Open Courses from
Massachusetts Institute of Technology (MIT)

Advanced Analytic Methods in Science and Engineering
Hung Cheng, Math — Massachusetts Institute of Technology (MIT)
Fall 2004This course provides a comprehensive look at advanced methods of applied mathematics.

Advanced Calculus for Engineers
Dionisios Margetis, John W. M. Bush, Math — Massachusetts Institute of Technology (MIT)
Fall 2004This course explains complex variable functions and calculus of residues.

Advanced Complexity Theory
Daniel Spielman, Math — Massachusetts Institute of Technology (MIT)
Fall 2001This is a theorybased class that explores topics in complexity theory.

Topics covered in this undergraduatelevel course include groups, vector spaces, linear transformations, symmetry groups, bilinear forms, and linear groups.

Algebra II
Michael Artin, Math — Massachusetts Institute of Technology (MIT)
Spring 2011Intended to follow Algebra I, topics covered in this undergrad course include group representations, rings, ideals, fields, polynomial rings, modules, factorization, integers in quadratic number fields, field extensions, and Galois theory.

Algebraic Combinatorics
Gregg Musiker, Math — Massachusetts Institute of Technology (MIT)
Spring 2009Students in this course are expected to have a background in basic linear algebra and finite groups, to learn the fundamentals of combinatorics.

In this class about algebraic geometry, students discuss fundamentals of algebraic varieties.

This course focuses on homology and cohomology theory in an introduction to algebraic topology.

The second course in algebraic topoology covers a variety of theories and applications.

This course covers the foundational principles of mathematical analysis.

This course covers multivariable calculus, theory of differential forms in ndimensional vector spaces, and manifolds.

In this class on analytic number theory, students explore various prime number theories.

Ancient Philosophy and Mathematics
Lee Perlman, Math — Massachusetts Institute of Technology (MIT)
Fall 2009In this course, students will learn about the ties between Western philosophy and theoretical mathematics.

Behavior of Algorithms
Daniel Spielman, Math — Massachusetts Institute of Technology (MIT)
Spring 2002This course discusses the behavior of algorithms and theoretical computer science.

Calculus of Several Variables
James McKernan, Math — Massachusetts Institute of Technology (MIT)
Fall 2010This course covers the intensive study of mathematical concepts in severalvariable calculus.

Calculus with Applications
Daniel Kleitman, Math — Massachusetts Institute of Technology (MIT)
Spring 2005This course for undergrads covers differential calculus in one and multiple dimensions.

Calculus with Theory
Christine Breiner, Math — Massachusetts Institute of Technology (MIT)
Fall 2010This course provides rigorous study of proofs, as an extension of elementary calculus.

Combinatorial Analysis
Alexander Postnikov, Math — Massachusetts Institute of Technology (MIT)
Fall 2005This course analyzes combinatorial problems and investigates various solutions.

Combinatorial Optimization
Santosh Vempala, Math — Massachusetts Institute of Technology (MIT)
Fall 2003This course provides an intensive explanation of linear programming and combinatorial optimization.

Combinatorial Theory: Hyperplane Arrangements
Richard Stanley, Math — Massachusetts Institute of Technology (MIT)
Fall 2004This graduate course explores modern enumerative and algebraic combinatorics and hyperplane arrangements in depth.

Combinatorial Theory: Introduction to Graph Theory, Extremal and Enumerative Combinatorics
Igor Pak, Math — Massachusetts Institute of Technology (MIT)
Spring 2005This class offers an introduction to modern enumerative and algebraic combinatorics.

This class provides an introduction to commutative algebra theories and applications, like Hilbert basis theorem, ClayeyHamilton theorem, integral dependence and more.

Complex Variables with Applications
Alar Toomre, Math — Massachusetts Institute of Technology (MIT)
Fall 2003Students in this course explore topics in complex algebra and its functions.

Computational Geometry
Nicholas Patrikalakis, Takashi Maekawa, Math — Massachusetts Institute of Technology (MIT)
N/AThis course will address the various aspects of computational geometry, covering topics that include bsplines, offsets, boundary representation models, and physically based deformable surfaces.

Computational Science and Engineering I
Gilbert Strang, Math — Massachusetts Institute of Technology (MIT)
Fall 2008Through this course students review various principles and applications of linear algebra.

This course is first in a twosemester sequence, covering various topics in differential analysis in mathematics.

Differential Analysis
Jeff Viaclovsky, Math — Massachusetts Institute of Technology (MIT)
Spring 2004This course is second in a twosemester sequence, providing a thorough foundation in elliptic and parabolic linear partial differential equations theory.

