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Astrophysics I

Prof. Deepto Chakrabarty

This course provides a graduate-level introduction to stellar astrophysics. It covers a variety of topics, ranging...

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Projection Theory

Prof. Lawrence D Guth

The class studies projection theory, starting from the first questions and building up to recent developments....

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Time Series Analysis

Prof. Anna Mikusheva

The course provides a survey of the theory and application of time series methods in econometrics. Topics covered...

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Systems Biology

Prof. Jeff Gore

This course provides an introduction to cellular and population-level systems biology with an emphasis on synthetic...

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Graph Theory and Additive Combinatorics

Prof. Yufei Zhao

This course examines classical and modern developments in graph theory and additive combinatorics, with a focus on...

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General Relativity

Prof. Scott Hughes

8.962 is MIT’s graduate course in general relativity, which covers the basic principles of Einstein’s general theory...

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Introduction to Stochastic Processes

Dr. Hao Wu

This course is an introduction to Markov chains, random walks, martingales, and Galton-Watsom tree. The course...

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Statistical Mechanics I: Statistical Mechanics of Particles

Prof. Mehran Kardar

Statistical Mechanics is a probabilistic approach to equilibrium properties of large numbers of degrees of freedom....

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Groundwater Hydrology

Prof. Charles Harvey

This course covers fundamentals of subsurface flow and transport, emphasizing the role of groundwater in the...

Engineering Environmental Engineering Earth Science

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Introduction to Computational Molecular Biology

Ross Lippert

This course introduces the basic computational methods used to understand the cell on a molecular level. It covers...

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Advanced Soil Mechanics

Prof. Charles Ladd

This class presents the application of principles of soil mechanics. It considers the following topics: the origin...

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The Brain and Cognitive Sciences I

Prof. Earl Miller

Survey of principles underlying the structure and function of the nervous system, integrating molecular, cellular,...

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Electromagnetic Theory

Prof. Leonid Levitov

Electromagnetic Theory covers the basic principles of electromagnetism: experimental basis, electrostatics, magnetic...

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Particle Physics of the Early Universe

Prof. Frank Wilczek

This course covers the basics of general relativity, standard big bang cosmology, thermodynamics of the early...

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Atomic and Optical Physics I

Prof. Wolfgang Ketterle

This is the first of a two-semester subject sequence that provides the foundations for contemporary research in...

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Introduction to Nuclear and Particle Physics

Prof. Markus Klute

This is an introductory graduate-level course on the phenomenology and experimental foundations of nuclear and...

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Number Theory I

Andrew V. Sutherland

This is the first semester of a one-year graduate course in number theory covering standard topics in algebraic and...

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Algebraic Topology I

Prof. Haynes Miller

This is a course on the singular homology of topological spaces. Topics include: Singular homology, CW complexes,...

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Commutative Algebra

Prof. Steven Kleiman

In this course students will learn about Noetherian rings and modules, Hilbert basis theorem, Cayley-Hamilton...

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Environmental Microbiology

Prof. Martin Polz

This class provides a general introduction to the diverse roles of microorganisms in natural and artificial...

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Probabilistic Methods in Combinatorics

Prof. Yufei Zhao

This course is a graduate-level introduction to the probabilistic methods, a fundamental and powerful technique in...

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Astrophysics II

Professor Prof. Mark Vogelsberger

This course broadly covers galactic dynamics and large-scale structure in the universe. Major topics include:...

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Geometry and Quantum Field Theory

Prof. Pavel Etingof

The main goal of this course is to present the basic ideas of quantum field theory (QFT) in a completely rigorous...

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Measure and Integration

Prof. Jeff Viaclovsky

This graduate-level course covers Lebesgue’s integration theory with applications to analysis, including an...

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Synthetic Organic Chemistry II

Prof. Rick Danheiser

This course focuses on general methods and strategies for the synthesis of complex organic molecules. Emphasis is on...

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Topics in Biophysics and Physical Biology

Prof. Mark Bathe

This course provides broad exposure to research in biophysics and physical biology, with emphasis on the critical...

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Lie Groups and Lie Algebras I

Prof. Pavel Etingof

This course is the first half of the year-long introductory graduate sequence 18.745/18.755 on Lie groups and Lie...

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Algebraic Geometry

Prof. Roman Bezrukavnikov

This is the first semester of a two-semester sequence on Algebraic Geometry. The goal of the course is to introduce...

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Principles of Inorganic Chemistry III

Prof. Christopher Cummins

This course covers the principles of main group (s and p block) element chemistry with an emphasis on synthesis,...

