to the end user. The objective is to provide an overview of the fundamental operations in exploration, drilling, production, processing, transportation, and refining of oil and gas. As additional topics it is planned to consider Permafrost Engineering and Flow Asuurance, which are actual for Russian Oil&Gas Industry. Within the framework of the course it is planned to invite speakers form industry. 
Evgeny Chuvilin  3  MA06064 
Introduction to Plant Biology
General biological courses give knowledge of eukaryotic features basing on processes in animals. Plants are out of focus as usual. This course aims to fill the gaps and show the plant specificity. The main purpose of the course is to consider the plant features that are absent in animals or that differ substantially from animal analogs. The characteristic features will be analyzed in plant biochemistry, cell organization and at the level of a whole organism. Last section will be devoted to applications in contemporary biotechnology. The course does not pretend to draw comprehensive picture of plant life; the focus will be on most important traits required to deep understanding of basic eukaryotic processes. Consequently, the general knowledge in eukaryotic biochemistry and cell biology is the prerequisite for this course.

Evgeny Lysenko  3  MA03261 
Introduction to Quantum Information and Quantum Computation
This course introduces the fundamental components of an emerging theory that is both reshaping the foundations of physics as well as leading to a new era of commercial highperformance computing.
The topics covered include: Introduction to information 
Jacob Biamonte  6  MA06266 
Introduction to Solid State Physics
This course gives an introduction to solid state physics, one of the cornerstones on which a modern technologies are based. We will begin with the conventional classification of solids on the basis of binding forces, to be followed by crystal structure description and experimental techniques for crystal studies. From there we will discuss classical and quantum aspects of lattice dynamics and begin the study of the electronic structure of solids, including energy band formalism and carrier statistics in metals, semiconductors and insulators. Next we will consider basics of the atomic and electronic processes at crystal surfaces and interfaces, kinetic effects and scattering of the electrons. We will continue with the study of the optical processes in solids, including nonequilibrium carrier dynamics and photovoltaic effects and their applications in technology.

Sergey Kosolobov  6  MA06027 
Introduction to Surface Physics
This course assumes the study of techniques able to provide information concerning electronic and atomic surface structure. The techniques can be applied to materials and nanostructures research. The students should learn how the surface is arranged, what are the specific properties of the surface, what processes occur at the surface and interfaces, including metalsemiconductor interface and some other interfaces typical for heterostructures. Adsorption, interfacial reactions and films growth are also considered. Vacuum techniques of surface characterization are accented.

Andrey Ionov  3  MA03218 
Introduction to The Quantum Field Theory (Term 12)
Introduction to basic notions of gauge theory: gauge invariance, SU(N) Lie algerbras and their representations, Yang Mills Largangian and its quantization, FaddeevPopov method, ghosts and unitarity, diagram technique, basics on perturbation theory, analysis of simplest Feynman diagramms, beta function in nonabelian YangMills theory, renormalization group, asymptotic freedom, Higgs mechanism, basic notions of QCD and electroweak interaction. Depending on progress: some advanced topics: anomalies, instantons.

Yaroslav Pugai  3  MA06273 
Introduction to The Theory of Disordered Systems (Term 12)
This course is mainly dealing with the quantum electronic properties of disordered materials. I start with a review of different types of disorder and general methods of their theoretical treatment. Then I give a detailed discussion of the two popular models of quenched disorder, widely used for description of quantum solid state systems: Anderson model and Lifshits model. I discuss the properties of the disordered systems in the insulating phase: the density of states, the tails in the optical absorption ( with the optimal fluctuation method) and different versions of hopping conductivity: the nearest neighbour hopping and the Mott's variable range hopping. I also take into account the longrange Coulomb correlations and derive the Coulomb gap in the density of states and the EfrosShklovskii law for the conductivity.
As to the vicinity of the metalinsulator transition, I give a qualitative discussion of the mechanism behind the transition, as well as the most powerful tools for probing the properties of the system near the transition: analysis of inverse participation ratios and the concept of multifractality of the wavefunctions. In the metallic phase I discuss the weak localization corrections, including magnetoresistance, inelastic phasebreaking mechanisms and interactioninduced anomalies in the density of states near the Fermi surface. At the end of the course I give a brief introduction to mesoscopics, including the Landauer formalism and quantization of the ballistic conductance. 
Alexey Ioselevich  3  MA06274 
Laser Spectroscopy (Term 1B4)  Alexander Makarov  1.5  MA06212 
Leadership for Innovators
Succesful innovators are distinguished not only by industrial and technology acumen, but also by superior leadership skills. Innovation is impossible without leading, presenting, managing, negotiating, and resilience from constant stress. This course present the comprehensive leadership skillset that includes theory and practice of:
– leadership & teamwork – personal presentation – stress management – emotional intelligence – negotiations The class is built as highly interactive action that starts with Q&A on a particular topic and then culminates in intensive group and personal exercises. Unlike your favorite hard skill classes, this course is light on homework, but hard on class participation. Student should be ready to attend at all costs or face course failure. You will not survive on hard skills only hence you have to suffer class attendance and participation. Please note that this class makes an effort to manage device addiction of students by removing tables from the audience. 
Dmitry Kulish, Maxim Kiselev 
3  MC03011 
Lie Groups and Lie Algebras, and Their Representations (Term 12)
We shall begin with the basics of the theory of Lie groups and Lie algebras. Then we shall provide an accessible introduction to the theory of finitedimensional representations of classical groups on the example of the unitary groups U(N).
Tentative plan: linear Lie groups and their Lie algebras; universal enveloping algebras; Haar measure on a linear Lie group; general facts about representations of compact groups and their characters; radial part of Haar measure; Weyl's formula for characters of the unitary groups; Weyl's unitary trick; classification and realization of representations; symmetric functions. 
Grigory Olshanski  3  MA06173 
Magnetic Phenomena At Macro, Micro and Nanoscales
Objectives of this course are as follows: the mastery of the fundamental concepts, laws and theories of physics of magnetic phenomena; introduction to basic experimental techniques to characterize magnetic materials; modern applications of magnetics. The importance of these topics results from application of thin magnetic films as the layers in heterostructures which control the operation of micro and cryolectronics devices. The straightforward scaling is impossible when one goes from the bulk magnetic materials to micro and nmsize systems because of the principle difference in dynamic behavior and appearance of new types of excitations.

Lyudmila Uspenskaya  3  MA03219 
Master Your English for Thesis (Term 57)
Writing is the key priority and the need of utmost importance for wouldbe scientists. Science demands not just writing, but good writing, that presupposes the skills to communicate ideas, theories and findings as efficiently and clearly as possible. Science lives and dies by how it is represented in print and a printed material is the final product of scientific endeavour. The primary goal of this course is to prepare master students for wiring, editing, and defending a Master Thesis.
This course is designed to explain how to write chapters of their Thesis through practical examples of good writing taken from the authentic linguistic environment. The course teaches how to overcome certain typical problems in writing a text of a thesis and abounds in useful linguistics assistance on its various parts. Feedback on students’ texts will constitute the major part of the course. 
Anastasiia Sharapkova  1.5  MO03003ls 
Master Your English for Thesis (Term 57)
The key to efficient professional communication is the ability to convey ideas clearly, coherently and correctly both orally and in writing.
The Course offers concise and practical guidelines for writing and defending a Master Thesis at Skoltech. The course focuses on the main parts of the Thesis in terms of structure, vocabulary and grammar, and their transformations for a presentation with slides. Students will develop a conscious approach to own writing and presentations through thorough analyses of the best authentic examples combined with intensive writing and editing practice. The ‘processforproduct’ approach teaches the students to write – use (peer) reviewer’s advice – revise/edit – repeat, and creates linguistic awareness needed to avoid the typical pitfalls. The Course is offered in two modules which gradually build on the necessary writing and presentation skills. 
Elizaveta Tikhomirova  1.5  MO03003 
Materials Chemistry
The goal of this course is to provide a survey of materials chemistry and their characterization techniques with an emphasis on chemical, electrical, optical and magnetic properties. Further emphasis will be placed application of materials chemistry to energy storage and conversion processes (batteries, fuel and solarcells)
Upon completion of this course the students will be able to master: 1.Classes of Materials crystalline solids ionic, covalent, metallic, polymers 2. Property of Materials Electrical 3. Materials Chemistry Analysis Methods Surface Sensitivity and Specificity 
Keith Stevenson  6  MA06042 
Mathematical Modeling in Biology
The course aims to teach students to quantify biological observations into conceptual models, frame these models in mathematical terms, and analyze these models, both qualitatively and numerically.
It includes considering strategies to choose the relevant variables, parameters and observables, model nature (e.g. discrete vs continuous), modeling technique (e.g. agentbased simulations vs. dynamical system approach), and visualization and interpretation of the results. The following classes of systems will be used as examples: 1. Population models 
Yaroslav Ispolatov  6  MA06033 
Mathematical Modeling in Manufacturing and Applied Sciences
The course introduces essential mathematical modeling techniques emphasizing analytical methods and their use in solving various problems of applied science and manufacturing. The topics include: asymptotic and perturbation methods for ordinary and partial differential equations, singular perturbations, homogenization, analysis of models of heat transfer, fluid and solid mechanics, electromagnetism, chemical kinetics, chemical reactors, convection in porous media, onedimensional twophase flow, linear and nonlinear stability, alloy solidification, interfacial instabilities and pattern formation.

Aslan Kasimov  6  MA06325 
Micromechanics
Micromechanics studies materials that are heterogeneous at microscale. They may be manmade (concrete, metals, composites, coatings) or naturally occurring (porous and cracked rocks, bone). Matrix composites – continuous matrices containing various inhomogeneities (pores, cracks, fibers, foreign particles) – constitute an important example. The goal of micromechanics is to relate the physical behavior of such material – in particular, their overall (effective) properties – to the microstructure (geometric arrangement of the constituents and their properties). The course focuses on two groups of effective properties: the elastic and the conductive ones. The course covers the following topics:
Background results on elasticity and thermal/electric conductivity. Quantitative characterization of microstructure. Isolated inhomogeneity problem (Eshelby problem) in the context of elasticity and thermal or electrical conductivity. Property contribution tensors for effective elastic, thermal, and electric properties. Effective properties of heterogeneous materials: Variational bounds Noninteraction approximation Differential scheme Effective field approaches Crossproperty connections. The material will be illustrated by examples from various applications – plasma sprayed coatings, composites, metal foams, bones. The lectures will be supplemented by weekly homework assignments. The students will be evaluated on the basis of two midterm exams and final exam. 
Sergey Abaimov  6  MA06247 
Molecular Biology (Term 1B2)
Molecular biology course is based on learning the principles of replication, recombination, DNA repair. Additionally, replication strategies of phages and viruses will be discussed. Mitosis and meiosis will be described in a context of DNA biosynthesis. Also, the principles of RNA biosynthesis, i.e. transcription and processing, as well as protein biosynthesis, i.e. translation, maturation and transport will be described.
The goal of the course is obtaining a comprehensive knowledge on the structure of DNA and processes of DNA replication, recombination and repair in bacteria and eukaryotes, as well as on replication of phages and viruses. To obtain a detailed knowledge on the processes of transcription, in bacteria and eukaryotes, on the regulation of transcription in bacteria and eukaryotes, on examples of complex networks of transcriptional regulation in bacteria and eukaryotes, on maturation of RNA in eukaryotes, on protein biosynthesis in bacteria and eukaryotes, on the transport of protein in bacteria and eukaryotes. Students activities include: 
Petr Sergiev  3  MA06034 
Molecular Biology Seminar
For each class, there will be a paper that two people will present to the rest of the class. We will go down to the details of experiments – how things were done and what do the data/figures really show, so be prepared to answer indepth questions. Presenters will start by stating the name of the paper/main authors and telling the take home message of the paper – why it is signficant, what problem it solved. Then they will proceed to the actual work. If there are methods/results mentioned in the paper that refer to prior work, you shall be prepared to answer questions about it too. The audience is supposed to read the paper being discussed beforehand and participate in discussions.
To pass, one would need to present a paper at least once during the module and actively take part in discussions of other papers. One absence is allowed no questions asked. Additional absences when unexplained will be a cause for nopass grade. There will be a few home assignments. They must be submitted in time, typed–not written up–and done professionally (written in good language, be concise and free of spelling errors – consider them as part of academic writing exercises). It is gonna be fun – students tend to like the seminar and its atmosphere 
Konstantin Severinov  3  MA03052 
Molecular Spectroscopy (Term 1B4)  Vladimir Mironenko  1.5  MA06209 
Numerical Linear Algebra
Numerical linear algebra forms the basis for all modern computational mathematics. It is not possible to develop new large scale algorithms and even use existing ones without knowing it.
In this course I will show, how numerical linear algebra methods and algorithms are used to solve practical problems. Matrix decompositions play the key role in numerical linear algebra. We will study different matrix decompositions in details: what are they, how to compute them efficiently and robustly, and most importantly, how they are applied to the solution of linear systems, eigenvalue problems and data analysis applications. For largescale problems iterative methods will be described. I will try to highlight recent developments when it is relevant to the current lecture. This course should serve as a basis for other IT Skoltech courses. It will also serve as a firsttime place where programming environment and infrastructure is introduced in a consistent manner. 
Ivan Oseledets  6  MA06024 
Pedagogical Experience
The main function of this course is to articulate Skoltech's expectations on Phdstudents who do their pedagogical TA assignment as Skoltech. The course describes the intended learning outcomes and how they are assessed.
The course also offers a forum for TA and allows Skoltech TAs to collect and discuss resources and issues relevant for their TA experience. The forum provides a peertopeer feedback opportunity but also enables instructors to participate in the conversation when asked to. The main bulk of the 81 hours of the course is spent in the actual courses in which the PhDstudents do their TAassignments. The assignments in the course itself require less than 10 hours of time. 
Magnus Gustaffson  3  PE03005 
Perception in Robotics
This course will present the fundamental theory and application of perception techniques in robotics. Today we are witnessing an explosion on the applications for this technology, e.g. selfdriving cars, autonomous robots, etc., and yet there are many challenges to be solved on a wide variety of research topics. The word perception on the context of this course will refer to the problems of Localization, Mapping and in general State Estimation. The content of the course will be mainly based on a probabilistic approach to robot perception problems and will examine a selected set of contemporary algorithms in depth. Topics include Bayesian filtering; motion and sensor models for mobile robots; algorithms for mapping, localization and simultaneous localization and Mapping (SLAM); application to autonomous ground, marine and air vehicles.
Read below about the course policy, final project and other details. 
Gonzalo Ferrer  6  MA06283 
Petroleum Geophysics
The course will provide an overview of geophysical methods of hydrocarbon (HC) exploration; including classification, applications, integration; physical properties of rocks (density, susceptibility, resistivity, and seismic wave velocities). All types of geophysical methods (gravity and magnetic methods, electrical and electromagnetic (EM) methods, seismic methods, and borehole geophysical methods) will be thoroughly reviewed from the comprehensive geophysical applications but also from the standpoint of fundamental mathematical and physical principles.

Marwan Charara  6  MA06076 
Petroleum Reservoir Engineering
Review of petroleum reservoir types, their rock and fluid properties;
discussion of reservoir drive mechanisms; reserves estimation using volumetric and material balance methods in different gas and oil reservoirs; introduction to singlephase fluid flow in porous media; theory and techniques for well testing in different petroleum reservoirs; decline analysis implementation; aquifer modeling; introduction to immiscible reservoir recovery processes by waterflooding; essentials of petroleum reservoir development forecasting using 3D hydrodynamic models. 
Stanislav Ursegov  3  MA03290 
Petrophysics and Well Log Interpretation
Formation evaluation (or well log analysis or petrophysics) is at the intersection of a number of disciplines, including, but not limited to, geology, geophysics, and reservoir engineering. Each discipline that encounters and uses well log data does so from its own perspective. In doing so, each discipline sometimes uses the data without a full understanding of how the measurements are made. That incomplete understanding can encompass the processing of the actual measurements into the raw data provided by the data logging companies and to the interpretation methods that convert that data into usable information about the subsurface. It is this incomplete understanding of well log data that commonly produces conflicting interpretations from different sources, when the goal should be a single cohesive model of the subsurface that can be consistently applied by all disciplines.
The course includes lectures in laboratory petrophysics and formation evaluation using modern well logging methods. 
Andrey Kazak  3  MA03289 
Physics of Human Body
We will work on creating a «digital twin» for a human, with physics and mathematics being placed at the focus of the study. The course will overview different organs and macroscopic systems that are responsible for the way our bodies function. Topics include: the mechanics of the static and the moving body, the material properties of its tissues, the body metabolism and the energetic needs, the fluid and the air flow in the cardiovascular and the respiratory systems, the acoustics of sound waves in speaking and hearing, the vision and the optics of the eye, the electrical/magnetic properties of the body, as well as the advanced principles of feedback and control in regulating all aspects of the body operation.
The second goal of the course is to teach how to approach modeling of the complex dynamical processes in the human body looking beyond the scope of biology. The joint representation of the macro and microphysical phenomena will be connected with the measurable signals, and with the consequent signal analytics. The lectures will include a brief review of the underlying physics, basic medical terminology and anatomy, and mathematical modeling and analytical tools for data analysis. 
Dmitry Dylov  6  MA06304 
Physics of Partially Disordered Systems
Principle notions and phenomena being specific for partially ordered media and amorphous state are considered. Examples and illustrations are provided for liquid crystals, plastic crystals (rotary crystals), nanocrystals, and partially ordered polymer structures. Phase transitions in these systems are accented, as well as the role of defects and dislocations. Optical properties of partially disordered systems are addressed. The systems consisting of nm and submkmsize particles are also discussed.

