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Mathematics

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MIT OCW
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Discrete Stochastic Processes
Prof. Robert Gallager
Discrete stochastic processes are essentially probabilistic systems that evolve in time via random changes occurring...
Mathematics Science & Math
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MIT OCW
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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...
Engineering Mathematics Science & Math
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MIT OCW
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Advanced Stochastic Processes
Prof. David Gamarnik
This class covers the analysis and modeling of stochastic processes. Topics include measure theoretic probability,...
Mathematics Science & Math
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MIT OCW
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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...
Biological Engineering Biology Engineering
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MIT OCW
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Relativistic Quantum Field Theory I
Prof. Hong Liu
This course is a one-term self-contained subject in quantum field theory. Concepts and basic techniques are...
Physics Science & Math
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MIT OCW
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Convex Analysis and Optimization
Prof. Dimitri Bertsekas
This course will focus on fundamental subjects in convexity, duality, and convex optimization algorithms. The aim is...
Algorithms and Data Structures Computer Science Data Science, Analytics & Computer Technology
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MIT OCW
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Essential Numerical Methods
Prof. Ian H. Hutchinson
This half-semester course introduces computational methods for solving physical problems, especially in nuclear...
Engineering Mathematics Nuclear Engineering
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MIT OCW
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Numerical Methods for Partial Differential Equations
Dr. Benjamin Seibold
This graduate-level course is an advanced introduction to applications and theory of numerical methods for solution...
Algorithms and Data Structures Computer Science Data Science, Analytics & Computer Technology
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MIT OCW
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Game Theory for Managers
Prof. David McAdams
This half-term course examines the choices that we make which affect others and the choices others make that affect...
Business & Management Economics Management
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MIT OCW
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Geometric Disciplines and Architecture Skills: Reciprocal Methodologies
Brandon Clifford
This course is an intensive introduction to architectural design tools and process, and is taught through a series...
Architecture Art, Design & Architecture
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MIT OCW
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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...
Mathematics Science & Math
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MIT OCW
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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...
Mathematics Science & Math
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MIT OCW
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Probability and Statistics in Engineering
Prof. Daniele Veneziano
This class covers quantitative analysis of uncertainty and risk for engineering applications. Fundamentals of...
Civil Engineering Engineering Mathematics
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MIT OCW
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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....
Mathematics Science & Math
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MIT OCW
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Mathematical Statistics
Dr. Peter Kempthorne
This course provides students with decision theory, estimation, confidence intervals, and hypothesis testing. It...
Economics Mathematics Science & Math
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MIT OCW
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Fundamentals of Probability
Prof. Yury Polyanskiy
This is a course on the fundamentals of probability geared towards first or second-year graduate students who are...
Mathematics Science & Math
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MIT OCW
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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...
Mathematics Science & Math
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MIT OCW
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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...
Mathematics Science & Math
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MIT OCW
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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...
Mathematics Science & Math
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MIT OCW
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Relativistic Quantum Field Theory III
Prof. Frank Wilczek
This is the third and last term of the quantum field theory sequence. The course is devoted to the standard model of...
Physics Science & Math
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MIT OCW
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Game Theory with Engineering Applications
Prof. Asuman Ozdaglar
This course is an introduction to the fundamentals of game theory and mechanism design. Motivations are drawn from...
Economics Engineering Mechanical Engineering
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MIT OCW
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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...
Mathematics Science & Math
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MIT OCW
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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...
Engineering Mathematics Mechanical Engineering
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Quantitative Reasoning & Statistical Methods for Planners I
Ezra Haber Glenn
This course develops logical, empirically based arguments using statistical techniques and analytic methods....
Mathematics Science & Math Social Sciences
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MIT OCW
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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...
Mathematics Science & Math
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MIT OCW
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Geometry of Manifolds
Prof. Denis Auroux
This is a second-semester graduate course on the geometry of manifolds. The main emphasis is on the geometry of...
Mathematics Science & Math
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MIT OCW
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Mathematical Methods in Nanophotonics
Prof. Steven G. Johnson
Find out what solid-state physics has brought to Electromagnetism in the last 20 years. This course surveys the...
Engineering Mathematics Mechanical Engineering
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MIT OCW
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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...
Mathematics Science & Math
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MIT OCW
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Integral Equations
Dr. Dionisios Margetis
This course emphasizes concepts and techniques for solving integral equations from an applied mathematics...