Chemistry Science & Math

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Mathematical Methods for Engineers II

Prof. Gilbert Strang

This graduate-level course is a continuation of Mathematical Methods for Engineers I (18.085). Topics include...

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Advanced Calculus for Engineers

Dr. Dionisios Margetis

This course analyzes the functions of a complex variable and the calculus of residues. It also covers subjects such...

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Nonlinear Econometric Analysis

Prof. Victor Chernozhukov

This course presents micro-econometric models, including large sample theory for estimation and hypothesis testing,...

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Advanced Partial Differential Equations with Applications

Prof. Rodolfo Rosales

The focus of the course is the concepts and techniques for solving the partial differential equations (PDE) that...

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Differential Analysis

Prof. Richard Melrose

This is the first semester of a two-semester sequence on Differential Analysis. Topics include fundamental solutions...

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Human Memory and Learning

Prof. Anthony Wagner

Surveys the literature on the cognitive and neural organization of human memory and learning. Includes consideration...

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Networks for Learning: Regression and Classification

Prof. Tomaso Poggio

The course focuses on the problem of supervised learning within the framework of Statistical Learning Theory. It...

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Molecular Aspects of Chemical Engineering

Prof. Paula Hammond

This class covers molecular-level engineering and analysis of chemical processes. The use of chemical bonding,...

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Statistical Mechanics II: Statistical Physics of Fields

Prof. Mehran Kardar

This is the second term in a two-semester course on statistical mechanics. Basic principles are examined in this...

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How to Win at Texas Hold'em Poker

Will Ma

Offered during MIT’s Independent Activites Period (IAP), this short course covers the poker concepts, math concepts,...

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Statistical Method in Economics

Prof. Anna Mikusheva

This course is divided into two sections, Part I and Part II. Part I, found here, provides an introduction to...

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Active Directory sites, topology, and replication

Design Active Directory site topology and analyze Active Directory replication metadata, including Windows Server...

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Cryptography

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Operational Research for Decision Optimization

Master Operational Research techniques to solve complex business problems, optimize resources, and make smarter...

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Automated Reasoning: Symbolic Model Checking

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离散优化建模高阶篇 Advanced Modeling for Discrete Optimization

优化问题是一种常见的决策问题，它在我们的社会中很常见。它的应用可以从数独问题的解决涵盖到婚礼的座次安排。同样的技术可以用于航班与机组成员的安排，钢铁生产的调节，和钢铁从矿区到港口的调度问题。在生产中，人力资源与生产材料的合理决策可以使...

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Introduction to Complex Analysis

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Games without Chance: Combinatorial Game Theory

This course will cover the mathematical theory and analysis of simple games without chance moves.

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Stanford University Semantics Of First Order Logic

Logic

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Analytic Combinatorics

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Category Theory

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Commutative Ring Theory

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Complex Analysis

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Computability and Complexity

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Convex Analysis

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Differentiable Manifolds

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Differentiation and Integration in Several Real Variables

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Distribution Theory

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Fermat's Last Theorem

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Finite Model Theory

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Fourier Analysis

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Functional Analysis

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General Ring Theory

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Harmonic Function Theory

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Knot Theory

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LMi for Minimizing Eigenvalues of a Matrix

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MPSolve

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Measure Theory

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Numerical Methods

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Numerical Methods Qualification Exam Problems and Solutions (University of Maryland)

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On 2D Inverse Problems

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Order Theory

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Parallel Spectral Numerical Methods

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Real Analysis

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Representation Theory

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Riemann Hypothesis

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Shelf:Category theory

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Monte Carlo Methods

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Atomic and Optical Physics II

Prof. Wolfgang Ketterle

This is the second of a two-semester subject sequence beginning with Atomic and Optical Physics I (8.421) that...

Physics Science & Math

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Soil Behavior

Prof. Charles Ladd

This class presents a detailed study of soil properties with emphasis on interpretation of field and laboratory test...

Earth Science Civil Engineering Engineering

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Aquatic Chemistry

Dr. Jeff Seewald

This course details the quantitative treatment of chemical processes in aquatic systems such as lakes, oceans,...

Environmental Engineering Chemistry Engineering

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Cell Biology: Structure and Functions of the Nucleus

Prof. Phillip Sharp

The goal of this course is to teach both the fundamentals of nuclear cell biology as well as the methodological and...

Biology Science & Math

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Integral Equations

Dr. Dionisios Margetis

This course emphasizes concepts and techniques for solving integral equations from an applied mathematics...