Pavel Dolganov  3  MA03215 
Physics of Semiconductor Bulk Crystals and Nanostructures
The course focuses on the presentation of foundations of the modern physics of semiconductors. Along with the traditional branches (band theory, phenomena in the contacts, single particle excitations and interparticle interactions) developed for bulk semiconductors, the course includes the problems of composite quasiparticles and collective excitations in low dimensional semiconductor nanostructures (quantum wells, quantum wires and quantum dots) and microcavities. The basic principles and features of semiconductor lasers are also addressed.

Vladimir Kulakovsky  3  MA03214 
Quantum Theory of Radiation and Quantum Optics (Term 1B4)  Yuri Lozovik  1.5  MA06314 
Research Methodology: Computational and Data Science and Engineering
A modern researcher needs to have a set of various skills in order to conduct research efficiently. In addition to high level of research skills and understanding of the research environment of one’s particular field, a researcher should be able to manage researchrelated business processes, be personally effective, have high level of communication and presentation skills, build effective professional relationship with colleagues and effectively manage the career development. The course covers all these topics and implies active interaction between the tutor and students during the classes. In the end of the course each student will be asked to write an essay.

Maxim Fedorov  3  PA03102cds 
Research Methodology: Molecular Biology Seminar  Konstantin Severinov  3  PA03102ls 
Research Methodology: Space Center Seminar (Term 14)  Anton Ivanov  3  PA03102es 
Research Seminar "Advanced Materials Science" (Term 28)
This is the main research seminar of the Skoltech Center for Electrochemical Energy Storage and Materials Science Education program featuring presentations of young researchers: MSc students, PhD students, postdocs. Every MSc and PhD student of Materials Science program should deliver at least one presentation per two years. The range of topics is broad and includes any aspects of materials science and engineering.
Please see the seminar webpage at http://crei.skoltech.ru/cee/education/wednesdayscientificseminar/ 
Keith Stevenson  0.43  MA03302 
Research seminar "Modern Problems of Mathematical Physics" (Term 18)
Course "Modern problems of mathematical physics" is a student seminar, so participants are expected to give talks based on the modern research papers. Current topic of the seminar can vary from time to time: now it is devoted to the study of N=2 supersymmetric gauge theory and its links with random matrix models, complex curves, and integrable systems. Other topics that were already covered, or can be covered in the future, are: classical integrable equations, complex curves and their thetafunctions, quantum integrable models (quantummechanical and fieldtheoretical), models of statistical physics.

Andrei Marshakov  1.5  MA12268 
Research seminar "Modern Problems of Theoretical Physics" (Term 18)
Research seminar "Modern Problems of Theoretical Physics" is supposed to teach students to read, understand and represent to the audience recent advances in theoretical physics. Each student is supposed 1) to choose one of recent research papers from the list composed by the instructor in the beginning of each term, 2) read it carefully, 3) present the major results of the paper to his/her colleagues during the seminar talk, 4) answer the questions from the audience about the content of the paper. The papers in the list are selected, normally, from the condensed matter theory and related fields, like: physics quantum computing, statistical physics, etc. The papers to the list are usually chosen from most competitive physics journals, like Nature Physics, Science, Physical Review Letters, Physical Review X and others.

Mikhail Feigelman, Konstantin Tikhonov 
1.5  MA12319 
Research seminar "Strings and Cluster Varieties" (Term 18)
The course is directed to substantive work of the master and PhD students in order to understand recently found relations among supersymmetric gauge theories, refined topological strings, cluster varieties and integrable systems. The plan of wrk on the course consists of several introductive lectures on the various consistuents of the subject as well as student talks on recent original papers and results of their own investigation. The core topics include relation between cluster varieties and Painleve equations and approaches to the SeibergWitten theories with fundamental matter based on Toda systems and spin chains.

Andrei Marshakov  1.5  MA12176 
Selected Topics in Energy: Physical, Chemical and Geophysical Challenges (Term 24)
The course provides an introduction to the modern topics related to fundamentals of exploration of energy resources, energy generation, storage, conversion and use. It identifies the corresponding practical challenges to be addressed at the fundamental research level and familiarizes the students with the stateoftheart approaches, methods and techniques in use in related scientific areas. The course seeks to emphasize and maintain interdisciplinary nature of the energyrelated topics, in particular, combination of micro and macroscopic approaches of geophysics, mechanics and chemistry in hydrocarbon exploration and development, relation between the physical and chemical processes of energy generation and conversion, integration of physical, chemical and mechanical approaches to perspective materials (physical and chemical synthesis, micro and macroscopic characterization, structureproperty relations, etc.) and related theoretical methodologies. These interdisciplinary links are mostly demonstrated by horizontal knowledge exchange among the students reporting and discussing practical examples from their own research field or from modern review or research publications. Topical lectures are included for further exploration of these links. The secondary aim of the course is the development of presentation skills (oral and writing), as well as scientific peerreview experience. The seminar format chosen for most activities allows students free exchange of knowledge and ideas, broader vision of their research projects and methodologies, better assessments of their own research skills and demands for further education.

Alexei Buchachenko  2  PA06106 
Space Center Seminar (Term 14)
The seminar will cover current topics in the space domain: latest news, discoveries. Also planned that all PhD students and some Master students will present their research. External lecturers will be invited regularly to focus on the main applications of space technologies: science, telecommunication, navigation and remote sensing. Aspects of space technologies will also be discussed: structures, software, attitude determination and control systems, on board computers, communication system power supply systems and others. The seminar will be offered in English.

Anton Ivanov  0.25  MO01004 
Structural Analysis and Design
The Structural analysis and Design course gives students basics of strength analysis and design of typical structural members. Theoretical sections include stress and strain theories, failure criteria, basics of elasticity theory, nonlinear material behavior and analysis of tension, compression, bending and shear structural members. Students learn finite element software Abaqus and work on development of FE models and stress analysis of structural parts taking into account mechanical and thermal interactions.

Ivan Sergeichev  6  MA06067 
Systems Engineering
The course introduces students to the fundamentals of systems engineering as an interdisciplinary approach and means to enable the realization of successful systems, as defined by the International Council of Systems Engineering.
The course covers the entire spectrum of lifecycle management of a system, encompassing conception, design, implementation, assemblyIntegration and Test, operations, and disposal of systems. Being a foundational course for the Space and Engineering Systems students of Skoltech, the course discusses many applications of systems engineering including some parts of space systems engineering . The course also discusses systems architecture principles. The Systems Engineering course follows the systems engineering Vmodel as an educational guideline throughout the term. Tradeoff analysis and systems architecture will be introduced as part of the course, but more detailed coverage of these topics will be provided by the adhoc Systems Architecture course already in place at Skoltech. The course includes a journal club to review academic articles and standards pertinent to systems engineering, which form a complement to weekly homework assignments and a design project that is conducted throughout the term. 
Clement Fortin, Anton Ivanov 
6  MA06023 
Theoretical Methods of Deep Learning  Dmitry Yarotsky  3  MA03327 
Theory of Phase Transitions (Term 12)
The role of longrange thermal fluctuations in the condensed matter
physics is considered. We give a theory of the second order transitions starting from the Landau expansion in the order parameter. As an introduction we consider the mean field theory, then we take into account fluctuations the role of which can be examined in the framework of the perturbation theory and the socalled renormgroup formalism. The peculiarities of a weak crystallization transition where fluctuations qualitatively change the nature of the phase transition in comparison with the mean field picture are treated on the same diagrammatic language. The theoretical approach based on the Landau expansion is utilized to examine thermal fluctuation effects far from phase transition points. We consider the longscale properties of smectics where fluctuations destroy the longrange order. The smectics are treated in the framework of the renormgroup approach. The same renormgroup technique is developed also for twodimensional ferromagnets where the effective coupling constant increases with increasing scale what drastically change longscale properties of the system. Longrange fluctuations are also relevant for membranes which are twodimensional objects immersed into a threedimensional fluid. Elastic modules of a membrane are logarithmically renormalized, the renormalization law can be found by using renormgroup methods. Of special interest is BerezinskiiKosterlitzThouless phase transition in superfluid, crystal or hexatic films which is related to appearing free point defects (vortices, dislocations or disclinations). The problem can be mapped into sineGordon model and then examined by renormgroup methods. We present some facts concerning critical dynamics and the socalled KPZ (KardarParisiZhang) problem. Then we consider peculiarities of the 2d hydrodynamics and passive scalar. 
Vladimir Lebedev  3  MA06138 
Thermal Petrophysics and Geothermy
The course presents theoretical and experimental background of thermal petrophysics and geothermics in application to solution of modern problems of fundamental and applied geophysics and geology of unconventional hydrocarbon resources. The recent essential evolution in experimental and theoretical basis of the thermal petrophysics and oil&gas geothermics are described. Reasons of significant extension of applications of methods and equipment developed recently within these scientific directions are explained. Qualitatively new possibilities in prospecting, exploration and development of unconventional hydrocarbon fields based on advanced theoretical and experimental basis of thermal petrophysics and geothermics are shown. Peculiarities in applications of methods of thermal petrophysics and geothermics to heavy oil fields and shale oil fields are illustrated. Necessity of wide implementation of new thermophysical and geothermal technologies is demonstrated on graphic examples of their implementation for investigations of many unconventional oil&gas resevoirs. Cardinal changes in effectiveness of oil&gas thermal petrophysics and geothermics caused due to development of optical scanning and continuous thermal core logging technologies are revealed. It is shown that significant improvement of reliability of basin and petroleum system modeling as well as hydrodynamic modeling was reached after new methods of thermal petrophysics and geothermics became obligatory components of prospecting, exploration and development of unconventional resource fields. The advanced methods, technologies and equipment of thermal petrophysics and geothermics are effective also for prospecting, exploration and development of conventional resource fields.

Yuri Popov  6  MA06295 
Thinking Disruptive for a Big Future (Term 23)
The goal is to open the mind of the audience showing that there is not only one predetermined path for a career after the studies, that the world is big, fantastic and that the problems we face are huge, but fascinating. The goal is also to show that there is no, or should not be any Chinese Wall between mathematicians, physicists and engineers. Finally, the goal is to show how some ideas, some of them being very theoretical and some others not, can bring to the creation of startups. It will rely on the more than 30 years of experience of JeanFrancois Geneste who will exemplify with encountered concrete examples he met along his career. We shall go through "the law of the mean", disruptive systems (airships, pseudosatellites, launchers, mining in space, fractionation and responsive space), disruptive equipment (infinite impulse propulsion, CVC jet engine, thermal solar arrays), systems intrinsically resistant to terrorist attacks, Disruptive science (some contradictions of physics, coherent alternative, new potential sources of energy, high temperature superconductivity with a new model of the atom, communications quicker than light, analog quantum computers, infinite power quantum computers, disruptive cosmology)

JeanFrancois Geneste  3  MC06010 
Topics in Neurobiology Seminar
A research paperbased course.
Overview of current research relating to various ‘hot topics’ in neurobiology and discussion of current research articles on the subject. Analysis of experiments and research described in scientific papers are presented by students and critically discussed by the class led by the instructor. Novel methods in neurobiology – optogenetics, molecular magneto technique, FLARE, transparent tissues imaging will be discussed in depth. Topics include mapping of the brain and behavior, optogenetic manipulation of memory engrams, mouse models of Alzheimer disease, synaptic plasticity, dendritic spines morphology, pathology and neurodegenerative diseases. 
Dmitry Artamonov  3  MA03104 
Transport in Mesoscopic Systems
The course aims to provide introduction to a modern direction of the solidstate physics, devoted to studying charge transport (charge currents) in mesoscopic structures. Mesoscopic structures are intermediate between micro and macroscopic systems; in our context, this name refers to systems with many electron in which mechanics (in particular, quantum mechanics) of single electrons is still important. The course consists of two parts, devoted to normal (i.e., nonsuperconducting) and superconducting systems. A number of these systems form a basis for nanoelectronics devices. The course assumes participation of students interested in both experimental and theoretical aspects of mesoscopic research.

Yakov Fominov  6  MA06217 
Course Title  Lead Instructors  ECTS credits  Course Code 

Academic Communication: Preparatory English for Phd Exam
Efficient professional communication is the key to Academic success. The course is designed for PhD students who want to maximize their academic potential by boosting their ability to write research papers, present in front of multidisciplinary audiences, participate in scholarly discussions and engage in other forms of academic communication.
The main goal of the course is to enable PhD students to produce clear, correct, concise and coherent texts acceptable for the international professional community. The course is designed for a multidisciplinary audience. The course serves as a preparation for the qualification language exam, which is a prerequisite for the Thesis defense. 
Elizaveta Tikhomirova  3  PE03029 
Academic Writing Essentials (Term 34)
Academic writing skills are necessary for effective research, innovation, and educational activities in a multinational setting. The aim of the course is to provide guidelines and strategies for writing academic texts, focusing on relevant aspects of grammar, vocabulary, and style. The course includes analysis and practice of various forms of scientific and technical writing, and builds writing skills from sentences to paragraph structure, from summary to abstract, and lays the foundations for writing scientific papers and Master Thesis.
Modern science is, for most purposes, a collective collaborative effort, so the course is designed to promote individual and group responsibility by providing mutually related and timedependent tasks, such as peer review. The course is writingintensive with ample opportunity to practice editing and peerreviewing. 
Anastasiia Sharapkova  1.5  MO03002 
Academic Writing Essentials (Term 34)
Academic writing skills are necessary for effective research, innovation, and educational activities in a multinational setting. The aim of the course is to provide guidelines and strategies for writing academic texts, focusing on relevant aspects of grammar, vocabulary, and style. The course includes analysis and practice of various forms of scientific and technical writing, and builds writing skills from sentences to paragraph structure, from summary to abstract, and lays the foundations for writing scientific papers and Master Thesis.
Modern science is, for most purposes, a collective collaborative effort, so the course is designed to promote individual and group responsibility by providing mutually related and timedependent tasks, such as peer review. The course is writingintensive with ample opportunity to practice editing and peerreviewing. 
Elizaveta Tikhomirova  1.5  MO03002 
Additive Manufacturing
Additive manufacturing (AM), also called 3D printing, has become an extremely promising technology nowadays. Unlike traditional manufacturing processes such as welding, milling and melting that involve multistage processing and treatments, AM allows to create products with new level of performance and shapes. Moreover, this technique allows to produce prototypes rapidly and leads to reducing costs and risks. Another crucial advantage of the technology is the unprecedented design flexibility that let us create the samples of high quality based on different materials such as metals, alloys, ceramics, polymers, composite materials etc.
The main goal of this course is to represent the latest developments in the field of additive manufacturing to the students. In this course a wide range of questions will be addressed, beginning from the process of designing the structures up to various printing technologies, as well as analysis of the final structures. Various kinds of applications of these materials from engineering to bio regenerative medicine will be considered. During laboratory class we will get acquainted with the additive technologies on various printing machines. Students will be able to create their own models, print them in metals, ceramics and polymers, and also analyze the properties of the final samples. During this course a complete cycle of production of samples using various 3D printing techniques will be explored both theoretically and practically. 
Iskander Akhatov  6  MA06243 
Advanced Molecular Biology Laboratory Practice
This course offers students the opportunity to work individually on laboratory projects assigned by the course instructor. During the term students are expected to have at least one entire working day in the lab, although additional days may be required. Final grades are determined by the students' final presentations, which describe their project/goals along with the results/progress accomplished. Participation in the course requires approval from the students' own advisors, as well as the instructors of the course

Konstantin Severinov  6  MA06046 
Advanced Statistical Methods
This course introduces the main notions, approaches, and methods of nonparametric statistics. The main topics include smoothing and regularization, model selection and parameter tuning, structural inference, efficiency and rate efficiency, local and sieve parametric approaches. The study is mainly limited to regression and density models. The topics of this course form an essential basis for working with complex data structures using modern statistical tools.
Course structure: lectures, seminars, exam. 
Vladimir Spoikoiny  3  MA03132 
Basic Molecular Biology Techniques 1
The purpose of this course is to provide students with the opportunity to obtain and develop the basic set of skills needed to be successful in a molecular biology laboratory. The course consists of handson laboratory work, as well as lectures from course instructors. Students without any significant background in the biological sciences should be advised that additional reading outside of the scheduled classes may be necessary to maximize classroom success (instructors are happy to provide resources at the students’ request).

Svetlana Dubiley  6  MA06022 
Biostatistics
This introductory course to statistics and probability theory is modeled as an extension of a traditional university Statistics course and Advanced Placement Course in Statistics to a broader spectrum of topics, while keeping the spirit of quantitative discourse applied to reallife problems. The material is offered in 5 consecutive modules (see Course Outline below), each containing a lecture, a discussion section, and a practicum. For practical exercises we use R programming language and RStudio software. However, this course is focused on statistics rather than R; therefore, each practicum is designed with the purpose to demonstrate and reinforce understanding of concepts introduced in the lecture rather than to provide a training in R.