Differential Equations
Arthur Mattuck, Haynes Miller, Jeremy Orloff, John Lewis, Math — Massachusetts Institute of Technology (MIT)
Fall 2011In this course students learn about the math equations and techniques commonly used in science and engineering.

With a concentration on geometry and the notion of curvature, this course introduces differential geometry.

Double Affine Hecke Algebras in Representation Theory, Combinatorics, Geometry, and Mathematical Physics
Pavel Etingof, Math — Massachusetts Institute of Technology (MIT)
Fall 2009In this class, students will discuss the representation of Double affine Hecke algebras (DAHA) in a number of different contexts.

ErrorCorrecting Codes Laboratory
Daniel Spielman, Math — Massachusetts Institute of Technology (MIT)
Spring 2004In this course students will be introduced to iterative decoding algorithms and their related codes.

Fourier Analysis  Theory and Applications
Richard Melrose, Math — Massachusetts Institute of Technology (MIT)
Spring 2004This course is intended to follow an introductory analysis course, emphasizing theory of the Lebesgue integral, Fourier series, and Fourier integrals.

Functions of a Complex Variable
Sigurdur Helgason, Math — Massachusetts Institute of Technology (MIT)
Fall 2008Intended for advancedlevel graduate students, this course explores one complex variablecalculus with geometric emphasis.

In this class, students will discuss teaching methods in combinatorial geometry and receive an introduction to discrete and computational geometry.

This course from MIT explores geometric folding, including linkages, origami, and polyhedra.

Geometry and Quantum Field Theory
Pavel Etingof, Math — Massachusetts Institute of Technology (MIT)
Fall 2002Geared toward math majors, this course provides an intensive introduction to perturbative quantum field theory, through functional integrals language.

This graduate level course discusses the geometry of manifolds and dives into topics like Lie groups, differentiable manifolds, and vector fields.

Honors Differential Equations
Vera Mikyoung Hur, Math — Massachusetts Institute of Technology (MIT)
Spring 2009This course is an extension of differential equations studies, with added emphasis on mathematical theory.

Infinite Random Matrix Theory
Fall 2004In this class, students will learn about theories and methods behind the characterization of infinite random matrices.

Integral Equations
Dionisios Margetis, Math — Massachusetts Institute of Technology (MIT)
Spring 2006In this class, students explore theories and techniques and applied mathematics perspectives on solving integral equations.

Introduction to Analysis
Arthur Mattuck, Math — Massachusetts Institute of Technology (MIT)
Fall 2012This course provides a gentle, nontraditional introduction to the various elements of mathematical analysis.

Introduction to Functional Analysis
Richard Melrose, Math — Massachusetts Institute of Technology (MIT)
Spring 2009This course covers various functions and operators in functional mathematical analysis.

Introduction to Lie Groups
Sigurdur Helgason, Math — Massachusetts Institute of Technology (MIT)
Fall 2004Drawing from the text Differential Geometry, Lie Groups and Symmetric Spaces by Sigurdur Helgason, this class focuses on the theory of Lie groups and its connection to differential geometry.

Introduction To MATLAB Programming
Yossi Farjoun, Math — Massachusetts Institute of Technology (MIT)
Fall 2011This course examines the basics of general and MATLAB

Introduction to Numerical Analysis
Laurent Demanet, Math — Massachusetts Institute of Technology (MIT)
Spring 2012The curriculum in this course is centered on basic techniques for efficiency in numerical science and engineering problems and solutions.

Introduction to Numerical Methods
Steven G. Johnson, Math — Massachusetts Institute of Technology (MIT)
Fall 2010This course covers advanced introductory topics in numerical linear algebra.

Introduction to Partial Differential Equations
Jared Speck, Math — Massachusetts Institute of Technology (MIT)
Fall 2011This course explores diffusion, elliptic, and hyperbolic as the three main types of partial differential equations.

Introduction to Probability and Statistics
Dmitry Panchenko, Math — Massachusetts Institute of Technology (MIT)
Spring 2005This course provides a basic introduction to practical probability and statistics.

Introduction to Representation Theory
Pavel Etingof, Math — Massachusetts Institute of Technology (MIT)
Fall 2010This course provides an introduction of representation theory to undergraduatelevel students.

Introduction to Topology
James Munkres, Math — Massachusetts Institute of Technology (MIT)
Fall 2004This course explores various introductory topics in topology, including fundamental to modern analysis and geometry.

In this course students learn about matrix theory and linear algebra.

Linear Algebra  Communications Intensive
Andrew BrookeTaylor, Anna Lachowska, Math — Massachusetts Institute of Technology (MIT)
Spring 2004Intended as a supplement to linear algebra, this course provides a communicationsbased intensive study in the subject.