Science & Math Physics Mathematics

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Special Topics in Mathematics with Applications: Linear Algebra and the Calculus of Variations

Prof. Rohan Abeyaratne

This course forms an introduction to a selection of mathematical topics that are not covered in traditional...

Mathematics Mechanical Engineering Engineering

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Topics in Computational and Systems Biology

Prof. Christopher Burge

This is a seminar based on research literature. Papers covered are selected to illustrate important problems and...

Biology Biological Engineering Engineering

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Combinatorial Theory: Introduction to Graph Theory, Extremal and Enumerative Combinatorics

Prof. Igor Pak

This course serves as an introduction to major topics of modern enumerative and algebraic combinatorics with...

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String Theory and Holographic Duality

Prof. Hong Liu

This string theory course focuses on holographic duality (also known as gauge / gravity duality or AdS / CFT) as a...

Physics Science & Math

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Category Theory for Scientists

Dr. David I. Spivak

The goal of this class is to prove that category theory is a powerful language for understanding and formalizing...

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Geometry of Manifolds

Prof. Tomasz Mrowka

Geometry of Manifolds analyzes topics such as the differentiable manifolds and vector fields and forms. It also...

Mathematics Science & Math

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Differential Analysis II: Partial Differential Equations and Fourier Analysis

Prof. Lawrence D Guth

In this course, we study elliptic Partial Differential Equations (PDEs) with variable coefficients building up to...

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Topics in Geometry: Mirror Symmetry

Prof. Denis Auroux

This course will focus on various aspects of mirror symmetry. It is aimed at students who already have some basic...

Physics Mathematics Science & Math

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Algebraic Topology II

Prof. Haynes Miller

This is the second part of the two-course series on algebraic topology. Topics include basic homotopy theory,...

Mathematics Science & Math

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Number Theory II: Class Field Theory

Dr. Sam Raskin

This course is the continuation of 18.785 Number Theory I. It begins with an analysis of the quadratic case of Class...

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Topics in Algebraic Number Theory

Prof. Kiran Kedlaya

This course is a first course in algebraic number theory. Topics to be covered include number fields, class numbers,...

Mathematics Science & Math

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The Polynomial Method

Prof. Lawrence D Guth

This course offers an introduction to the polynomial method as applied to solving problems in combinatorics in the...

Mathematics Science & Math

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Representations of Lie Groups

Prof. Pavel Etingof

The goal of this course is to give an introduction to the representation theory of compact and non-compact Lie...

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Graduate Topology Seminar: Kan Seminar

Prof. Haynes Miller

This is a literature seminar with a focus on classic papers in Algebraic Topology. It is named after the late MIT...

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Lie Groups and Lie Algebras II

Prof. Pavel Etingof

This course is the second half of the year-long introductory graduate sequence Lie Groups and Lie Algebras I &...

Mathematics Science & Math

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Advanced Analytic Methods in Science and Engineering

Prof. Hung Cheng

Advanced Analytic Methods in Science and Engineering is a comprehensive treatment of the advanced methods of applied...

Science & Math Mathematics

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Effective Field Theory

Prof. Iain Stewart

Effective field theory is a fundamental framework to describe physical systems with quantum field theory. Part I of...

Physics Science & Math

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Doctoral Seminar in Research Methods II

Prof. Jesper B. Sorensen

A large proportion of contemporary research on organizations, strategy and management relies on quantitative...

Mathematics Science & Math

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Introduction to Lie Groups

Prof. Sigurdur Helgason

This course is devoted to the theory of Lie Groups with emphasis on its connections with Differential Geometry. The...

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Particle Physics II

Prof. Min Chen

8.811, Particle Physics II, describes essential research in High Energy Physics. We derive the Standard Model (SM)...

Physics Science & Math

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Algebraic Techniques and Semidefinite Optimization

Prof. Pablo Parrilo

This research-oriented course will focus on algebraic and computational techniques for optimization problems...

Mathematics Systems Engineering Systems Thinking

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Strongly Correlated Systems in Condensed Matter Physics

Prof. Leonid Levitov

In this course we shall develop theoretical methods suitable for the description of the many-body phenomena, such as...

Physics Science & Math

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Noncommutative Algebra

Prof. Roman Bezrukavnikov

Noncommutative algebra studies algebraic phenomena involving multiplication for which commutativity law fails, such...

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Random Matrix Theory and Its Applications

Prof. Moe Win

This course is an introduction to the basics of random matrix theory, motivated by engineering and scientific applications.

Mathematics Science & Math

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