Dmitry Pervouchine  6  MA06036 
Carbon Nanomaterials
The course covers the subject of carbon nanomaterials (fullerenes, nanodimond, nanotubes, and graphene). The history of carbon compounds since antiquity till our days starting from charcoal to carbon nanotubes and graphene will be reviewed. The students will have opportunity to synthesize carbon nanotubes (by aerosol and CVD methods) and graphene, to observe the materials in transmission (TEM) and scanning (SEM) electron microscopes as well as by atomic force (AFM) microscope and to study optical and electrical properties of the produced carbon nanomaterials. A few lectures are presented by various specialists on the topic of their research.
Totally 32 hours of lectures, 12 hours of exercises and 4 hours of discussion work. During the courses each student is supposed to give a short presentation (15 min) on a selected topic, to write an essay on other selected topic and to prepare an exercise report. 
Albert Nasibulin  6  MA06044 
Computational Materials Science Seminar (Term 14)
This is the main research seminar at Skoltech for Computational Materials scientists. All students of Computational Materials Science subtrack of Materials Science MSc program should attend this seminar. Topics include materials modeling (at atomistic scale), theoretical and computational chemistry, theoretical and computational physics of materials, underlying mathematical methods and algorithms etc. Invited lectures are top scientists in their research field.
Please see the seminar webpage at https://www.skoltech.ru/en/cms/ 
Dmitry Aksenov  0.75  MO03005 
Condensed Matter Spectroscopy and Physics of Nanostructures (Term 1B4)
The first part of this course covers major topics of the modern optical spectroscopy of solid state systems, including nanomaterials and novel topological materials. The introductory part of the course outlines the basic classical and quantum theory of electromagnetic response, and basics of the solid state spectroscopy. Then the major research directions in the modern condensed matter spectroscopy are considered, such as spectroscopy of graphene, topological materials, and transition metal dichalcogenides.
The second part of the course describes the physics of lowdimensional electron systems and nanostructures. Twodimensional electron and electronhole systems, lowdimensional disordered systems, quantum Hall effect, carbon nanostructures, photonic crystals and optical microcavities will be considered. 
Alexey Sokolik  1.5  MA06313 
Differential Topology (Term 34)
We plan to discuss two topics, which are central in topology of smooth manifolds, the hcobordism theorem and theory of characteristic classes. The hcobordism theorem proved by S. Smale in 1962 is the main (and almost the only) tool for proving that two smooth manifolds (of dimension greater than or equal to 5) are diffeomorphic. In particular, this theorem implies the highdimensional Poincare conjecture (for manifolds of dimensions 5 and higher). Characteristic classes, in particular, Pontryagin classes are very natural invariants of smooth manifolds. Computation of characteristic classes can help one to distinguish between nondiffeomorphic manifolds. We plan to finish the course with the theorem by J. Milnor on nontrivial smooth structures on the 7dimensional sphere. This theorem is based both on methods of Morse theory and theory of characteristic classes

Alexander Gaifulin  3  MA06258 
Dynamical Systems and Ergodic Theory (Term 34)
Dynamical systems in our course will be presented mainly not as an independent branch of mathematics but as a very powerful tool that can be applied in geometry, topology, probability, analysis, number theory and physics. We consciously decided to sacrifice some classical chapters of ergodic theory and to introduce the most important dynamical notions and ideas in the geometric and topological context already intuitively familiar to our audience. As a compensation, we will show applications of dynamics to important problems in other mathematical disciplines. We hope to arrive at the end of the course to the most recent advances in dynamics and geometry and to present (at least informally) some of results of A. Avila, A. Eskin, M. Kontsevich, M. Mirzakhani, G. Margulis.
In accordance with this strategy, the course comprises several blocks closely related to each other. The first three of them (including very short introduction) are mainly mandatory. The decision, which of the topics listed below these three blocks would depend on the background and interests of the audience. 
Aleksandra Skripchenko, Anton Zorich 
3  MA06257 
Energy Colloquium
The Energy Colloquium educates the audience in the presentday research and applications within the broader field of Energy Science and Technology. The Colloquium consists of a series of presentations by invited academic and industry speakers. The presentations target a nonspecialist audience.
All Master and Ph.D. students within the Energy Program are encouraged to attend the Energy Colloquium during the entire period of their studies. Students can earn 1 credit, if he/she participates in the Energy Colloquium over the course of any 2 terms of the academic year. Students who passed one round can make next (for credit) over the course of their subsequent studies. 
Alexei Buchachenko  1  MA01092 
Energy Efficient Microclimate Control
This course is focused on the experimental studies in recently developed microclimate polygon (Room #403). Our experimental setup permits the fine monitoring of the dynamics of the thermodynamic and chemical data (CO2 concentration, humidity, air pressure, temperature) of the room where they are installed. We’ll discuss how heating, ventilation and airconditioning (HVAC) systems maintain the indoor quality of air and temperature at acceptable levels in any building that hosts people and what particular control strategies can be implemented to improve energy efficiency.
The core of the course is individual experimental work including problem justification, experimental plan development, getting data, explanation and interpretation of the obtained results. 
Elena Gryazina  3  MA03281 
English. Candidate Examinations
This is a metacourse which allows PhD students to register for English Qualification Exam for the Russian PhD Degree. There will be no lectures or seminars, only the exam. The preparatory course is also available in course catalog (look for "Academic Communication for PhD students" course).
The Exam has two parts: Part 1 – Preexam activities (Assignments 1, 2a, 2b) 
Elizaveta Tikhomirova  3  PE03003 
Evolutionary, Population and Medical Genomics
Nothing in biology makes sense except in the light of evolution. This course introduces the fundamentals of evolutionary science as applied to genomics. It will allow to see how the basic population genetics processes create, maintain and affect variability in populations and lead to their changes with time. The focus will be on molecular evolution, i.e., the manifestation of these processes in genomes. As humans, we will be particularly interested in evolutionary aspects of medicine. The course assumes no prior familiarity with evolutionary biology, although knowledge of the basics of molecular biology and genetics is expected. The themes covered will include basic concepts in evolutionary biology and generalizations in evolutionary genomics; population genetics and factors of microevolution; and basics of quantitative genetics.

Georgii Bazykin  6  MA06222 
Fabrication technology of nanodevices
This course concerns fundamental and practical aspects of fabriction technologies widely used for fabrication of nanoscale devices. Course start with introduction of clean room environment, code of practise and safety for operation in Nanofabrication centres. There are discussed a range of technologies and methods: UV and Electron Beam lithographies, wet and dry etching, thin film deposition, thermal annealing, controllable oxidation and ion beam implantation, metrology of nanoscale devices. An introduction to chemicals used for fabrication and safety operation are given. Finally examples of fabrication of devices are discussed. Students will have a chance to learn practical operation on some equipment.

Vladimir Antonov  3  MA03311 
Foundations of Engineering Physics (Term 1B4)
The course is dedicated to basics of building interfaces ”experimentcomputer” in the modern scientific research. In most general configuration such interface comprises three stages:
1) “input” analog frontend feeding the electronic signals from sensors, transducers, 2) analogtodigit as well as digittoanalog conversion “bridges” and 3) logical channels conveying the ultimate digital information to a computer. The consideration of the three stages is made with emphases on the principle aspects of scientific measurements rather than detailed schematic/circuitry of the instrumentation. All stages of the measurement systems will be reviewed from the point of view of the fundamental imperatives of signal conditioning like impedance matching, optimal choice of the bandwidth solving the ubiquitous tradeoff “precision versus rate” of data acquisition and et al. As well important peculiarities of configuring the elements of the system – such as prefiltering, modulationdemodulation techniques, the choice of the type and bit width of ADCs/DACs – will also be thoroughly discussed. At all stages a short concomitant overview of the modern commercially available electronic equipment will be given in order to improve students’ ability to select a proper set of the electronic devices among a great variety of those available on the market. 
Yuri Romanovskiy  1.5  MA06213 
Foundations of Multiscale Modelling: Kinetics
The course is devoted to fundamental principles of modelling of kinetic processes at different time and space scales. The basic concepts are introduced, along with the theoretical and numerical techniques, which application to practical problems is illustrated. The course starts with the description of molecular kinetics in fluids, colloidal and polymer solutions; applications for molecular machines and nanorobotics is considered. Langevin and FokkerPlanck equations are introduced, supplemented with the theoretical and numerical tools of their solution.
Next, the Boltzmann kinetic equation is analyzed. An application of the fundamental theoretical and numerical techniques, such as Grad and ChapmanEnskog methods, Lattice Boltzmann and Direct Simulation Monte Carlo is illustrated. Derivation of transport coefficients and hydrodynamics equations, including these for dissipative fluids, is given. GreenKubo relations as an alternative method for practical computation of transport coefficients is presented and compared with other methods. Based on the Boltzmann equation, the theory of aggregationfragmentation kinetics is developed, leading to the generalized Smoluchowski equations. The basic concepts like Scaling, Generation functions, etc. are introduced for theoretical analysis and Gillespe algorithm and fast solvers for practical computations. In the rest of the course the above theoretical and numerical techniques are illustrated for the following applications: Surface growth, Phase transition kinetics, Random sequential adsorption, Nucleation & Growth and Nanotribology. Theory of Active Matter, Traffic Models, Sociodynamics and Complex Networks dynamics are also considered. The knowledge of undergraduate mathematics – the basics of calculus, linear algebra and probability theory, as well as reasonable skills in Matlab and Python are needed. A familiarity with the basic open source software is desirable. 
Nikolay Brilliantov  6  MA06326 
Fracture Mechanics
Fracture mechanics is a large and always growing field since it focuses at one of the most significant problems in the industrialized world and a theoretical and practical basis for design against fracture is needed. Fracture mechanics deals essentially with the following questions: Given a structure or machine component with a preexisting crack or cracklike flaw what loads can the structure take as a function of the crack size, configuration and time? Given a load and environmental history how fast and in what directions will a crack grow in a structure? At what time or number of cycles of loading will the crack propagate catastrophically? What size crack can be allowed to exist in component and still operate it safely?
Fracture can and is being approached from many scales. For example at the atomic level, fracture can be viewed as the separation of atomic planes. At the scale of the microstructure of the material, the grains in a polycrystalline material, or the fibers in a composite, the fracture of the material around these features can be studied to determine the physical nature of failure. From the engineering point of view, the material is treated as a continuum and through the analysis of stress, strain and energy we seek to predict and control fracture. In this course, the emphasis is on continuum mechanics models for crack tip fields and energy flows. A brief discussion of computational fracture, fracture toughness testing and fracture criteria will be given. This course is designed for students who want to begin to understand, apply and contribute to this important field. 
Sergey Abaimov  6  MA06248 
Functional Methods in The Theory of Disordered Systems (Term 34)
The course provides an extensive overview of contemporary functional methods in the theory of disordered systems. Starting from the theory of random matrices, it covers various aspects of electron motion in disordered media. The concept of the nonlinear supersymmetric sigma model is introduced and used as a unique language to describe such phenomena as energy level statistics, weak localization, renormalization group analysis, nonperturbative solution of the localization problem in quantum wires. Finally, functional integral method is used to address electronelectron interaction in disordered metals and nonequilibrium phenomena in quantum dots.

Mikhail Skvortsov  3  MA06262 
Fundamentals of Remote Sensing This course introduces students to the first principles and methods of the observation of Earth surface, monitoring of Earth atmosphere and detection of different kind of radiation coming from Space. The course will cover wide range of the satellites, aircraft, rockets and balloon based techniques designed for environmental monitoring, meteorology, map making etc. Goals of the course include: a comprehensive knowledge of the principles and approaches to the creation and operation of remote sensing systems; acquisition of analysis skills of modern ERS programs; practical application of acquired knowledge and Course will also include a module on geomatics, i.e. platforms, sensors and methodologies related to the collection, processing, analysis and interpretation of (2D/3D) data related to Earth's surface. This includes platforms like satellite or drones, sensors like LiDAR or airborne cameras and techniques like photogrammetry, laser scanning, geodesy, topography, etc. Major learning outcomes include operational principles and design of different sensors used in remote sensing of the Earth, practical skills to design an experiment in remote sensing with applications to a practical business need. 
Gershenzon  6  MA06186 
Gauge Theory and Gravitation (Term 34)
The present course could be also entitled 'Classical Field Theory', which menas it deals with all basic material needed in a study of fields preceeding to a study of their quantum properties. This requires in particular understanding such tools as Lagrangian, action functional, field equations (EulerLagrange equations). We shall also learn what are the most important symmetry principles which put certain constraints on a field theory. With this are related conservation laws. Typical important symmetries to mention are Lorentz and Poincare symmetry, conformal symmetry, gauge symmetry, general coordinate covariance.
A traditional approach to Classical Field Theory has a perfect base in the 2nd volume of LandauLifshitz' course. However, since that prominent book was written, new elements came forward, which required more knowledge of differential geometry and topology. In our lecture course, we shall get familiar with most important basic facts from these branches of mathematics with application to field theory. For example, understanding instantons (even at a classical level) requires good knowledge of a number of notions from modern math courses, such as vector bundles, connections, homotopy groups. Therefore our course has to go beyond the reach of LandauLifshitz' volume 2. 
Alexey Rosly  3  MA06178 
Geomechanics and Hydraulic Fracturing
In this short course we present main basic principles of construction selfconsistent hydrogeomechanical models for reservoir physics description.
We start with several practical examples which demonstate the need for geomechanics in each of considered technological application with special application to hydraulic fracturing technology. We then stop on continuum mechanics formulations for one phase models, suitable for onepointview description of reservoir and well flow deformation processes. We also describe twophase models, although intentionally do not go too deep in the topic. We also do not goal to make our formulations rigorous enough in mathematical sense. We do not thing that Master students need that at this stage. Instead, we put significant effort (and number of contact hours) to let Master students fell free in practical solutions of the governing equations they were just taught. To make the procedure more effective, the governing equations are divided into several (20) basic groups with their own specific modelling recipes which are taught to students at classes until they ensure that the procedures are simple. For doing that we developed 20 matlab codes. During their further project exercises, students will utilize these 20 "bricks" to construct solutions for real field and/or technological problems, presented in the first section of the course. It has to be noticed, that the course is suitable for PhD students as well, although the project topics for them would be more complicated that that for the master students 
Artem Myasnikov  6  MA06190 
Heterogeneous Volume Modeling and Digital Fabrication
The course covers methods and techniques of digital modeling of volumetric point sets with attributes presenting pointwise properties such as material fractions, color, and other volumetric object properties. Modelled objects are characterized by complex volumetric geometry, multiscale microstructures and volumetric multimaterial density distribution. Stress will be made on using continuous and discrete scalar fields for modelling both geometry and attributes. Associated methods of multimaterial digital fabrication will be outlined.

Alexander Pasko  6  MA06299 
Immunology
The purpose of this course is to lay the foundation for understanding the principles of the immune system functioning. Such a basis is necessary for further professional growth either in the field of fundamental immunology or applied research and development in medical immunology and oncology. This course will also be important for those who want to professionalize in medical practice, pharmaceutical industry, epidemiology and health services management, engineering and business in the field of biomedicine.
The course is focused on the human immune system. The main medical aspects related to the functioning of the immune system will be considered, such as: autoimmune diseases, allergies, tumorimmune system interactions, immunotherapy, vaccinations and transplantation. Particular attention will be paid to the adaptive part of the immune system and immunogenomics: application of the new sequencing technologies and associated computational data analysis approaches to the studying of the antibody and Tcell receptor repertoires in health and disease. The course is designed for students of different biomedical background. The necessary foundation will be given in the form of lectures. Independent work of students, mainly in the form of presentations aimed to dissect the particular immunological questions at the seminars, will be differentiated in compliance with individual background. A workshop in applied bioinformatics is included within the course. In a few hours of guided and independent work it will cover the data analysis of immune receptor highthroughput sequencing. 
Dmitry Chudakov  6  MA06172 
Information and Coding Theory
The aim of the course is to explain basic ideas and results of information and coding theory, some of which has been used for rather long time in data science, in particular various entropy inequalities, and some emerged just very recently, for instance, usage of errorcorrecting codes for improvements of kmeans method for clustering. The course is divided into two parts: introduction to information theory and elements of modern coding theory. In the first part, we consider the measure of information, mutual information, entropy, evaluation of channel capacity for single user and multiuser channels. In the second part, we consider foundations of coding theory such as block codes, linear codes, bounds on the code’s parameters and the most popular algebraic coding methods (Hamming, ReedMuller, BCH and ReedSolomon codes). Then we consider modern coding techniques, i.e. iterative decoding systems and graphical models to represent them. Iterative techniques have revolutionized the theory and practice of coding and have been applied in numerous communications standards. We discuss lowdensity paritycheck (LDPC) codes, factor graphs and SumProduct decoding algorithm.

Alexey Frolov  6  MA06122 
Innovation and Intellectual Property Studies Doctoral Seminar (Term 14)
This course is a compulsory academic seminar series for all Ph.D. students in the Innovation and Intellectual Property Management Ph.D. Program. It consists of weekly research seminars that address the state of the art in research about the role of intellectual property in technological innovation. Specific topics and themes in the course will vary from year to year, but will typically include: theories of innovation; concepts and theories in IP management; practical issues in IP management; case studies in IP strategy; valuation of IP; Russian and international trends in intellectual property law; topics in technology entrepreneurship; product development and new technology; IP and design; patent analytics for innovation research; commercialization strategies of technology startups; organizational issues in technology innovation; conceptual issues at the interface of technology, science and business; public policy for technology, science and innovation; ethical and social issues related to IP and technological innovation; case studies in innovation management; philosophy of technology and philosophy of intellectual property; theory and methodology in IP management research; technology transfer and commercialization of university research; international collaboration and international trade in technology. As part of their seminar obligations, all students must prepare a formal written research paper on a topic that may or may not be directly related to their thesis research and make a presentation about the paper to the seminar group. The paper will be assessed.