Linear Partial Differential Equations
Matthew Hancock, Math — Massachusetts Institute of Technology (MIT)
Fall 2006This course covers classical partial differential equations of applied mathematics.

Linear Partial Differential Equations: Analysis and Numerics
Steven G. Johnson, Math — Massachusetts Institute of Technology (MIT)
Fall 2010This course explains the basic analytical and computational tools of linear partial differential equations for practical use.

Mathematical Exposition
Emma Carberry, Math — Massachusetts Institute of Technology (MIT)
Spring 2005This course teaches students how to effectively present mathematical material.

Mathematical Methods for Engineers II
Gilbert Strang, Math — Massachusetts Institute of Technology (MIT)
Spring 2006Intended to follow Mathematical Methods for Engineers I, this graduatelevel course explores numerical methods, initialvalue problems, network flows, and optimization.

Mathematical Methods in Nanophotonics
Steven G. Johnson, Math — Massachusetts Institute of Technology (MIT)
Spring 2008In this class, students will explore the physical and mathematical components of nanophotonics.

Mathematical Statistics
Richard Dudley, Math — Massachusetts Institute of Technology (MIT)
Spring 2003Students will learn about decision theory, estimation, confidence intervals, hypothesis testing, and sample theory in this course, which is based on a book by the professor, Richard Dudley.

Measure and Integration
Jeff Viaclovsky, Math — Massachusetts Institute of Technology (MIT)
Fall 2003In this graduatelevel course students are introduced to Lebesgue's integration theory, as well as convolution and the Fourier transform.

In this course students explore differential, integral and vector calculus for multivariable functions.

Multivariable Calculus with Theory
Christine Breiner, Math — Massachusetts Institute of Technology (MIT)
Spring 2011This is the second in a twopart course in multivariable calculus, but with added emphasis on reasoning and understanding of proofs.

Nonlinear Dynamics and Chaos
Rodolfo R. Rosales, Math — Massachusetts Institute of Technology (MIT)
Fall 2004This class uses demonstration software to illustrate nonlinear dynamics with applications.

Numerical Methods for Partial Differential Equations
Benjamin Seibold, Math — Massachusetts Institute of Technology (MIT)
Spring 2009This course discusses fundamental ideas behind numerical methods for solving partial differential equations.

Principles of Applied Mathematics
Aslan Kasimov, Math — Massachusetts Institute of Technology (MIT)
Spring 2009This course explores how to mathematically analyze the continuum models of a variety of natural phenomena.

Probability and Random Variables
Scott Sheffield, Math — Massachusetts Institute of Technology (MIT)
Spring 2011Students are introduced to probability and random variables in this course.

Problem Solving Seminar
Hartley Rogers, Kiran Kedlaya, Richard Stanley, Math — Massachusetts Institute of Technology (MIT)
Fall 2007In this undergraduate seminar course, students explore various techniques for mathematical problemsolving.

In this class, students will discuss basic theories in quantum computation for practical application.

Quantum Information Science
Isaac Chuang, Math — Massachusetts Institute of Technology (MIT)
Spring 2006This course is for advanced graduates and educates on quantum computation and quantum information, which requires prior knowledge of quantum mechanics.

Random Matrix Theory and Its Applications
Spring 2004This class explores engineering and scientific applications in basic random matrix theory.

Random Walks and Diffusion
Martin Bazant, Math — Massachusetts Institute of Technology (MIT)
Fall 2006This class discusses various application in random walks and diffusion.

Students will learn about the fundamentals of mathematical analysis in this course, covering topics such as convergence of sequences and series, continuity, and differentiability.

Seminar in Algebra and Number Theory: Computational Commutative Algebra and Algebraic Geometry
Steven Kleiman, Math — Massachusetts Institute of Technology (MIT)
Fall 2008Topics in this undergraduatelevel studentled seminar course may include computational algebra and algebraic geometry.

Seminar in Algebra and Number Theory: Rational Points on Elliptic Curves
Daniel Rogalski, Math — Massachusetts Institute of Technology (MIT)
Fall 2004Students present a variety of topics in algebra and number theory in this seminar class led by math majors.

Seminar in Analysis: Applications to Number Theory
Dan Ciubotaru, Math — Massachusetts Institute of Technology (MIT)
Fall 2006Undergraduate math majors in this seminar course integrate current journals and books into group discussions on analysis.

Students take turns giving lectures on Robert Osserman's classic book A Survey of Minimal Surfaces in this course.

Students in this seminar are introduced to topology, covering topics including fundamental group, homology, and cohomology in mathematical terms.