Mathematics Physics Science & Math
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MIT OCW
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Nonlinear Dynamics and Chaos
Prof. Rodolfo Rosales
This graduate level course focuses on nonlinear dynamics with applications. It takes an intuitive approach with...
Mathematics Science & Math
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MIT OCW
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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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MIT OCW
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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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MIT OCW
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Relativistic Quantum Field Theory II
Prof. Hong Liu
This course is the second course of the quantum field theory trimester sequence beginning with Relativistic Quantum...
Physics Science & Math
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MIT OCW
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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...
Mathematics Science & Math
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MIT OCW
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Game Theory
Prof. Mihai Manea
This course provides a rigorous treatment of non-cooperative solution concepts in game theory, including...
Economics Social Sciences
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MIT OCW
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Genomics and Computational Biology
Dr. George Church
This course will assess the relationships among sequence, structure, and function in complex biological networks as...
Biological Engineering Biology Biomedical Technologies
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MIT OCW
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Theory of Probability
Prof. Scott Sheffield
This course covers topics such as sums of independent random variables, central limit phenomena, infinitely...
Mathematics Science & Math
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MIT OCW
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Non-Equilibrium Statistical Mechanics
Jianshu Cao
This course discusses the principles and methods of non-equilibrium statistical mechanics. Basic topics covered are...
Chemistry Mathematics Physics
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MIT OCW
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Topics in Applied Mathematics: Waves and Imaging
Prof. Laurent Demanet
This class covers the mathematics of inverse problems involving waves, with examples taken from reflection...
Mathematics Science & Math
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MIT OCW
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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...
Mathematics Science & Math
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MIT OCW
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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,...
Mathematics Science & Math
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MIT OCW
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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...
Economics Mathematics Science & Math
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MIT OCW
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High-Dimensional Statistics
Prof. Philippe Rigollet
This course offers an introduction to the finite sample analysis of high- dimensional statistical methods. The goal...
Mathematics Science & Math
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MIT OCW
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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...
Mathematics Science & Math
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MIT OCW
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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...
Mathematics Science & Math
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MIT OCW
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Computational Quantum Mechanics of Molecular and Extended Systems
Prof. Bernhardt Trout
The theoretical frameworks of Hartree-Fock theory and density functional theory are presented in this course as...
Chemical Engineering Chemistry Engineering
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MIT OCW
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Numerical Methods for Partial Differential Equations (SMA 5212)
Prof. Boo Cheong Khoo
A presentation of the fundamentals of modern numerical techniques for a wide range of linear and nonlinear elliptic,...
Mathematics Science & Math
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MIT OCW
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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...
Mathematics Science & Math
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MIT OCW
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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...
Mathematics Science & Math
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MIT OCW
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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...
Mathematics Science & Math
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MIT OCW
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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...
Mathematics Science & Math
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MIT OCW
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Numerical Marine Hydrodynamics (13.024)
Prof. Jerome Milgram
This course is an introduction to numerical methods: interpolation, differentiation, integration, and systems of...
Engineering Mathematics Mechanical Engineering
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MIT OCW
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Statistical Physics in Biology
Prof. Mehran Kardar
Statistical Physics in Biology is a survey of problems at the interface of statistical physics and modern biology....
Biological Engineering Biology Engineering
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MIT OCW
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Nonlinear Dynamics II: Continuum Systems
Prof. Jörn Dunkel
This course introduces the basic ideas for understanding the dynamics of continuum systems, by studying specific...
Mathematics Physics Science & Math
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MIT OCW
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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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MIT OCW
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Topics in Algebraic Combinatorics
Prof. Richard Stanley
The course consists of a sampling of topics from algebraic combinatorics. The topics include the matrix-tree theorem...
Mathematics Science & Math
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MIT OCW
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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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MIT OCW
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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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MIT OCW
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Topics in Statistics: Nonparametrics and Robustness
Prof. Richard Dudley
This graduate-level course focuses on one-dimensional nonparametric statistics developed mainly from around 1945 and...
Mathematics Science & Math
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MIT OCW
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Noncommutative Algebra
Prof. Roman Bezrukavnikov
Noncommutative algebra studies algebraic phenomena involving multiplication for which commutativity law fails, such...
Mathematics Science & Math
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MIT OCW
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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...