Kelvin Willoughby  1.5  PC06009 
Instrumental Analysis in Molecular Biology  Timofey Zatsepin  3  MA06250 
Intellectual Property and Technological Innovation (Term 34)
Intellectual property (IP) is a critically important aspect of technological innovation and a key factor in the management of technologyintensive enterprises. Prowess in the management of intellectual property is important for technology leaders in both established corporations and entrepreneurial ventures.
Entrepreneurial technology ventures flourish according to how well their intellectual property assets are managed, leveraged and enforced. Additionally, it is almost impossible for engineers or scientists to avoid confronting issues related to intellectual property. These include: the risk of violating the IP rights of others; an obligation to respect the IP policies of one’s employer; the need to obtain IP protection for one’s own inventions and creative works; the obligation to become involved in the management of the IP belonging to ones employer; and the challenge of ensuring that one’s own IP rights are not infringed by others, including by one’s own employer or one’s clients. In addition, with such a large amount of contemporary business—in both the private sector and government—involving outsourcing and interorganizational collaboration, expertise in the licensing of intellectual property rights is in high demand. This course will survey basic concepts of intellectual property and provide an introduction to a variety of types of intellectual property and IPrelated rights, such as patents, copyright, trade secrets, trade marks, design rights, database rights, domain names, and demarcations of origin. The will also examine the strategic management of IP in the process of technology commercialization, and the resolution of IPrelated conflicts between technology based enterprises. It will also explore social, economic and ethical issues associated with the accumulation and exploitation of intellectual property. 
Kelvin Willoughby  3  MC06006 
Intellectual Property, Technological Innovation and Academic Research (Term 34)
Intellectual property (IP) is a critically important aspect of technological innovation and a key factor in the management of technologyintensive enterprises. Basic knowledge of intellectual property principles and practices is increasingly important for university researchers, and expertise in the management of intellectual property is a key skill set of technology leaders in both established corporations and entrepreneurial ventures.
Intellectual property affects not only technology commercialization strategy but also the direction of scientific research itself. University research groups increasingly compete with each other for scientific reputation and access to resources on the basis of their ability to obtain patent protection for the practical applications of their research; but also on the basis of their ability to plot research pathways to maneuver around the "proprietary territory" of other research groups. Skill in using IP data bases, and associated analytical tools, can empower university scientific teams to craft more powerful research strategies. This course will survey basic concepts of intellectual property and provide an introduction to a variety of types of intellectual property and IPrelated rights, such as patents, copyright, trade secrets, trademarks, design rights, database rights, domain names, and demarcations of origin. The classroom sessions will include lively discussions of case studies of the management of IP and the resolution of IPrelated problems in the process of technology commercialization. Each student will conduct an analysis of intellectual property issues related to his or her own Ph.D. research topic. Use will be made of special IP data and IP analytics tools. 
Kelvin Willoughby  3  PC06006 
Laser Physics
The course includes fundamental basics of laser physics and quantum photonics, both theoretical fundamentals and the application of the theory to different types of lasers. Theoretical fundamentals start from consideration of MaxwellBloch equations, which allows one to describe intensity of laser generation. Then the homogeneous broadening is described via electromagnetic field quantization. Extension of twolevel system up to three or fourlevel system is given. Impulse regime and passive modelocking of laser generation and are considered. Optical methods which found their applications in laser technologies are considered. After that, we consider gas lasers discussing the process of pumping, their efficiency and the generation line width; fiber lasers, including fiber amplifiers; diode lasers, including heterostructures, band zone description, process of pumping, dependence of the laser efficiency on electrical current and temperature; and solidstate lasers, including types of pumping and types of crystals.

Sergei Vergeles  6  MA06143 
Laser Spectroscopy (Term 1B4)  Alexander Makarov  1.5  MA06212 
Machine Learning
The course is a general introduction to machine learning (ML) and its applications. It covers fundamental modern topics in ML, and describes the most important theoretical basis and tools necessary to investigate properties of algorithms and justify their usage. It also provides important aspects of the algorithms’ applications, illustrated using realworld problems. The course starts with an overview of canonical ML applications and problems, learning scenarios, etc. and introduction into theoretical foundations of ML. We present the most novel theoretical tools and concepts trying to be as succinct as possible. Then we discuss in depth fundamental ML algorithms for classification, regression, boosting, etc., their properties as well as their practical applications. The last part of the course is devoted to advanced ML topics such that metric learning, kernel mean embedding of distributions, anomaly detection, reinforcement learning, etc. Within practical sections, we show how to use the methods above to crack various realworld problems. Home assignments include application of existing algorithms to solve applied industrial problems, development of modifications of ML algorithms, as well as some theoretical exercises. The students are assumed to be familiar with basic concepts in linear algebra, probability and real analysis.

Evgeny Burnaev  6  MA06018 
Master Your English for Thesis (Term 57)
Writing is the key priority and the need of utmost importance for wouldbe scientists. Science demands not just writing, but good writing, that presupposes the skills to communicate ideas, theories and findings as efficiently and clearly as possible. Science lives and dies by how it is represented in print and a printed material is the final product of scientific endeavour. The primary goal of this course is to prepare master students for wiring, editing, and defending a Master Thesis.
This course is designed to explain how to write chapters of their Thesis through practical examples of good writing taken from the authentic linguistic environment. The course teaches how to overcome certain typical problems in writing a text of a thesis and abounds in useful linguistics assistance on its various parts. Feedback on students’ texts will constitute the major part of the course. 
Anastasiia Sharapkova  1.5  MO03003ls 
Master Your English for Thesis (Term 57)
The key to efficient professional communication is the ability to convey ideas clearly, coherently and correctly both orally and in writing.
The Course offers concise and practical guidelines for writing and defending a Master Thesis at Skoltech. The course focuses on the main parts of the Thesis in terms of structure, vocabulary and grammar, and their transformations for a presentation with slides. Students will develop a conscious approach to own writing and presentations through thorough analyses of the best authentic examples combined with intensive writing and editing practice. The ‘processforproduct’ approach teaches the students to write – use (peer) reviewer’s advice – revise/edit – repeat, and creates linguistic awareness needed to avoid the typical pitfalls. The Course is offered in two modules which gradually build on the necessary writing and presentation skills. 
Elizaveta Tikhomirova  1.5  MO03003 
Material Structure Characterization Methods
The course teaches theoretical and practical fundamentals of diffraction and electron microscopy methods applied to the analysis of the crystal structure, nano and microstructure of materials. The course delivers basic knowledge on the theory of crystal structure analysis with various kinds of radiation, modern techniques of crystal structure determination, the analysis of the local structure of matter, defects and microstructure, theory of image formation in the electron microscope and a review on modern spectroscopic techniques with atomic resolution. The competences acquired in this course can be further used in all branches of material science dealing with crystalline matter. The course consists of lectures, seminars/practical lessons, laboratory works and exam.

Artem Abakumov  6  MA06116 
Materials Selection in Design
This course illustrates the need for a scientific and practical method of selection of appropriate materials for industrial application. It includes review of the principles of materials science including materials classification, hierarchical structuring, related properties, and performance of different class of materials such as natural materials, metals, ceramics, plastics, cellular solids. Ashby’s material selection algorithm for rational selection of materials for specific applications will be taught here in comprehensive way – analysis of function, objectives and constraints, deducing of performance indices. All the concepts covered in lectures will be practiced by using a commercially available software known as CES EduPack to implement data intensive learning. Team projects are aimed to taste the CDIO approach in Materials Selection.

Alexey Salimon  6  MA06099 
Mechanics and Physics of Advanced Manufacturing
This course is developed to give students a broad background and hands on experience in manufacturing of advanced composite materials. Both materials and manufacturing methods are discussed. A brief introduction to advanced composite materials and processes is presented. The course is focused on the innovative nonautoclave technologies of thermosetting resin based/fiber reinforced advanced composites. Manufacturing is covered in terms of the major steps required to fabricate laminated composite parts. These will be described and discussed in details and worked out experimentally through conducting a set of lab projects. The following technologies and methods will be covered: Vacuum Infusion, Press Molding, Pultrusion, Filament Winding, and Mechanical Testing. Typical problems of materials, tooling, cure, and technological defects will be discussed. The physics, chemistry, and mechanics to develop the fundamental and constitutive laws describing the processing steps of the polymer composite fabrication processes will be discussed.

Iskander Akhatov  6  MA06240 
Molecular Biology Seminar
For each class, there will be a paper that two people will present to the rest of the class. We will go down to the details of experiments – how things were done and what do the data/figures really show, so be prepared to answer indepth questions. Presenters will start by stating the name of the paper/main authors and telling the take home message of the paper – why it is signficant, what problem it solved. Then they will proceed to the actual work. If there are methods/results mentioned in the paper that refer to prior work, you shall be prepared to answer questions about it too. The audience is supposed to read the paper being discussed beforehand and participate in discussions.
To pass, one would need to present a paper at least once during the module and actively take part in discussions of other papers. One absence is allowed no questions asked. Additional absences when unexplained will be a cause for nopass grade. There will be a few home assignments. They must be submitted in time, typed–not written up–and done professionally (written in good language, be concise and free of spelling errors – consider them as part of academic writing exercises). It is gonna be fun – students tend to like the seminar and its atmosphere 
Konstantin Severinov  3  MA03052 
Molecular Spectroscopy (Term 1B4)  Vladimir Mironenko  1.5  MA06209 
New Product Design: from Idea to Market Launch
Ability for finding and addressing real customer/market needs, using technology to enable unique customer experiences, communicating effectively your new product/service ideas to your target audience, as well as the business model validating – are among the core factors of managing innovation successfully. This is essentially the task of the navigating through the first stages of the iterative innovation process also known as “Fuzzy Front end of Innovation”.
In this course the students will learn about In particular, students will learn how to get insights into customer needs, get handson knowledge on different approaches to market research and customer cocreation. As well the course reviews modern methods for generating market insights, turning them into promising concepts, validating and enhancing the concepts through rapid prototyping, experimentation and user tests. Special focus is given to modern Digital Products and technologies in the areas of Internet of Things, Smart and Connected Devices, Industry 4.0. 
Alexey Nikolaev  3  MC03012 
NonEquilibrium Processes in Energy Conversion
Classical thermodynamics is useful to describe equilibrium states, while nonequilibrium states and irreversibility characterize real physical processes. If one is interested in actual processes at work during energy conversion, a classical thermodynamic description of equilibrium states is insufficient as it yields very incomplete information on the processes. Irreversible thermodynamics accounts for the rates of physical processes, and provides relationships between "measurable quantities" such as transport coefficients. This graduate course, which constitutes the natural continuation of the course Energy Systems Physics & Engineering, provides the students with basic knowledge of outofequilibrium and finitetime thermodynamics, which describe irreversible processes that routinely take place in physical systems and permits a fine understanding of the processes ensuring energy conversion. Thermoelectric generators serve as the main example to illustrate in a simple fashion the outofequilibrium formalism, and other systems such as, e.g., solar cells and batteries are studied.
Essential notions which are taught include: Onsager’s approach to linear nonequilibrium thermodynamics; coupled transport theory; Boltzmann equation; thermal conductivity; electrical conductivity; electrochemical potential in solidstate systems; forceflux formalism and its application to thermoelectric systems; device optimization modelling accounting for dissipative coupling to heat reservoirs; solar energy conversion; batteries. The course is organized around the learning of essential concepts and an awareness development of current energy technologies. It is based both on "teaching with lecture" and "teaching with discussions" methods. In addition to home assignments and project, students will solve problems during tutorials and discuss their solutions. 
Henni Ouerdane  6  MA06200 
Numerical Methods in Engineering and Science
Engineering science and technology are undergoing a revolution. With continuous rapid advances in hardware and software information technology, computer simulations have emerged as a new way of scientific discovery enabling scientists and engineers to build and test models of multiscale/multiphysics phenomena that are either too complex, costly, hazardous, vast, small, or even impossible for direct experimentation. In industry, computer modeling and simulations provide a competitive edge by transforming business and engineering practices. Increasingly, computer simulations are replacing physical tests to ensure product reliability and quality, while noticeably shortening design cycle.
The course is intended to provide the understanding and working knowledge of numerical methods required for modeling and simulation of complex phenomena. The course focuses on understanding fundamentals of numerical methods such as accuracy, stability, convergence, and consistency rather than learning how to use canned computer codes. The course involves a fair amount of firsthand experience with programing and solving real problems on computers. Although the solid knowledge of calculus, linear algebra, complex variables is essential, only basic understanding of the theory of ordinary and partial differential equations as governing equations for physical and engineering systems as well as basic programming skills are required. The following topics are discussed: interpolation, numerical differentiation, numerical integration, numerical solutions of ordinary differential equations, and numerical solution of partial differential equations. Students will have to complete four computer projects, midterm and final exams. 
TBD  6  MA06239 
Numerical Modeling
Many complex systems developed by engineers (e.g. labs on chips, iPads, magnetic resonance imaging scanners, nationwide electrical/gas/oil transportation networks, or buildings/automotive/aircraft frames or supply chains and economical/social networks) or found in nature (e.g. the human cardiovascular system, the brain neural network, biological systems, or the geophysical network of oil/water/gas reservoirs) can be viewed as large collections of interconnected dynamical system components. The performance and characteristics of each individual component critically depends on what engineers or scientists refer to as second order effects, and can be captured only by resorting to expensive partial differential equation solvers. In this course we will survey several techniques for modeling and simulation of a large variety of engineering and physical complex systems. In particular, detailed examples will be presented, drawn from the following engineering disciplines: Electrical Engineering (interconnect networks including parasitics; electromagnetic structures; analog and digital circuits including nonlinear semiconductor devices and MicroElectroMechanical Devices), Mechanical Engineering (frame modeling, heat diffusion, fluiddynamics and oil transport), Civil Engineering (structural problems, vibrations), Material Sciences (inverse problems for identification of material properties), Biomedical Engineering (human cardiovascular system).
This course provides students access to the state of the art in numerical tools in order to help them with their research projects involving analysis, design and optimization problems in a variety of different engineering and science disciplines dealing with complex systems. The focus of the course will not be on mathematical formalism and rigorous theorem proving, but rather on developing general intuition and practical implementation skills. 
Alexander Shapeev  6  MA06005 
OneDimensional Quantum Systems (Term 34)
In the framework of the course, quantum systems (fieldtheoretic and discrete) in one spacial dimension, and some their classical statistical mechanics counterparts are discussed. The scope of systems includes sineGordon and Thirring model, O(n) sigma model, Heisenberg chain and sixvertex model, Kondo problem. We consider several techniques to obtain exact results for these systems, including operator product expansions, bosonfermion correspondence, YangBaxter equation, different versions of Bethe Ansatz.

Michael Lashkevich  3  MA06276 
Optical Communications
Communication is an important part of our daily life. The communication process involves information generation, transmission, reception and interpretation. As needs for various types of communication such as voice, images, video and data communications increase demands for large transmission capacity also increase. This need for large capacity has driven the rapid development light wave technology; a worldwide industry has developed. An optical or light wave communication system is a system that uses light waves as the carrier for transmission. An optical communication system mainly involves three parts: transmitter, receiver and channel. In optical communication transmitters are light sources, receivers are light detectors and the channels are mainly waveguides (e.g. optical fibers) or free space.