This course explores major concepts in the study of simple theories.

Single Variable Calculus
David Jerison, Math — Massachusetts Institute of Technology (MIT)
Fall 2010Students in this course study differentiation and integration of onevariable functions, and also touches on the infinite series.

Statistics for Applications
Richard Dudley, Math — Massachusetts Institute of Technology (MIT)
Spring 2009This course presents a broad interpretation of statistics, with a focus on science and industry statistical techniques.

In this course students explore ways to research counting the number of elements of a finite set.

The Mathematics in Toys and Games
Spring 2010In this course, students will explore mathematical strategies behind popular toys, games, and puzzles.

In this class, students will participate in advanced discussions about computability and complexity.

Students in this course will learn elementary principles in number theory with no algebraic prerequisites.

Theory of Probability
Dmitry Panchenko, Math — Massachusetts Institute of Technology (MIT)
Fall 2008In this course students will explore the laws of large numbers and central limit theorems for sums of independent random variables.

Topics in Algebraic Combinatorics
Richard Stanley, Math — Massachusetts Institute of Technology (MIT)
Spring 2006This class is a survey of major topics in algebraic combinatorics.

Topics in Algebraic Geometry: Algebraic Surfaces
Abhinav Kumar, Math — Massachusetts Institute of Technology (MIT)
Spring 2008This course in algebraic geometry focuses on algebraic surfaces, the classification of surfaces, and various applications.

Topics in Algebraic Geometry: Intersection Theory on Moduli Spaces
Izzet Coskun, Math — Massachusetts Institute of Technology (MIT)
Spring 2006This course covers varying subject in algebraic geometry each semester, with this section covering intersection theory on moduli spaces.

Topics in Algebraic Number Theory
Abhinav Kumar, Math — Massachusetts Institute of Technology (MIT)
Spring 2010This course covers various introductory topics in algebraic number theory.

Topics in Algebraic Topology: The Sullivan Conjecture
Jacob Lurie, Math — Massachusetts Institute of Technology (MIT)
Fall 2007Taught by Jacob Lurie, this course on algebraic topology focuses on Sullivan's conjecture.

Topics in Combinatorial Optimization
Michel Goemans, Math — Massachusetts Institute of Technology (MIT)
Spring 2004In this class geared toward doctoral students, advanced theories in combinatorial optimization are discussed.

Topics in Geometry: Dirac Geometry
Marco Gualtieri, Math — Massachusetts Institute of Technology (MIT)
Fall 2006This class covering selected topics in generalized geometry focuses on Dirac geometry and generalized complex geometry.

Topics in Geometry: Mirror Symmetry
Denis Auroux, Math — Massachusetts Institute of Technology (MIT)
Spring 2009Students who are familiar with symplectic and complex geometry will explore mirror symmetry in this graduate level course.

Topics in Lie Theory: Tensor Categories
Pavel Etingof, Math — Massachusetts Institute of Technology (MIT)
Spring 2009This class provides students with a thorough introduction to theory of tensor categories and their connection to various ring theories.

Topics in Several Complex Variables
Victor Guillemin, Math — Massachusetts Institute of Technology (MIT)
Spring 2005This course covers various topics including complex manifold harmonic theory, the Hodge decomposition theorem, the Hard Lefschetz theorem, and Vanishing theorems.

Topics in Statistics: Nonparametrics and Robustness
Richard Dudley, Math — Massachusetts Institute of Technology (MIT)
Spring 2005In this class, students learn about early 20th century onedimensional nonparametric statistics.

Topics in Statistics: Statistical Learning Theory
Dmitry Panchenko, Math — Massachusetts Institute of Technology (MIT)
Spring 2007This class explores empirical process theory and other machine learning algorithms.

Topics in Theoretical Computer Science: An Algorithmist's Toolkit
Jonathan Kelner, Math — Massachusetts Institute of Technology (MIT)
Fall 2009This course covers geometric applications in modern algorithm design.

Topics in Theoretical Computer Science: Internet Research Problems
Bruce Maggs, Math — Massachusetts Institute of Technology (MIT)
Spring 2002In this class, students will discuss and research current mathematical issues affecting the internet.

Undergraduate Seminar in Discrete Mathematics
Daniel Kleitman, Math — Massachusetts Institute of Technology (MIT)
Spring 2006This is a seminarbased course presented by students that covers combinatorics, graph theory, and discrete mathematics in general.

Wavelets, Filter Banks and Applications
Gilbert Strang, Math — Massachusetts Institute of Technology (MIT)
Spring 2003In this class, students learn how to use wavelets to represent short term events.