Mathematics Science & Math
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MIT OCW
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Topics in Combinatorics: Analysis of Boolean Functions
Prof. Dor Minzer
In this course, we will mostly be studying Fourier analysis of Boolean functions, which is a useful tool in...
Mathematics Science & Math
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MIT OCW
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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...
Mathematics Science & Math
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MIT OCW
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Combinatorial Theory: Hyperplane Arrangements
Prof. Richard Stanley
This is a graduate-level course in combinatorial theory. The content varies year to year, according to the...
Mathematics Science & Math
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MIT OCW
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Topics in Algebraic Geometry: Algebraic Surfaces
Prof. Abhinav Kumar
The main aims of this seminar will be to go over the classification of surfaces (Enriques-Castelnuovo for...
Mathematics Science & Math
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MIT OCW
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Simplicity Theory
Dr. Itay Ben-Yaacov
This is an advanced topics course in model theory whose main theme is simple theories. We treat simple theories in...
Mathematics Science & Math
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MIT OCW
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Topics in Geometry: Dirac Geometry
Prof. Marco Gualtieri
This is an introductory (i.e. first year graduate students are welcome and expected) course in generalized geometry,...
Mathematics Science & Math
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MIT OCW
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Topics in Several Complex Variables
Prof. Victor Guillemin
This course covers harmonic theory on complex manifolds, the Hodge decomposition theorem, the Hard Lefschetz...
Mathematics Science & Math
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MIT OCW
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Strong Interactions: Effective Field Theories of QCD
Prof. Iain Stewart
This is a course in the construction and application of effective field theories, which are the modern tool of...
Physics Science & Math
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MIT OCW
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Topics in Lie Theory: Tensor Categories
Prof. Pavel Etingof
This course will give a detailed introduction to the theory of tensor categories and review some of its connections...
Mathematics Science & Math
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MIT OCW
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Universal Random Structures in 2D
Prof. Scott Sheffield
This graduate-level course introduces students to some fundamental 2D random objects, explains how they are related...
Mathematics Science & Math
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MIT OCW
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Classical Mechanics: A Computational Approach
Prof. Gerald Sussman
We will study the fundamental principles of classical mechanics, with a modern emphasis on the qualitative structure...
Engineering Physics Science & Math
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MIT OCW
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Double Affine Hecke Algebras in Representation Theory, Combinatorics, Geometry, and Mathematical Physics
Prof. Pavel Etingof
Double affine Hecke algebras (DAHA), also called Cherednik algebras, and their representations appear in many...
Mathematics Science & Math
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MIT OCW
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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...
Biological Engineering Biology Engineering
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MIT OCW
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Computational Models of Discourse
Prof. Regina Barzilay
This course is a graduate level introduction to automatic discourse processing. The emphasis will be on methods and...
AI Computer Science Data Science, Analytics & Computer Technology
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MIT OCW
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Introduction to Numerical Simulation (SMA 5211)
Prof. Jacob White
6.336J is an introduction to computational techniques for the simulation of a large variety of engineering and...
Engineering Systems Engineering
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MIT OCW
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System Identification
Prof. Munther Dahleh
This course is offered to graduates and includes topics such as mathematical models of systems from observations of...
Engineering Mathematics Science & Math
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MIT OCW
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Stochastic Processes, Detection, and Estimation
Prof. Gregory Wornell
This course examines the fundamentals of detection and estimation for signal processing, communications, and...
Electrical Engineering Engineering Mathematics
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MIT OCW
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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...
Business & Management Engineering Mathematics
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MIT OCW
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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...
Mathematics Physics Science & Math
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MIT OCW
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Topics in Algebraic Geometry: Intersection Theory on Moduli Spaces
Dr. Izzet Coskun
The topics for this course vary each semester. This semester, the course aims to introduce techniques for studying...
Mathematics Science & Math
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MIT OCW
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Special Seminar in Applied Probability and Stochastic Processes
Prof. David Gamarnik
This seminar is intended for doctoral students and discusses topics in applied probability. This semester includes a...
Mathematics Science & Math
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MIT OCW
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Topics in Algebraic Topology: The Sullivan Conjecture
Prof. Jacob Lurie
The goal of this course is to describe some of the tools which enter into the proof of Sullivan’s conjecture.
Mathematics Science & Math
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