Arkady Shipulin  6  MA06157 
Optimization Methods
The course is devoted to optimization methods and optimization problems design with a special attention to those motivated by data science, engineering and industrial applications.
The course starts with a brief reminder of the foundations of convex analysis. Then we discuss zero, first and second order methods with a special focus on their efficient implementation. We distinguish between various problem classes, discuss suitable methods for every class. The problem formulation and its proper reformulation is the critical issue for an optimizer. We’ll learn about optimization models and convex relaxations. Special attention will be addressed to Linear Matrix Inequalities (LMI) that arise in optimization problem formulations. One of the home assignments is devoted to understanding the constraints of performance for different software packages. At the last part of the course we move further to advanced first order optimization methods such as proximal mirror descent and extra gradient methods and discuss how to utilize problem structure (e.g. sparsity and separability) to speed up the methods. Within engineering and practical sections, we show how to use the methods above to crack convex and nonconvex problems arises in engineering, energy systems, machine learning and related fields. 
Elena Gryazina  6  MA06002 
Organic Materials for Electronics, Photonics, Energy Generation and Storage
The course provides an overview of the latest achievements in the field of material design for electronics, energy conversion and storage.
The main purpose of the course is studying the basic chemical, physical and physicochemical, e.g. surface and structural, aspects of designing novel materials with the desired properties. This course will be focused mainly on organic and hybrid materials as well as on different types of electronic devices made thereof: fieldeffect transistors and electronic circuits, sensors, memory elements, light emitting diodes, solar cells, photodetectors, lithium and sodium batteries. Using a set of examples it will be shown how the discovery of novel materials results in the development of novel technologies, innovative products and, in some cases, even leads to revolutionary changes in specific fields of science and technology. This course is designed for MS students planning to perform experimental studies in the interdisciplinary fields at the boarder of physics and chemistry with the aim of solving relevant challenges of modern materials science. 
Pavel Troshin  6  MA06119 
Pedagogical Experience
The main function of this course is to articulate Skoltech's expectations on Phdstudents who do their pedagogical TA assignment as Skoltech. The course describes the intended learning outcomes and how they are assessed.
The course also offers a forum for TA and allows Skoltech TAs to collect and discuss resources and issues relevant for their TA experience. The forum provides a peertopeer feedback opportunity but also enables instructors to participate in the conversation when asked to. The main bulk of the 81 hours of the course is spent in the actual courses in which the PhDstudents do their TAassignments. The assignments in the course itself require less than 10 hours of time. 
Magnus Gustaffson  3  PE03005 
Pedagogy of Higher Education
The course offers an introduction to facilitating learning in higher education for PhD students who are asked to act as teaching assistants or supervisors. The course content focuses on aligning learning outcomes with learning activities and assessment strategies. Constructive alignment in the course is defined at high resolution such that learning outcomes for a course are elaborated into separate activities and assignments for students. In other words, learning outcomes need to be articulated at every level of learning activities from course to assignment.
The course also rests on the approach that learning is promoted by feedback. The assessment design that participants in the course design will therefore be required to reflect significant and effective use of continuous formative assessment. Such formative assessment requires strategic learning activities and assignments, and the course therefore comes with an emphasis on communicationtolearn activities including peer learning. Skoltech is an English medium instruction environment, and the course contains discussion topics to highlight ways of addressing the potential effects of language and culture barriers for high quality student learning. All topics in the course are applied by participants on their own teaching and learning experiences and are meant to be used as they prepare and plan for their teaching assistantships or their supervisory activities to come. All participants will have a task to produce a reflection on their future actions to evolve as facilitators and meet the requirements of the scholarship of teaching and learning. 
Magnus Gustaffson  3  PE03025 
Physics of Colloids and Interfaces
The interface science is the basis for modern nanotechnology. Objects of the microworld are dominated by surface effects rather than gravitation and inertia. The applications of interface science are important for labonchip technologies, microfluids, biochips, tissue engineering, biophotonics, theranostics. The peculiarity of modern interface science is a good example of interdisciplinarity. The interface science has become a really interdisciplinary field of research including physics, biology, chemical engineering, medicine. During this course the students gain not only theoretical knowledge, but also receive practical skills related to: 1) preparation of iron oxide nanoparticles and their characterization by dynamic light scattering method for determination of size and Zpotential of nanoparticles; 2) synthesis of calcium carbonate cores at micro and submicron size;3) loading of calcium carbonate particles by inorganic nanoparticles and proteins; 4) preparation of microcapsule shell using Layer by Layer assembly method formed on the surface of calcium carbonate microparticles and their characterization by fluorescent microscopy and Raman spectroscopy.They will receive a knowledge that can be used for analysis of phenomena in the microworld from point of view of interface science.

Dmitry Gorin  3  MA03310 
Power Electronics
The course provides an overview of the latest achievements in power electronics. The main purpose of the course is to analyze different circuit topologies, to understand how they work and which are their benefits and limitations. The course starts with reviewing the basics in electric circuit theory, and then, it introduces different kind of semiconductor devices such as diodes, thyristors and transistors. After this, power electronics circuits are presented: rectifiers, DCDC converters and inverters. The course gives the tools to analyze any kind of power converters, and provides different examples related with microgrids and energy storage applications. It has three parts: lectures, home tasks and experimental activities in the lab. By the end of the course, the students should be able to analyze a power converter, to simulate it and to understand the possible applications.

Federico Ibanez  6  MA06198 
Practicum in Experimental Physics  Valery Ryazanov  6  MA06208 
Quantum Field Theory (Term 34)
The main task of the course is to calculate the anomalous moment of the electron. The main methods of quantum field theory are studied by the example of solving this problem: the construction of the Fock state space of identical particles, continuum integral as a way to work with such a state space, quantization of free scalar, spinor and electromagnetic fields, Smatrix approach to accounting for interaction, perturbation theory in the form of Feynman's diagram technique, divergence in quantum field theory and their renormalization. The course involves writing three test papers and a written exam.

Vladimir Losyakov  3  MA06316 
Quantum Integrable Systems (Term 34)  Anton Zabrodin  3  MA06315 
Quantum Mechanics (Term 34)  Andrei Semenov  3  MA06322 
Quantum Mesoscopics. Quantum Hall Effect (Term 34)  Igor Burmistrov  3  MA06278 
Quantum Phenomena in Nanostructures
The course "Quantum Phenomena in Nanostructures" is aimed at description of various quantum phenomena in nanostructures and mesoscopic systems which became in the focus of condensed matter research during last 50 years. The topics include quantum oscillations in twodimensional electron systems in the presence of magnetic fields, quantum corrections to conductivity at low temperatures, Anderson transitions, topological insulators and superconductors, and BerezinskiiKosterlitsThouless transition.

Igor Burmistrov  3  MA03205 
Quantum Software Master Class
This course connects those attending with stateoftheart methods in quantum computer science. Starting with the theory of ground state quantum computation, the course builds the tools needed to understand modern day quantum simulation algorithms, as executed on quantum computers.
The topics covered include: Penalty functions and embedding problems into the ground state of Ising spins 
Jacob Biamonte  6  MA06285 
Quantum Theory of Radiation and Quantum Optics (Term 1B4)  Yuri Lozovik  1.5  MA06314 
Random Matrices, Random Processes and Integrable Systems (Term 34)
In recent years, researchers have found remarkable connections between, at first glance, completely different problems of mathematics and theoretical physics. Mathematically, these are combinatorial and probabilistic problems about systems with a large number of degrees of freedom. Among them, the problem of describing the eigenvalues of matrices with random elements, the problem of statistics of random Young diagrams, the problem of tiling various regions of the plane by dominoes or lozenges, the problem of enumerating nonitersecting paths on lattices. On the physical side, these are the problems of interface growth, traffic flows, polymers in random media, and so on.
It turns out that all these problems have a general mathematical structure, which can be encoded in the term "integrability". This structure is behind a lot of beautiful exact mathematical results. Moreover, these results have remarkable universality property, which play the same role as the law of large numbers and the central limit theorem in the probability theory. Looking at our random systems from afar, we find that they posess completely nonrandom limiting forms. Random fluctuations around these forms are described by a small number of universal probability distributions that are completely independent of the details of original system. The course attendees are going to get acquainted with the range of issues described and to learn about the latest achievements in the field. 
Alexander Povolotsky  3  MA06318 
Representations of Affine KacMoody Algebras (Term 34)
Affine KacMoody Lie algebras play a prominent role in the theory of infinitedimensional Lie algebras. The two main reasons are the beauty of the theory and the vast number of applications in various fields of mathematics and mathematical physics such as conformal field theory, algebraic geometry, number theory, combinatorics, statistical mechanics, theta functions. In particular, integrable representations of the affine KacMoody algebras form a background of the famous WessZuminoWitten CFT. The course will be devoted to the general questions of the representation theory of affine KacMoody Lie algebras and to the study of several special classes of modules, in particualr, integrable modules. We will be mainly interested in algebraic and combinatorial parts of the theory. Time permitting, we will also touch upon some related geometric constructions such as affine Grassmannians.

Evgeny Feigin  3  MA06320 
Research Methodology: Computational and Data Science and Engineering
A modern researcher needs to have a set of various skills in order to conduct research efficiently. In addition to high level of research skills and understanding of the research environment of one’s particular field, a researcher should be able to manage researchrelated business processes, be personally effective, have high level of communication and presentation skills, build effective professional relationship with colleagues and effectively manage the career development. The course covers all these topics and implies active interaction between the tutor and students during the classes. In the end of the course each student will be asked to write an essay.

Maxim Fedorov  3  PA03102cds 
Research Methodology: Molecular Biology Seminar  Konstantin Severinov  3  PA03102ls 
Research Methodology: Space Center Seminar (Term 14)  Anton Ivanov  3  PA03102es 
Research Seminar "Advanced Materials Science" (Term 28)
This is the main research seminar of the Skoltech Center for Electrochemical Energy Storage and Materials Science Education program featuring presentations of young researchers: MSc students, PhD students, postdocs. Every MSc and PhD student of Materials Science program should deliver at least one presentation per two years. The range of topics is broad and includes any aspects of materials science and engineering.
Please see the seminar webpage at http://crei.skoltech.ru/cee/education/wednesdayscientificseminar/ 
Keith Stevenson  0.43  MA03302 
Research seminar "Modern Problems of Mathematical Physics" (Term 18)
Course "Modern problems of mathematical physics" is a student seminar, so participants are expected to give talks based on the modern research papers. Current topic of the seminar can vary from time to time: now it is devoted to the study of N=2 supersymmetric gauge theory and its links with random matrix models, complex curves, and integrable systems. Other topics that were already covered, or can be covered in the future, are: classical integrable equations, complex curves and their thetafunctions, quantum integrable models (quantummechanical and fieldtheoretical), models of statistical physics.

Andrei Marshakov  1.5  MA12268 
Research seminar "Modern Problems of Theoretical Physics" (Term 18)
Research seminar "Modern Problems of Theoretical Physics" is supposed to teach students to read, understand and represent to the audience recent advances in theoretical physics. Each student is supposed 1) to choose one of recent research papers from the list composed by the instructor in the beginning of each term, 2) read it carefully, 3) present the major results of the paper to his/her colleagues during the seminar talk, 4) answer the questions from the audience about the content of the paper. The papers in the list are selected, normally, from the condensed matter theory and related fields, like: physics quantum computing, statistical physics, etc. The papers to the list are usually chosen from most competitive physics journals, like Nature Physics, Science, Physical Review Letters, Physical Review X and others.

Mikhail Feigelman, Konstantin Tikhonov 
1.5  MA12319 
Research seminar "Strings and Cluster Varieties" (Term 18)
The course is directed to substantive work of the master and PhD students in order to understand recently found relations among supersymmetric gauge theories, refined topological strings, cluster varieties and integrable systems. The plan of wrk on the course consists of several introductive lectures on the various consistuents of the subject as well as student talks on recent original papers and results of their own investigation. The core topics include relation between cluster varieties and Painleve equations and approaches to the SeibergWitten theories with fundamental matter based on Toda systems and spin chains.

Andrei Marshakov  1.5  MA12176 
Review of Materials and Devices for Nano and Optoelectronics (Term 34)
The lectures are presented by the scientists working actively in various directions of nanoelectronics and optoelectronics in Russia and abroad. Seminars assume the discussion of recent original papers in the area (including superconducting electronics and spintronics, terahertz waves technology and applications, quantum coherent systems (qubits), single electron devices). The classical papers presenting a physical basis for devices operation will be also considered. The papers are distributed in February. Each student is expected to report two papers during the period FebruaryMay.

Valery Ryazanov  3  MA06206 
Robotics
The lecture course introduce you to basics knowledge of methods for robot design, simulation, and control of robotic system. Topics include robot kinematics, dynamics, control, design, simulation, motion planning, and AI. The course slightly touches the research in wearable, space and telexistence robotics. The projects in robotics done by the lecturer, such as NurseSim, iFeel_IM!, FlexTorque, NAVIgoid, TeleTA will be presented. The lecture aims at student preparation and motivation to conduct projects in Robotics, Automation, Advanced manufacturing, and Intelligent Systems.

Dzmitry Tsetserukou  6  MA06050 
Selected Topics in Energy: Physical, Chemical and Geophysical Challenges (Term 24)
The course provides an introduction to the modern topics related to fundamentals of exploration of energy resources, energy generation, storage, conversion and use. It identifies the corresponding practical challenges to be addressed at the fundamental research level and familiarizes the students with the stateoftheart approaches, methods and techniques in use in related scientific areas. The course seeks to emphasize and maintain interdisciplinary nature of the energyrelated topics, in particular, combination of micro and macroscopic approaches of geophysics, mechanics and chemistry in hydrocarbon exploration and development, relation between the physical and chemical processes of energy generation and conversion, integration of physical, chemical and mechanical approaches to perspective materials (physical and chemical synthesis, micro and macroscopic characterization, structureproperty relations, etc.) and related theoretical methodologies. These interdisciplinary links are mostly demonstrated by horizontal knowledge exchange among the students reporting and discussing practical examples from their own research field or from modern review or research publications. Topical lectures are included for further exploration of these links. The secondary aim of the course is the development of presentation skills (oral and writing), as well as scientific peerreview experience. The seminar format chosen for most activities allows students free exchange of knowledge and ideas, broader vision of their research projects and methodologies, better assessments of their own research skills and demands for further education.

Alexei Buchachenko  2  PA06106 
Signal and Image Processing
Nowadays, digital signals and images can be found everywhere, in a plethora of scientific (e.g., astronomical, biomedical) and consumer applications (e.g., computational photography). Therefore, the ability to analyze and process digital signals and images is an extremely important skill for engineering/science master students to obtain. Indeed, digital signal and image processing is mainly responsible for the multimedia technology revolution that we are experiencing today. Important tasks that signal and image processing techniques can successfully tackle are inverse problems, such as image enhancement and restoration, which involve the removal of degradations that signals and images suffer during acquisition (e.g. removing the blur from the digital picture of a moving object, or removing the noise from a picture taken under low light conditions).
This course will cover the fundamentals of signal and image processing. We will provide a mathematical framework to describe and analyze images as two or threedimensional signals in the spatial and frequency domains. The students will become familiar with the theory behind fundamental processing tasks including image enhancement, recovery and reconstruction. They will also learn how to perform these key processing tasks in practice using current stateoftheart techniques and computational tools. A wide variety of such tools will be introduced including largescale optimization algorithms and statistical methods. Emphasis will also be given on sparsity, which plays a central role in modern image processing systems 
Stamatios Lefkimmiatis  6  MA06121 
Space Center Seminar (Term 14)
The seminar will cover current topics in the space domain: latest news, discoveries. Also planned that all PhD students and some Master students will present their research. External lecturers will be invited regularly to focus on the main applications of space technologies: science, telecommunication, navigation and remote sensing. Aspects of space technologies will also be discussed: structures, software, attitude determination and control systems, on board computers, communication system power supply systems and others. The seminar will be offered in English.

Anton Ivanov  0.25  MO01004 
Spacecraft and Mission Design
The main objective of the course is to introduce the concept of space system design and engineering. The course will describe the various subsystems involved in the design of a satellite. It will also describe the techniques of systems engineering that are used to obtain a coherent satellite design.
This class will focus on concept preparation in the Vdiagram logic. Further results can be explored either in the Space Sector course, where commercial aspects of the mission can be considered, as well as in the PLM course, where technical details can be worked out in a systematic fashion. 
Anton Ivanov  6  MA06074 
Spectroscopy of Quantum Materials
The term “quantum materials” unites a broad class of very different materials demonstrating genuinely quantum behavior. Quantum materials include superconductors, stronglycorrelated systems, systems of massless Dirac electrons such as graphene, topological materials, novel twodimensional crystals, engineered heterostructures etc. Research of quantum materials is in the vanguard of modern photonics and condensed matter physics. Unique properties of quantum materials have arise due to wave function entanglement, interactions, competing orders, quantum topological effects, quasiparticle dressing and other emergent quantum phenomena.
The goal of this course is to give a broad review of modern photonic and spectroscopic studies of quantum materials. The course requires basic knowledge of quantum mechanics, optics and solid state physics. In the introductory part of the course, the basic theory of electromagnetic response of quantum systems, centered around linear response functions and their spectral properties, is outlined. The rest of the course describes such quantum materials as graphene and graphenebased structures, topological insulators, topological Dirac and Weyl semimetals, hightemperature superconductors, exotic magnetics, transition metal dichalcogenides, oxide interfaces, and novel electromagneticallyengineered quantum materials. The students will be introduced to basic models and to both conventional and ultrafast pumpprobe spectroscopy studies of these materials. 
Alexey Sokolik  3  MA03162 
Statistical Physics (Term 78)
This is a course on rigorous results in statistical physics and random fields. Most of it will be dedicated to the theory of phase transitions, uniqueness or nonuniqueness of the lattice Gibbs fields.
The topics will include: grand canonical, canonical and microcanonical ensembles, DLR equation, Thermodynamic limit, Gibbs distributions and phase transitions, onedimensional models, correlation inequalities ( GKS, GHS, FKG), spontaneous symmetry breaking at low temperatures, uniqueness at high temperatures and in nonzero magnetic field, Nontranslationinvariant Gibbs states and interfaces, Dobrushin Uniqueness Theorem Pirogov–Sinai Theory O(N)symmetric models the Mermin–Wagner Theorem Reflection Positivity and the chessboard estimate infrared bounds 
Semen Shlosman  3  MA06180 
Structure and Properties of Materials
This course is an introductory subject in the field of materials science and crystallography. The goal is to introduce students to basic concepts of structureproperty relations for materials at the microscopic level.
Independent student work on discipline includes preparation for lectures, seminars, labs and other learning activities, as well as the implementation of individual tasks / independent works / projects and others. Educational and methodical support of Independent student work presented by topics of all kinds of tasks and guidelines for their implementation. 
Artem R. Oganov  6  MA06075 
Systems Architecture  Alessandro Golkar  6  MA06010 
Thinking Disruptive for a Big Future (Term 23)
The goal is to open the mind of the audience showing that there is not only one predetermined path for a career after the studies, that the world is big, fantastic and that the problems we face are huge, but fascinating. The goal is also to show that there is no, or should not be any Chinese Wall between mathematicians, physicists and engineers. Finally, the goal is to show how some ideas, some of them being very theoretical and some others not, can bring to the creation of startups. It will rely on the more than 30 years of experience of JeanFrancois Geneste who will exemplify with encountered concrete examples he met along his career. We shall go through "the law of the mean", disruptive systems (airships, pseudosatellites, launchers, mining in space, fractionation and responsive space), disruptive equipment (infinite impulse propulsion, CVC jet engine, thermal solar arrays), systems intrinsically resistant to terrorist attacks, Disruptive science (some contradictions of physics, coherent alternative, new potential sources of energy, high temperature superconductivity with a new model of the atom, communications quicker than light, analog quantum computers, infinite power quantum computers, disruptive cosmology)

JeanFrancois Geneste  3  MC06010 
Unconventional Hydrocarbons
The course provides an introduction to unconventional (shale) hydrocarbons as a perspective source of oil and gas. It consists of several parts describing existing oil and gas shale formations in a world and in Russia (Bazhenov, Domanik, Khadum formations), detailed data on lithology, petrophysics, geochemistry and geomechanics of shale rock and modern methods for prospecting, exploration and production of unconventional hydrocarbons. The course includes lectures, seminars and laboratory works. During the course students work individually and in teams compiling a comprehensive data set, analyzing of research results and developing of technological strategy on prospecting, exploration and production of shale hydrocarbons.

Mikhail Spasennykh  6  MA06189 
Course Title  Lead Instructors  ECTS credits  Course Code 

Academic Communication: Preparatory English for Phd Exam
Efficient professional communication is the key to Academic success. The course is designed for PhD students who want to maximize their academic potential by boosting their ability to write research papers, present in front of multidisciplinary audiences, participate in scholarly discussions and engage in other forms of academic communication.
The main goal of the course is to enable PhD students to produce clear, correct, concise and coherent texts acceptable for the international professional community. The course is designed for a multidisciplinary audience. The course serves as a preparation for the qualification language exam, which is a prerequisite for the Thesis defense. 
Elizaveta Tikhomirova  3  PE03029 
Academic Writing Essentials (Term 34)
Academic writing skills are necessary for effective research, innovation, and educational activities in a multinational setting. The aim of the course is to provide guidelines and strategies for writing academic texts, focusing on relevant aspects of grammar, vocabulary, and style. The course includes analysis and practice of various forms of scientific and technical writing, and builds writing skills from sentences to paragraph structure, from summary to abstract, and lays the foundations for writing scientific papers and Master Thesis.
Modern science is, for most purposes, a collective collaborative effort, so the course is designed to promote individual and group responsibility by providing mutually related and timedependent tasks, such as peer review. The course is writingintensive with ample opportunity to practice editing and peerreviewing. 
Anastasiia Sharapkova  1.5  MO03002 
Academic Writing Essentials (Term 34)
Academic writing skills are necessary for effective research, innovation, and educational activities in a multinational setting. The aim of the course is to provide guidelines and strategies for writing academic texts, focusing on relevant aspects of grammar, vocabulary, and style. The course includes analysis and practice of various forms of scientific and technical writing, and builds writing skills from sentences to paragraph structure, from summary to abstract, and lays the foundations for writing scientific papers and Master Thesis.
Modern science is, for most purposes, a collective collaborative effort, so the course is designed to promote individual and group responsibility by providing mutually related and timedependent tasks, such as peer review. The course is writingintensive with ample opportunity to practice editing and peerreviewing. 
Elizaveta Tikhomirova  1.5  MO03002 
Bioinformatics Lab
The course will introduce students to the handson practical analysis of novel biological “omics” data with a specific focus on the stateoftheart analysis of the genome, epigenome, and transcriptome. The course will integrate various types of omics data generated by new generation sequencing technologies and will include the following parts: genome assembly, genotyping and GWAS analyses in the genome section; histone modifications, DNA methylation and 3D chromatin organization in the epigenetics section; transcriptome assembly, splicing analysis, RNA editing, differential transcription, noncoding RNA analysis and functional characterization in transcriptome section. In addition, the course will integrate various types of omics data, including data generated by mass spectrometrybased approaches, as well as axillary data new generation sequencing technologies.
The course will include practical data analysis work conducted by the student in front of a computer, but also introductory lectures into principles of data analysis and basic elements of statistical analysis of largescale biological data. At the end of the course, students would be expected to accomplish an independent data analysis project on a model dataset including several heterogeneous types of biological “omics” data. 
Philipp Khaitovich  6  MA06065 
Biomedical Application of Photonics
The overview of current state of photonics application in the biology and medicine will be presented including optical properties of cell, biological tissue, body (absorption, reflection, scattering, fluorescence). Now the photonic tools are used for imaging, diagnostics, manipulation, therapy and surgery at three different levels – cellullar, tissue and body, therefore the course aims to teach students to understand basic principles of the current biomedical applications of photonics tools. The every level is required to apply different approach, for example for cellular level imaging, manipulation, Confocal LS Microscopy (including technology of quotative analysis as FRAP, photoconversion, FLIP, FLAP, FRET, FLIM, FCS, FCCS), dark field microscopy; optical tweezers approach, laser cell poration; for diagnostics – Raman microscopy, CARS, in vitro and in vivo fluorescent flow cytometry, in vivo flow photoacoustic (PA) cytometry; and for therapy – laser induced necrosis and apoptosis; in vivo flow PA setup for theranostics are used. Tissue level requires for imaging, multiphoton microscopy, SHG and THG microscopy, OCT, rasterscan optoacoustic mesoscopy (RSOM); for manipulation – laser 3D printing, laser skin perforation. Body level includes for imaging – OCT, MRI, CT, MRI, fluorescence and optoacoustic imaging, US, PET; for diagnostics – different types of in vivo sensors including implantable medical devices, smart tattoo; for therapy – photodynamic and photothermal therapy; for surgery – photonic approach guided surgery including endoscopy, high speed surgery with the highest resolution. Topics also include description of different types of contrast and optical clearing agents. The course will also offer a practice in operation of imaging systems on the cell, tissue and body level such as fluorescent microscopy, RSOM, fluorescence imaging. Students will have experience related to application the most appropriate photonic tools for their own research projects.

Dmitry Gorin  3  MA03158 
Biomedical Imaging and Analytics
This course is designed for Machine Learning and DataScience students who would like to concentrate their research on the analysis of biomedical images. This cohort of specialists – especially early on in their careers – is known for dismissing both the physical mechanisms of an image formation and the very biological rationale behind a given imaging modality. In this course, we will attempt to reunite the three disciplines in order to help students develop a systematic analytical expertise and a biological intuition. The course is also aligned with the curriculum of the centers of life sciences and photonics and should be used for enriching those offerings with the modern machine learning and image analytics skills.
Students will learn what forms the backbone of biomedical imaging, drawing from the mathematical, physical, chemical and biological sciences, including the subjects of: There will be one midterm takehome exam devoted to image formation and a related biomedical application. And a final computer vision project on a dataset from an imaging modality of a student’s choice. 
Dmitry Dylov  3  MA03305 
Business Communication
Business Communication is an intensive hands on, practical course, designed to provide Skoltech students with the set of skills needed to effectively communicate with others – their classmates, working teams, professors and any audiences inside and outside of Skoltech. The course learning outcomes correspond directly with the Group 3 of Skoltech learning outcomes – “Relating to Others – Communication and Collaboration”. The course will show students the secrets and technologies to becoming confident when speaking in public – developing the skills they will be able to use throughout their career and their life. In a highly interactive, informative and supportive manner through inclass activities, games and simulations the course will enable students to: Speak with confidence and overcome their nervousness; Establish rapport with any audience; Present their message in a clear, concise, and engaging manner; Successfully manage impression they make onto audience; Create—and repurpose—presentations quickly and efficiently; Make successful and memorable pitch; Sharpen the story they want to tell; Use confidently body language and movement, strengthening their speech; Respond to questions and comments without getting flustered; Gain people’s attention, respect, and cooperation.

Maxim Kiselev  3  MC03014 
Cell Biology Lab Course
Lab course in Cell biology provides students an opportunity to explore how the techniques of molecular and cell biology may be used to understand cell function. Laboratory practice in cell biology will provide the experience in genetic manipulations with cell lines, immunostaining and fluorescence or confocal microscopy analysis. The main aspects for FACSanalysis and cell sorting will be introduced. The approaches for gene expression analysis by RTqPCR, Western blot and differential proteome analysis will be used to understand the influence of genetic manipulation to the cell function. The introduction in powerful approach to understand the protein interaction such as SPR optical biosensor will be provided.
The introduction in highthroughput screening of biologically active compounds will be provided. The course will provide students with a handson understanding of modern methods of cellular manipulation and understanding the mechanism of cell functioning. 
Olga Dontsova  6  MA06134 
Comparative Genomics
The course will touch upon both basics and some deeper topics of comparative genomics, including but not limited to homology and its relationship to function, horizontal gene transfer, genome rearrangements, pangenomes, metagenomes, gene networks, and functional annotation of genes and proteins. The students will get an understanding of molecular evolution at the genome level and be able to apply this understanding to both theoretical and reallife molecular biology problems. “Nothing in Biology Makes Sense except in the Light of Evolution” (Theodosius Dobzhansky).

Mikhail Gelfand  3  MA03133 
Composite Materials and Structures
This course aims to provide knowledge about manufacturing, properties, and contemporary problems in composite materials. The emphasis is on the practical applications, theoretical background, and the use of composite materials in industry. The course cuts across several domains, covering mechanics of materials, design, manufacturing, and in service issues:
• Introduction: What is a composite? Classification. Metals vs composites, advantages and disadvantages. Applications in industry. Participants will learn fundamentals of these areas through active participation in teamwork. The course will provide practical knowledge on applications of composite materials in aerospace and mechanical engineering. 
Sergey Abaimov  6  MA06241 
Computational Materials Science Seminar (Term 14)
This is the main research seminar at Skoltech for Computational Materials scientists. All students of Computational Materials Science subtrack of Materials Science MSc program should attend this seminar. Topics include materials modeling (at atomistic scale), theoretical and computational chemistry, theoretical and computational physics of materials, underlying mathematical methods and algorithms etc. Invited lectures are top scientists in their research field.
Please see the seminar webpage at https://www.skoltech.ru/en/cms/ 
Dmitry Aksenov  0.75  MO03005 
Condensed Matter Spectroscopy and Physics of Nanostructures (Term 1B4)
The first part of this course covers major topics of the modern optical spectroscopy of solid state systems, including nanomaterials and novel topological materials. The introductory part of the course outlines the basic classical and quantum theory of electromagnetic response, and basics of the solid state spectroscopy. Then the major research directions in the modern condensed matter spectroscopy are considered, such as spectroscopy of graphene, topological materials, and transition metal dichalcogenides.
The second part of the course describes the physics of lowdimensional electron systems and nanostructures. Twodimensional electron and electronhole systems, lowdimensional disordered systems, quantum Hall effect, carbon nanostructures, photonic crystals and optical microcavities will be considered. 
Alexey Sokolik  1.5  MA06313 
Data analysis for space weather
The course introduces students to SolarTerrestrial physics, Space Weather and practically useful approaches of data analysis for study, forecasting, and mitigation of space weather effects. The course provides an overview of SunEarth connections, starting from the interior of the Sun and ending in the Earth's magnetosphere. To gain insight into this field, we focus on such topics as: solar interior and solar structure, solar atmosphere, solar wind, solar flares and coronal mass ejections, as well as associated geomagnetic storms and polar auroras. These phenomena drive Space Weather with the implications for spaceborne and groundbased technological systems (satellites, human spaceflight, airlines, power systems and pipelines). We also examine the space weather effects on technology and human health, hazard assessment, mitigation and forecasting, space environment data, scientific and service products.

Tatiana Podladchikova  6  MA06309 
Deep Learning
The course is about Deep Learning, i.e. a new generation of neural networkbased methods that have dramatically improved the performance of AI systems in such domains as computer vision, speech recognition, natural language analysis, reinforcement learning, bioinformatics. The course covers the basics of supervised and unsupervised deep learning. It also covers the details of the two most successful classes of models, namely convolutional networks and recurrent networks. In terms of application, the class emphasizes computer vision and natural language analysis tasks. The course involves a significant practical component with a large number of practical assignments.

Victor Lempitsky  6  MA06057 
Differential Topology (Term 34)
We plan to discuss two topics, which are central in topology of smooth manifolds, the hcobordism theorem and theory of characteristic classes. The hcobordism theorem proved by S. Smale in 1962 is the main (and almost the only) tool for proving that two smooth manifolds (of dimension greater than or equal to 5) are diffeomorphic. In particular, this theorem implies the highdimensional Poincare conjecture (for manifolds of dimensions 5 and higher). Characteristic classes, in particular, Pontryagin classes are very natural invariants of smooth manifolds. Computation of characteristic classes can help one to distinguish between nondiffeomorphic manifolds. We plan to finish the course with the theorem by J. Milnor on nontrivial smooth structures on the 7dimensional sphere. This theorem is based both on methods of Morse theory and theory of characteristic classes

Alexander Gaifulin  3  MA06258 
Dynamical Systems and Ergodic Theory (Term 34)
Dynamical systems in our course will be presented mainly not as an independent branch of mathematics but as a very powerful tool that can be applied in geometry, topology, probability, analysis, number theory and physics. We consciously decided to sacrifice some classical chapters of ergodic theory and to introduce the most important dynamical notions and ideas in the geometric and topological context already intuitively familiar to our audience. As a compensation, we will show applications of dynamics to important problems in other mathematical disciplines. We hope to arrive at the end of the course to the most recent advances in dynamics and geometry and to present (at least informally) some of results of A. Avila, A. Eskin, M. Kontsevich, M. Mirzakhani, G. Margulis.
In accordance with this strategy, the course comprises several blocks closely related to each other. The first three of them (including very short introduction) are mainly mandatory. The decision, which of the topics listed below these three blocks would depend on the background and interests of the audience. 
Aleksandra Skripchenko, Anton Zorich 
3  MA06257 
Electrochemistry: Fundamentals to Applications
This course covers fundamental concepts of electrochemistry: oxidation and reduction processes, types of conductors, electrolytes, classification of electrodes and electrode reactions, Faraday’s Laws, and electroanalytical methods. In addition, some applied aspects of electrochemistry will be covered including industrial electrolytic processes, electrodeposition, and electrochemical power sources (batteries and fuel cells).
The prerequisites are: undergraduate math, chemistry, and physics. 
Keith Stevenson  6  MA06127 
Energy Colloquium
The Energy Colloquium educates the audience in the presentday research and applications within the broader field of Energy Science and Technology. The Colloquium consists of a series of presentations by invited academic and industry speakers. The presentations target a nonspecialist audience.
All Master and Ph.D. students within the Energy Program are encouraged to attend the Energy Colloquium during the entire period of their studies. Students can earn 1 credit, if he/she participates in the Energy Colloquium over the course of any 2 terms of the academic year. Students who passed one round can make next (for credit) over the course of their subsequent studies. 
Alexei Buchachenko  1  MA01092 
English. Candidate Examinations
This is a metacourse which allows PhD students to register for English Qualification Exam for the Russian PhD Degree. There will be no lectures or seminars, only the exam. The preparatory course is also available in course catalog (look for "Academic Communication for PhD students" course).
The Exam has two parts: Part 1 – Preexam activities (Assignments 1, 2a, 2b) 
Elizaveta Tikhomirova  3  PE03003 
Foundations of Engineering Physics (Term 1B4)
The course is dedicated to basics of building interfaces ”experimentcomputer” in the modern scientific research. In most general configuration such interface comprises three stages:
1) “input” analog frontend feeding the electronic signals from sensors, transducers, 2) analogtodigit as well as digittoanalog conversion “bridges” and 3) logical channels conveying the ultimate digital information to a computer. The consideration of the three stages is made with emphases on the principle aspects of scientific measurements rather than detailed schematic/circuitry of the instrumentation. All stages of the measurement systems will be reviewed from the point of view of the fundamental imperatives of signal conditioning like impedance matching, optimal choice of the bandwidth solving the ubiquitous tradeoff “precision versus rate” of data acquisition and et al. As well important peculiarities of configuring the elements of the system – such as prefiltering, modulationdemodulation techniques, the choice of the type and bit width of ADCs/DACs – will also be thoroughly discussed. At all stages a short concomitant overview of the modern commercially available electronic equipment will be given in order to improve students’ ability to select a proper set of the electronic devices among a great variety of those available on the market. 
Yuri Romanovskiy  1.5  MA06213 
Functional Methods in The Theory of Disordered Systems (Term 34)
The course provides an extensive overview of contemporary functional methods in the theory of disordered systems. Starting from the theory of random matrices, it covers various aspects of electron motion in disordered media. The concept of the nonlinear supersymmetric sigma model is introduced and used as a unique language to describe such phenomena as energy level statistics, weak localization, renormalization group analysis, nonperturbative solution of the localization problem in quantum wires. Finally, functional integral method is used to address electronelectron interaction in disordered metals and nonequilibrium phenomena in quantum dots.

Mikhail Skvortsov  3  MA06262 
Fundamentals Device Physics
The course will provide a graduate level overview of physical principles of electronic and optoelectronic devices.
Lecture 1: Introduction to silicon based devices for logic electronics 
Vasili Perebeinos  6  MA06016 
Gauge Theory and Gravitation (Term 34)
The present course could be also entitled 'Classical Field Theory', which menas it deals with all basic material needed in a study of fields preceeding to a study of their quantum properties. This requires in particular understanding such tools as Lagrangian, action functional, field equations (EulerLagrange equations). We shall also learn what are the most important symmetry principles which put certain constraints on a field theory. With this are related conservation laws. Typical important symmetries to mention are Lorentz and Poincare symmetry, conformal symmetry, gauge symmetry, general coordinate covariance.
A traditional approach to Classical Field Theory has a perfect base in the 2nd volume of LandauLifshitz' course. However, since that prominent book was written, new elements came forward, which required more knowledge of differential geometry and topology. In our lecture course, we shall get familiar with most important basic facts from these branches of mathematics with application to field theory. For example, understanding instantons (even at a classical level) requires good knowledge of a number of notions from modern math courses, such as vector bundles, connections, homotopy groups. Therefore our course has to go beyond the reach of LandauLifshitz' volume 2. 
Alexey Rosly  3  MA06178 
Geometrical Methods of Machine Learning
The course is elective for MSc program in Data Science at Skoltech.
Many machine learning problems are fundamentally geometric in nature. The general goal of machine learning is to extract previously unknown information from data, which is reflected in the structure (underlying geometry) of the data. Thus, understanding the shape of the data plays an important role in modern learning theory and data analytics. Realworld data obtained from natural sources are usually non uniform and concentrate along lower dimensional structures, and geometrical methods allow discovering the shape of these structures from given data. Originally being part of dimensionality reduction research, geometrical methods in machine learning has now become the central methodology for uncovering the semantics of information from the data. The aim of the course is to explain basic ideas and results in using the modern geometrical methods for solving main machine learning problems such as classification, regression, dimensionality reduction, representation learning, clustering, etc. A large part of the course addresses to most popular geometrical model of highdimensional data called manifold model and introduces modern manifold learning methods. Necessary short information on differential geometry and topology will be given in the course. The course lets students to be involved in meaningful reallife machine learning projects, such as mobile robot navigation, neuroimaging, to cope with challenging problems. 
Alexander Bernstein  3  MA03169 
Geostatistics and Reservoir Simulation
The course includes lectures in reservoir simulation, history matching, and fundamentals of geostatistics.
Reservoir simulation and history matching embrace following: 1) Fundamentals of single phase and multiphase multicomponent fluid flow and storage in reservoirs 2) Numerical solution of governing equations using finite difference 3) Introduction to inverse theory and history matching 4) Application of reservoir simulators for field applications Fundamentals of geostatistics include following: 1) Stochastic reservoir simulation 2) Statistical measures 3) Univariate and multivariate Statistics 4) Covariance and variograms 5) Sequential Gaussian simulation 6) Uncertainty quantification Finally, reservoir simulation and geostatistical analysis are integrated for risk analysis and economy estimation. Laboratory computational exercises are also included. 
Dmitri Koroteev  6  MA06085 
High Performance Computing
High Performance Computing refers to accumulation and usage of computing power well beyond a typical desktop or laptop computer. This is a main course for various aspects of HPC and a further development of the Scientific Computing course. Together with the theoretical part and discussion of basic parallel algorithms, the course will have a practical component aimed at solving different research and industryrelated problems on different computing architectures, such as modern CPUs and GPUs. The course will provide sufficient knowledge and experience in using standard parallel libraries (such as OpenMP, MPI, OpenACC and CUDA) as well as visualization software (ParaView, Visit). Students will be given a chance of using Skoltech's worldclass HPC facilities to learn typical methods and rules of working on the largescale collectively used supercomputers. The course is designed in such a way that students who successfully pass the exam will be able to use advanced methods of HPC in their everyday work.

Sergey Rykovanov  6  MA06287 
Imaging in Biology
Overview of current imaging research techniques in basic biomedical research. Various applications in neurobiology, cancer biology and preclinical studies of novel and emerging advanced microscopy technologies. Analysis of experiments and research described in recent scientific papers. The introduction of the course also includes core mathematics, optics, and nuclear physics. Atop of studying different optical microscopy techniques and superresolution imaging the course will outline and compare the roles of CT (Computed Tomography), MRI (Magnetic Resonance Imaging), PET (Positron Emission Tomography) in biomedical research.
Topics also include clearing agents and techniques, optical imaging of brain activity in vivo using genetically encoded probes, immediate early gene mapping, intravital imaging, applications for functional analyses of neuronal circuits. The course aims to teach students to understand basic principles of the current imaging techniques, microscope design, and image formation. The course will also offer a practice in image analysis with open source software. Students will learn how to choose the most appropriate imaging method for their own research project. 
Dmitry Artamonov  6  MA06118 
Innovation and Intellectual Property Studies Doctoral Seminar (Term 14)
This course is a compulsory academic seminar series for all Ph.D. students in the Innovation and Intellectual Property Management Ph.D. Program. It consists of weekly research seminars that address the state of the art in research about the role of intellectual property in technological innovation. Specific topics and themes in the course will vary from year to year, but will typically include: theories of innovation; concepts and theories in IP management; practical issues in IP management; case studies in IP strategy; valuation of IP; Russian and international trends in intellectual property law; topics in technology entrepreneurship; product development and new technology; IP and design; patent analytics for innovation research; commercialization strategies of technology startups; organizational issues in technology innovation; conceptual issues at the interface of technology, science and business; public policy for technology, science and innovation; ethical and social issues related to IP and technological innovation; case studies in innovation management; philosophy of technology and philosophy of intellectual property; theory and methodology in IP management research; technology transfer and commercialization of university research; international collaboration and international trade in technology. As part of their seminar obligations, all students must prepare a formal written research paper on a topic that may or may not be directly related to their thesis research and make a presentation about the paper to the seminar group. The paper will be assessed.

Kelvin Willoughby  1.5  PC06009 
Intellectual Property and Technological Innovation (Term 34)
Intellectual property (IP) is a critically important aspect of technological innovation and a key factor in the management of technologyintensive enterprises. Prowess in the management of intellectual property is important for technology leaders in both established corporations and entrepreneurial ventures.
Entrepreneurial technology ventures flourish according to how well their intellectual property assets are managed, leveraged and enforced. Additionally, it is almost impossible for engineers or scientists to avoid confronting issues related to intellectual property. These include: the risk of violating the IP rights of others; an obligation to respect the IP policies of one’s employer; the need to obtain IP protection for one’s own inventions and creative works; the obligation to become involved in the management of the IP belonging to ones employer; and the challenge of ensuring that one’s own IP rights are not infringed by others, including by one’s own employer or one’s clients. In addition, with such a large amount of contemporary business—in both the private sector and government—involving outsourcing and interorganizational collaboration, expertise in the licensing of intellectual property rights is in high demand. This course will survey basic concepts of intellectual property and provide an introduction to a variety of types of intellectual property and IPrelated rights, such as patents, copyright, trade secrets, trade marks, design rights, database rights, domain names, and demarcations of origin. The will also examine the strategic management of IP in the process of technology commercialization, and the resolution of IPrelated conflicts between technology based enterprises. It will also explore social, economic and ethical issues associated with the accumulation and exploitation of intellectual property. 
Kelvin Willoughby  3  MC06006 
Intellectual Property, Technological Innovation and Academic Research (Term 34)
Intellectual property (IP) is a critically important aspect of technological innovation and a key factor in the management of technologyintensive enterprises. Basic knowledge of intellectual property principles and practices is increasingly important for university researchers, and expertise in the management of intellectual property is a key skill set of technology leaders in both established corporations and entrepreneurial ventures.
Intellectual property affects not only technology commercialization strategy but also the direction of scientific research itself. University research groups increasingly compete with each other for scientific reputation and access to resources on the basis of their ability to obtain patent protection for the practical applications of their research; but also on the basis of their ability to plot research pathways to maneuver around the "proprietary territory" of other research groups. Skill in using IP data bases, and associated analytical tools, can empower university scientific teams to craft more powerful research strategies. This course will survey basic concepts of intellectual property and provide an introduction to a variety of types of intellectual property and IPrelated rights, such as patents, copyright, trade secrets, trademarks, design rights, database rights, domain names, and demarcations of origin. The classroom sessions will include lively discussions of case studies of the management of IP and the resolution of IPrelated problems in the process of technology commercialization. Each student will conduct an analysis of intellectual property issues related to his or her own Ph.D. research topic. Use will be made of special IP data and IP analytics tools. 
Kelvin Willoughby  3  PC06006 
Introduction to Product Lifecycle Management (PLM)
The course "Introduction to PLM" is a basic course for 1st year MSc students devoted to PLM as applied to product development with an aircraft as an example. Some basic theory about CAD/CAE, MBSE, PLM is given during lectures. Practical classes are dedicated to real product development process. Students use System Synthesis for system models development and investigating the most appropriate aircraft parameters for particular requirements. Highlevel models, generated in System Synthesis then filled with functional models in LMS Amesim. Then some 3D analysis of aerodynamics and structural analysis are developed. Finally, students have to use Tecnomatix for aerial vehicle wings manufacturing simulation. Thus, during the course, students go through all the main stages of aerial vehicle development process in a simplified way

Ighor Uzhinsky  6  MA06148 
Laser Spectroscopy (Term 1B4)  Alexander Makarov  1.5  MA06212 
Leadership for Innovators
Succesful innovators are distinguished not only by industrial and technology acumen, but also by superior leadership skills. Innovation is impossible without leading, presenting, managing, negotiating, and resilience from constant stress. This course present the comprehensive leadership skillset that includes theory and practice of:
– leadership & teamwork – personal presentation – stress management – emotional intelligence – negotiations The class is built as highly interactive action that starts with Q&A on a particular topic and then culminates in intensive group and personal exercises. Unlike your favorite hard skill classes, this course is light on homework, but hard on class participation. Student should be ready to attend at all costs or face course failure. You will not survive on hard skills only hence you have to suffer class attendance and participation. Please note that this class makes an effort to manage device addiction of students by removing tables from the audience. 
Dmitry Kulish, Maxim Kiselev 
3  MC03011 
Management of Research & Development  Pavel Dorozhkin, Dmitry Kulish 
3  MC03015 
Mathematics and Machine Learning for Molecular modelling
This in an advanced course intended for students specializing in computational materials science. The course aims to prepare the students to use advanced methods of molecular (atomistic) modelling and develop/modify such algorithms. A particular emphasis is on application of machinelearning algorithms to molecular modelling.

Alexander Shapeev  3  MA03301 
Matrix and Tensor Factorizations  An Huy Phan, Andrzej Cichocki 
3  MA03303 
Methods for Enhanced Oil Recovery
Review of global oil resources and oil recovery technologies and mechanisms. Introduction to thermal oil recovery and EOR status. Heavy oil and oil sands: resources, reserves and recovery factor. Problems in heavy oil recovery and solutions. Comparison of recovery methods: nonthermal and thermal. Properties of rock, fluids, steam, steam additives, steamgas mixtures. Heat transfer: conduction heating (linear and radial). Steam injection systems. Formation heating: hot water and steam. Steamflooding: theory, OSR, patterns and mechanisms. Cyclic steam stimulation (CSS): variations, mechanisms and simplified prediction methods. Surface equipment and operation. Numerical simulation of steam injection processes: methods and limitations. Steam assisted gravity drainage (SAGD): principles, variations, field experience and limitations. Air injection based IOR processes, stoichiometry and kinetics. Laboratory and field performance evaluation of air injection based IOR processes. Field experience in Canada and the world.

Alexey Cheremisin  6  MA06117 
Molecular Biology Seminar
For each class, there will be a paper that two people will present to the rest of the class. We will go down to the details of experiments – how things were done and what do the data/figures really show, so be prepared to answer indepth questions. Presenters will start by stating the name of the paper/main authors and telling the take home message of the paper – why it is signficant, what problem it solved. Then they will proceed to the actual work. If there are methods/results mentioned in the paper that refer to prior work, you shall be prepared to answer questions about it too. The audience is supposed to read the paper being discussed beforehand and participate in discussions.
To pass, one would need to present a paper at least once during the module and actively take part in discussions of other papers. One absence is allowed no questions asked. Additional absences when unexplained will be a cause for nopass grade. There will be a few home assignments. They must be submitted in time, typed–not written up–and done professionally (written in good language, be concise and free of spelling errors – consider them as part of academic writing exercises). It is gonna be fun – students tend to like the seminar and its atmosphere 
Konstantin Severinov  3  MA03052 
Molecular Spectroscopy (Term 1B4)  Vladimir Mironenko  1.5  MA06209 
Multiphase Flows in Pipes
Course is focused on modeling and analyzing a number of transport phenomena accompanying transport of multiphase flows through pipes, mainly in application to hydrocarbon production.
In application to petroleum engineering, modeling is required to properly evaluate risks and identify hydrocarbon production strategy. The major topics, which will be considered: oil/water flows, emulsion formation, asphaltene deposition, wax deposition, turbulent drag reduction. Practicing engineers, trying to model these processes, frequently experience significant difficulties due to both absence of reliable modeling approaches and limited field/experimental data. Clear engineering approaches to modeling these complex processes will be given and critically discussed. 
Dmitry Eskin  3  MA03292 
Natural Language Modelling and Processing
The main purpose of this course is to introduce the basic concepts needed for computational processing of human languages.
The course is aimed at understanding the specifics of Natural Language as an object of computational analysis, the ability to choose the proper linguistic model (linguistic features related to different levels of NL system) and the proper method to address the problem and carry out meaningful linguistic interpretation of results. By the end of this course the students should have clear understanding of the issues involved in the main tasks of document classification and text analysis. They will have to complete a miniproject aimed at providing a completed system for one of the tasks. These projects can be carried out both on the basis of open source technologies and in the frameworks of special scientific programs such as ABBYY Compreno Based Research, largescale Internet corpora (GIKR) projects or DialogueEvaluation NLPtesting tracks. 
Vladimir Selegey  3  MA03131 
Numerical Methods in Continuum Mechanics
The objective of the course is to provide students with an overview of the modern computational approaches for solving continuum mechanics problems with the emphasis on advanced Computational Fluid Dynamics methods. The course will discuss competing formulations, suitable for continuum mechanics problems, i.e. finite difference, finite element, finite volume, and spectral methods. The course will discuss a variety of topics such as the methods of solution of elliptic, parabolic and hyperbolic systems of equations and application of the methods for solution of compressible and incompressible Euler and NavierStokes equations as well as solid mechanics problems. Modern approaches for mesh generation and solution of hyperbolic conservation laws will be also discussed.

TBD  6  MA06242 
Numerical photonics
Simulation and modeling using numerical methods is one of the key instruments in any scientific work. In the field of photonics, a wide range of numerical methods are used for studying both fundamental optics and applications such as design, development, and optimization of photonic components. Modeling is key for developing improved photonic devices and reducing development time and cost.
Choosing the appropriate computational method for a photonics modeling problem requires a clear understanding of the pros and cons of the available numerical methods. Numerical Methods in Photonics presents six of the most frequently used methods: FDTD, FDFD, 1+1D nonlinear propagation, modal method, Green’s function, and FEM. The Course outlines the basics of Maxwell’s equations and includes selfcontained information focusing on each of the methods. Each method is accompanied by a review of the mathematical principles in which it is based, along with sample scripts, illustrative examples of characteristic problem solving, and exercises. MATLAB® is used throughout the text. This course provides a solid basis to practice writing your own codes. The theoretical formulation is complemented by sets of exercises, which allow you to grasp the essence of the modeling tools. 
Arkady Shipulin  6  MA06312 
OneDimensional Quantum Systems (Term 34)
In the framework of the course, quantum systems (fieldtheoretic and discrete) in one spacial dimension, and some their classical statistical mechanics counterparts are discussed. The scope of systems includes sineGordon and Thirring model, O(n) sigma model, Heisenberg chain and sixvertex model, Kondo problem. We consider several techniques to obtain exact results for these systems, including operator product expansions, bosonfermion correspondence, YangBaxter equation, different versions of Bethe Ansatz.

Michael Lashkevich  3  MA06276 
Pedagogical Experience
The main function of this course is to articulate Skoltech's expectations on Phdstudents who do their pedagogical TA assignment as Skoltech. The course describes the intended learning outcomes and how they are assessed.
The course also offers a forum for TA and allows Skoltech TAs to collect and discuss resources and issues relevant for their TA experience. The forum provides a peertopeer feedback opportunity but also enables instructors to participate in the conversation when asked to. The main bulk of the 81 hours of the course is spent in the actual courses in which the PhDstudents do their TAassignments. The assignments in the course itself require less than 10 hours of time. 
Magnus Gustaffson  3  PE03005 
Power Markets and Regulations
The course will introduce the students to power system economics. After covering fundamentals of microeconomics, main types of electricity markets and regulation will be discussed including the Russian market. Economic dispatch and Optimal Power Flow with Locational Marginal Pricing will also be covered. The lectures will be supplemented by a laboratory exercise utilizing PowerWorld simulation package and group miniprojects.

Janusz Bialek  6  MB06002 
Practicum in Experimental Physics  Valery Ryazanov  6  MA06208 
Quantum Field Theory (Term 34)
The main task of the course is to calculate the anomalous moment of the electron. The main methods of quantum field theory are studied by the example of solving this problem: the construction of the Fock state space of identical particles, continuum integral as a way to work with such a state space, quantization of free scalar, spinor and electromagnetic fields, Smatrix approach to accounting for interaction, perturbation theory in the form of Feynman's diagram technique, divergence in quantum field theory and their renormalization. The course involves writing three test papers and a written exam.

Vladimir Losyakov  3  MA06316 
Quantum Integrable Systems (Term 34)  Anton Zabrodin  3  MA06315 
Quantum Mechanics (Term 34)  Andrei Semenov  3  MA06322 
Quantum Mesoscopics. Quantum Hall Effect (Term 34)  Igor Burmistrov  3  MA06278 
Quantum Optics
“Quantum optics, the union of quantum field theory and physical optics, is undergoing a time of revolutionary change” [Marlan O. Scully and M. Suhail Zubairy “Quantum Optics”, Cambridge University Press].
Quantum optics studies interactions between matter and the radiation field where quantum effects are important. The fundamental interest in quantum optics is connected with conceptual foundations of quantum mechanics, with nonclassical effects such as quantum interference and entanglement, photon antibunching and squeezing, as well as with numerous applications in precise measurements, protected information transfer, etc. This introductory course includes the following topics: quantization of electromagnetic field, Fock (number) states of the field, Lamb shift, Casimir effect, coherent states of the field, interaction of photons with atoms, Rabi and Jaynes – Cummings models. Dressed states. Dicke super and subradiation, quantum coherence and correlation measurements, quantummechanical detector of photons, singlephoton interferometer, quantum beam splitter, Young’s type interferometer, Michelson’s stellar interferometer, physics of HanburyBrownTwiss interferometer, nonclassical states of light, squeezing in nonlinear optical processes, bunching and antibunching of photons, “Schroedinger’s cat” states. 
Zadkov, Udson 
3  MA03161 
Quantum Theory of Radiation and Quantum Optics (Term 1B4)  Yuri Lozovik  1.5  MA06314 
RNA Biology
This course is devoted to the knowledge on the structures of RNA and RNAprotein complexes as well as their functioning in cells. The aim of this course is to provide an explanation of fundamental mechanisms such as translation, splicing and gene expression regulation based on the structural viewpoint. Thus the role of RNA in the maintenance of cell identity and cell metabolism will be defined. By focusing on modern techniques for RNA and RNAprotein structure and RNA modifications analysis, students will get aquainted with the approaches to study RNA input into cellular processes in vitro and in vivo.
The students will apply obtained knowledge and skills in presentations and a written exam. An examination commission, consisting of CTB faculty and of invited members, will conduct final evaluation of the overall product design completeness, quality of the results achieved, and of the presentations delivered. 
Timofey Zatsepin  3  MA03081 
Random Matrices, Random Processes and Integrable Systems (Term 34)
In recent years, researchers have found remarkable connections between, at first glance, completely different problems of mathematics and theoretical physics. Mathematically, these are combinatorial and probabilistic problems about systems with a large number of degrees of freedom. Among them, the problem of describing the eigenvalues of matrices with random elements, the problem of statistics of random Young diagrams, the problem of tiling various regions of the plane by dominoes or lozenges, the problem of enumerating nonitersecting paths on lattices. On the physical side, these are the problems of interface growth, traffic flows, polymers in random media, and so on.
It turns out that all these problems have a general mathematical structure, which can be encoded in the term "integrability". This structure is behind a lot of beautiful exact mathematical results. Moreover, these results have remarkable universality property, which play the same role as the law of large numbers and the central limit theorem in the probability theory. Looking at our random systems from afar, we find that they posess completely nonrandom limiting forms. Random fluctuations around these forms are described by a small number of universal probability distributions that are completely independent of the details of original system. The course attendees are going to get acquainted with the range of issues described and to learn about the latest achievements in the field. 
Alexander Povolotsky  3  MA06318 
Representations of Affine KacMoody Algebras (Term 34)
Affine KacMoody Lie algebras play a prominent role in the theory of infinitedimensional Lie algebras. The two main reasons are the beauty of the theory and the vast number of applications in various fields of mathematics and mathematical physics such as conformal field theory, algebraic geometry, number theory, combinatorics, statistical mechanics, theta functions. In particular, integrable representations of the affine KacMoody algebras form a background of the famous WessZuminoWitten CFT. The course will be devoted to the general questions of the representation theory of affine KacMoody Lie algebras and to the study of several special classes of modules, in particualr, integrable modules. We will be mainly interested in algebraic and combinatorial parts of the theory. Time permitting, we will also touch upon some related geometric constructions such as affine Grassmannians.

Evgeny Feigin  3  MA06320 
Research Methodology: Computational and Data Science and Engineering
A modern researcher needs to have a set of various skills in order to conduct research efficiently. In addition to high level of research skills and understanding of the research environment of one’s particular field, a researcher should be able to manage researchrelated business processes, be personally effective, have high level of communication and presentation skills, build effective professional relationship with colleagues and effectively manage the career development. The course covers all these topics and implies active interaction between the tutor and students during the classes. In the end of the course each student will be asked to write an essay.

Maxim Fedorov  3  PA03102cds 
Research Methodology: Molecular Biology Seminar  Konstantin Severinov  3  PA03102ls 
Research Methodology: Space Center Seminar (Term 14)  Anton Ivanov  3  PA03102es 
Research Seminar "Advanced Materials Science" (Term 28)
This is the main research seminar of the Skoltech Center for Electrochemical Energy Storage and Materials Science Education program featuring presentations of young researchers: MSc students, PhD students, postdocs. Every MSc and PhD student of Materials Science program should deliver at least one presentation per two years. The range of topics is broad and includes any aspects of materials science and engineering.
Please see the seminar webpage at http://crei.skoltech.ru/cee/education/wednesdayscientificseminar/ 
Keith Stevenson  0.43  MA03302 
Research seminar "Modern Problems of Mathematical Physics" (Term 18)
Course "Modern problems of mathematical physics" is a student seminar, so participants are expected to give talks based on the modern research papers. Current topic of the seminar can vary from time to time: now it is devoted to the study of N=2 supersymmetric gauge theory and its links with random matrix models, complex curves, and integrable systems. Other topics that were already covered, or can be covered in the future, are: classical integrable equations, complex curves and their thetafunctions, quantum integrable models (quantummechanical and fieldtheoretical), models of statistical physics.

Andrei Marshakov  1.5  MA12268 
Research seminar "Modern Problems of Theoretical Physics" (Term 18)
Research seminar "Modern Problems of Theoretical Physics" is supposed to teach students to read, understand and represent to the audience recent advances in theoretical physics. Each student is supposed 1) to choose one of recent research papers from the list composed by the instructor in the beginning of each term, 2) read it carefully, 3) present the major results of the paper to his/her colleagues during the seminar talk, 4) answer the questions from the audience about the content of the paper. The papers in the list are selected, normally, from the condensed matter theory and related fields, like: physics quantum computing, statistical physics, etc. The papers to the list are usually chosen from most competitive physics journals, like Nature Physics, Science, Physical Review Letters, Physical Review X and others.

Mikhail Feigelman, Konstantin Tikhonov 
1.5  MA12319 
Research seminar "Strings and Cluster Varieties" (Term 18)
The course is directed to substantive work of the master and PhD students in order to understand recently found relations among supersymmetric gauge theories, refined topological strings, cluster varieties and integrable systems. The plan of wrk on the course consists of several introductive lectures on the various consistuents of the subject as well as student talks on recent original papers and results of their own investigation. The core topics include relation between cluster varieties and Painleve equations and approaches to the SeibergWitten theories with fundamental matter based on Toda systems and spin chains.

Andrei Marshakov  1.5  MA12176 
Review of Materials and Devices for Nano and Optoelectronics (Term 34)
The lectures are presented by the scientists working actively in various directions of nanoelectronics and optoelectronics in Russia and abroad. Seminars assume the discussion of recent original papers in the area (including superconducting electronics and spintronics, terahertz waves technology and applications, quantum coherent systems (qubits), single electron devices). The classical papers presenting a physical basis for devices operation will be also considered. The papers are distributed in February. Each student is expected to report two papers during the period FebruaryMay.

Valery Ryazanov  3  MA06206 
Selected Topics in Energy: Physical, Chemical and Geophysical Challenges (Term 24)
The course provides an introduction to the modern topics related to fundamentals of exploration of energy resources, energy generation, storage, conversion and use. It identifies the corresponding practical challenges to be addressed at the fundamental research level and familiarizes the students with the stateoftheart approaches, methods and techniques in use in related scientific areas. The course seeks to emphasize and maintain interdisciplinary nature of the energyrelated topics, in particular, combination of micro and macroscopic approaches of geophysics, mechanics and chemistry in hydrocarbon exploration and development, relation between the physical and chemical processes of energy generation and conversion, integration of physical, chemical and mechanical approaches to perspective materials (physical and chemical synthesis, micro and macroscopic characterization, structureproperty relations, etc.) and related theoretical methodologies. These interdisciplinary links are mostly demonstrated by horizontal knowledge exchange among the students reporting and discussing practical examples from their own research field or from modern review or research publications. Topical lectures are included for further exploration of these links. The secondary aim of the course is the development of presentation skills (oral and writing), as well as scientific peerreview experience. The seminar format chosen for most activities allows students free exchange of knowledge and ideas, broader vision of their research projects and methodologies, better assessments of their own research skills and demands for further education.

Alexei Buchachenko  2  PA06106 
Sensors and Embedded Systems for Iot
This module will give a wideranging introduction to sensors and embedded systems in the scope of Internet of Things (IoT) paradigm. The module aims at providing full support to the nonengineering students with a series of carefully constructed concepts and exercises. It starts with setting the whole picture of IoT and its requirements for sensors and embedded systems. Then it introduces basic principles and simple projects, and moves towards more advanced IoT system design. Finally, the module will make overview of targeted applications including SmartX, Oil & Gas industry, wearables and medical applications.

Andrey Somov  6  MA06235 
Smart Grids
Power systems around the world are undergoing a period of unprecedented change. A typical 20th Century power system was characterized by unidirectional flow of power from a limited number of large controllable power stations to a highly predictable demand. There was no energy storage so that at any time generation had to be equal to demand and the infrastructure utilization rates were low (about 55% for generation, 30% for transmission and even lower for distribution). Generally planning and controlling such a system was relatively straightforward as it was based around principles of deterministic hierarchical control, usually based on (N1) reliability criterion.
On the other hand the emerging 21st Century power system is characterized by bidirectional flows between a very large number of uncontrollable and stochastic generators (usually, but not always, renewable ones such as wind or solar) and stochastic and often poorlypredictable demand. Demand ceases to be predictable as it consists of consumers equipped with smart meters and wind/solar generators hence possibly becoming net generators – socalled prosumers. Increased penetration of energy storage, both stationary and mobile due to a takeup of electric vehicles, offers buffering possibilities in dispatch (generation does not have to be equal to demand at any time). Controlling such a power system is the main research challenge in power systems and it is made possible by latest advances in ICT (Information and Control Technology), communication networks, Internet, GPS, sensors, etc. However it requires new tools and methodologies, the Smartgrid course will give the basis of this new grid scenario. 
Federico Ibanez  6  MA06056 
Space Center Seminar (Term 14)
The seminar will cover current topics in the space domain: latest news, discoveries. Also planned that all PhD students and some Master students will present their research. External lecturers will be invited regularly to focus on the main applications of space technologies: science, telecommunication, navigation and remote sensing. Aspects of space technologies will also be discussed: structures, software, attitude determination and control systems, on board computers, communication system power supply systems and others. The seminar will be offered in English.

Anton Ivanov  0.25  MO01004 
Space Sector Course
This course examines the domain of space from multiple vantage points — space as a business, a way of life, as industry, and as a fulfillment of human dreams. In addition, it examines spacerelated issues that drive key international regulatory, economic, and global policy. To gain insight into these different dimensions, we examine space through three different lenses: subsectors, technologies, and organizations.
Every topic is covered by a top expert from the field. The topics of lectures are: New space – a Russian view; System thinking; Economics of a firm; Critical thinking; Earth Observation; How a firm competes; Space Sector Agencies, Organizations and Plans: Russia; Launch Systems; Technology assessment; Capabilities of human spaceflight; Value chain analysis; Space navigation services; Space science payloads and missions 
Tatiana Podladchikova, Edward Crawley 
6  MB06003 
Special Topics in Quantum Computing
This research level course prepares students for research. The course is intended for those who are doing research in related topics and can help students prepare for a thesis. The course will contain a taught portion; were central results will be presented. It will also contain talks covering published research findings.
Students are expected to utilize the course to (i) design; (ii) conduct and (iii) present research. 
Jacob Biamonte  3  MA03286 
Statistical Physics (Term 78)
This is a course on rigorous results in statistical physics and random fields. Most of it will be dedicated to the theory of phase transitions, uniqueness or nonuniqueness of the lattice Gibbs fields.
The topics will include: grand canonical, canonical and microcanonical ensembles, DLR equation, Thermodynamic limit, Gibbs distributions and phase transitions, onedimensional models, correlation inequalities ( GKS, GHS, FKG), spontaneous symmetry breaking at low temperatures, uniqueness at high temperatures and in nonzero magnetic field, Nontranslationinvariant Gibbs states and interfaces, Dobrushin Uniqueness Theorem Pirogov–Sinai Theory O(N)symmetric models the Mermin–Wagner Theorem Reflection Positivity and the chessboard estimate infrared bounds 
Semen Shlosman  3  MA06180 
Technology Entrepreneurship
The course is designed to help teams with early stage projects/ideas (= guesses & hopes for new tech biz) to get transformed into viable biz concepts, validated prototypes/products, and, finally, fundable companies. The experiential learning, teambased and projectbased learning formats provide students with realworld, handson, immersive learning about what it takes to successfully transfer technologies into new products, businesses or startups that benefit society. It's not about how to write a business plan or prepare investor pitch. The result is not a publication or a deck of slides. Instead, it is the experience of being an entrepreneur – learning from the marketplace by talking to customers, partners, and competitors; working as a team to overcome failures and embrace successes; encountering the chaos and uncertainty of creating a startup – all under the guidance of Skoltech teaching team.
The course roadmap (and your project team journey) is built around: • Assessing the status of your project (team, technology, market, etc.) • Planning your “project progress sprints” – practical actions turbocharging your • Supporting your sprints with Customer Development and Lean Product • Final Demo Day to showcase your projects Course benefits: • Learn the advanced and practical skills in the area of Technology • Develop Lean Startup mindset/skillsets and build competence in customer, • Connect to topnotch mentors, investors and fellow entrepreneurs • Receive coaching from successful entrepreneurs and industry experts as well as • Propel your projects (IWbased or new ones) up to viable products, biz concepts, 
Alexey Nikolaev  3  MC03008 
Technology of Thin Films Deposition
This course presents the principle scientific aspects of technologies widely used to fabricate thin films and twodimensional heterostructures, as well as the engineering aspects (including specific vacuum devices). The requirements to supports for epitaxial and nonepitaxial films are addressed. The problems of adhesion and the most important features of the support/film interfaces are considered. The technologies based on physics are accented, and some aspects of chemical vapor deposition are also discussed.

Sergey Dorozhkin  3  MA03216 
Thermal Fluid Sciences
The course is designed to give an overview of the fluid mechanics, gas dynamics, thermodynamics, and electromagnetic phenomena in fluids and gasses. The following topics are discussed:
1. Kinematics of continuous media 2. Basic concepts and equations of fluid dynamics and thermodynamics 3. Models of fluid and gas media 4. Contact discontinuities in fluids, gases, and plasma 5. Flow of ideal, incompressible fluid 6. Incompressible viscous flow. Boundary layer theory. Turbulence 7. Compressible fluid flow. Gasdynamic 8. Electromagnetic phenomena in fluids Students will have to complete daily homework, theoretical, computer, and design projects, midterm and final exams. 
Iskander Akhatov  6  MA06053 
Thermodynamics and Transport at Nanoscale
The course introduces students to nanostructured systems, the factors that determine their behavior and main theoretical models to predict their structure and dynamics. The major focus is on the application of basic principles of colloid and surface science to nanostructured systems, the applicability of different concepts and modeling approaches. The particular topics include: thin films, nanosize droplets and bubbles, nanoparticles and polymer nanocomposites, nanoporous materials, liquid crystals and, finally, lipid membranes. Each topic will involve 12 lectures and a practical assignment on modeling phase equilibria or transport properties in nanostructured systems, completed by the students individually or in small teams. The lectures and home assignments emphasize the practical aspects of synthesis, characterization and applications or nanostructured materials.
The course will be useful to all students willing to improve their understanding of natural (e.g. mineral oil) and manmade colloids, such as suspensions, emulsions and foams, as well as natural and synthetic porous materials. 
Alexey Vishnyakov  3  MA03288 
Transgenic Models for Drug Discovery
The course consists of theoretical and practic parts.Theoreticla part is devoted to analysis of transgenesis in C.elegance, Drosophila, Zebra fish and mice with particular accent on the usage of these platforms in drug development. It also describes general principles of creation of genetically modified animals. Practical part enables students to obtain practical skills in all phases of the production of transgenic mice.
Transgenic animals are no alternative tool for studying gene function, modeling of human diseases, creating of animalproducing recombinant proteins for agricultural and pharmaceutical industries. Last years work on the creation of such organisms was intensified due to the widespread introduction of sitespecific nucleases technology: "zinc fingers», TALEN, CRISPR / Cas9 types of nuclease. Increasingly, it can be heard about the creation of new models of diseases, the use of gene knockout for medical purposes. The course "Transgenic animals" allows students not only to get acquainted with the theory of molecular biological and embryological basis of modern approaches to the modification of the genome, but also to apply their knowledge during practical training. 
Yuri Kotelevtsev  6  MA06223 
Uncertainty Quantification
Uncertainty Quantification (UQ) marks a new approach to mathematical modelling and design at all levels. Instead of deterministic models, we consider randomized setup which can include uncertainties in model parameters, computational domains, inputs and many others. Thus, instead of a single quantity the probability distribution of the output parameter has to be studied, and many other associated tasks that include risk estimation, variance analysis. This also requires new computational tools that include the approximation of multivariate functions and computation of multidimensional integrals.

Ivan Oseledets  3  MA03226 