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Mathematics


A pattern created by a fluid jet.

Surprising geometry emerges in the study of fluid jets. In this image, a vertical jet is deflected into a horizontal sheet by a horizontal impactor. At the sheet’s edge, fluid flows outward along bounding rims that collide to create fluid chains. (Photo courtesy A.E. Hasha and J.W.M. Bush.)

Featured Courses

An undergraduate degree in mathematics provides an excellent basis for graduate work in mathematics or computer science, or for employment in such mathematics-related fields as systems analysis, operations research, or actuarial science.

Because the career objectives of undergraduate mathematics majors are so diverse, each undergraduate’s program is individually arranged through collaboration between the student and his or her faculty advisor. In general, students are encouraged to explore the various branches of mathematics, both pure and applied.

Undergraduates seriously interested in mathematics are encouraged to elect an upper-level mathematics seminar. This is normally done during the junior year or the first semester of the senior year. The experience gained from active participation in a seminar conducted by a research mathematician is particularly valuable for a student planning to pursue graduate work.

There are three undergraduate programs that lead to the degree Bachelor’s of Science in Mathematics: a General Mathematics Option, an Applied Mathematics Option for those who wish to specialize in that aspect of mathematics, and a Theoretical Mathematics Option for those who expect to pursue graduate work in pure mathematics. A fourth undergraduate program leads to the degree Bachelor’s of Science in Mathematics with Computer Science; it is intended for students seriously interested in theoretical computer science.

In addition to the Mathematics courses listed below, see also OCW’s Supplemental Resources associated with the department.


Mathematics

Courses

    • Course #
    • Course Title
    • Level
    • 18.01SC

    • Single Variable Calculus
      (Fall 2010)

    • Undergraduate

    • 18.01

    • Single Variable Calculus
      (Fall 2006)

    • Undergraduate

    • 18.01

    • Single Variable Calculus
      (Fall 2005)

    • Undergraduate

    • 18.013A

    • Calculus with Applications
      (Spring 2005)

    • Undergraduate

    • 18.014

    • Calculus with Theory
      (Fall 2010)

    • Undergraduate

    • 18.02SC

    • Multivariable Calculus
      (Fall 2010)

    • Undergraduate

    • 18.02

    • Multivariable Calculus
      (Fall 2007)

    • Undergraduate

    • 18.02

    • Multivariable Calculus
      (Spring 2006)

    • Undergraduate

    • 18.022

    • Calculus of Several Variables
      (Fall 2010)

    • Undergraduate

    • 18.024

    • Multivariable Calculus with Theory
      (Spring 2011)

    • Undergraduate

    • 18.03SC

    • Differential Equations
      (Fall 2011)

    • Undergraduate

    • 18.03

    • Differential Equations
      (Spring 2010)

    • Undergraduate

    • 18.034

    • Honors Differential Equations
      (Spring 2009)

    • Undergraduate

    • 18.034

    • Honors Differential Equations
      (Spring 2004)

    • Undergraduate

    • 18.04

    • Complex Variables with Applications
      (Fall 2003)

    • Undergraduate

    • 18.04

    • Complex Variables with Applications
      (Fall 1999)

    • Undergraduate

    • 18.05

    • Introduction to Probability and Statistics
      (Spring 2014)

    • Undergraduate

    • 18.06SC

    • Linear Algebra
      (Fall 2011)

    • Undergraduate

    • 18.06

    • Linear Algebra
      (Spring 2010)

    • Undergraduate

    • 18.062J

    • Mathematics for Computer Science
      (Fall 2010)

    • Undergraduate

    • 18.062J

    • Mathematics for Computer Science
      (Fall 2005)

    • Undergraduate

    • 18.062J

    • Mathematics for Computer Science
      (Spring 2015)

    • Undergraduate

    • 18.06CI

    • Linear Algebra – Communications Intensive
      (Spring 2004)

    • Undergraduate

    • 18.091

    • Mathematical Exposition
      (Spring 2005)

    • Undergraduate

    • 18.098

    • Street-Fighting Mathematics
      (January IAP 2008)

    • Undergraduate

    • 18.100A

    • Introduction to Analysis
      (Fall 2012)

    • Undergraduate

    • 18.100B

    • Analysis I
      (Fall 2010)

    • Undergraduate

    • 18.100C

    • Real Analysis
      (Fall 2012)

    • Undergraduate

    • 18.101

    • Analysis II
      (Fall 2005)

    • Undergraduate

    • 18.102

    • Introduction to Functional Analysis
      (Spring 2009)

    • Undergraduate

    • 18.103

    • Fourier Analysis
      (Fall 2013)

    • Undergraduate

    • 18.104

    • Seminar in Analysis: Applications to Number Theory
      (Fall 2006)

    • Undergraduate

    • 18.112

    • Functions of a Complex Variable
      (Fall 2008)

    • Undergraduate

    • 18.152

    • Introduction to Partial Differential Equations
      (Fall 2011)

    • Undergraduate

    • 18.152

    • Introduction to Partial Differential Equations
      (Fall 2005)

    • Undergraduate

    • 18.238

    • Geometry and Quantum Field Theory
      (Fall 2002)

    • Undergraduate

    • 18.303

    • Linear Partial Differential Equations: Analysis and Numerics
      (Fall 2014)

    • Undergraduate

    • 18.303

    • Linear Partial Differential Equations
      (Fall 2006)

    • Undergraduate

    • 18.304

    • Undergraduate Seminar in Discrete Mathematics
      (Spring 2015)

    • Undergraduate

    • 18.310

    • Principles of Discrete Applied Mathematics
      (Fall 2013)

    • Undergraduate

    • 18.311

    • Principles of Applied Mathematics
      (Spring 2014)

    • Undergraduate

    • 18.312

    • Algebraic Combinatorics
      (Spring 2009)

    • Undergraduate

    • 18.314

    • Combinatorial Analysis
      (Fall 2014)

    • Undergraduate

    • 18.330

    • Introduction to Numerical Analysis
      (Spring 2012)

    • Undergraduate

    • 18.330

    • Introduction to Numerical Analysis
      (Spring 2004)

    • Undergraduate

    • 18.352J

    • Theoretical Environmental Analysis
      (Spring 2015)

    • Undergraduate

    • 18.353J

    • Nonlinear Dynamics I: Chaos
      (Fall 2012)

    • Undergraduate

    • 18.361J

    • Introduction to Modeling and Simulation
      (Spring 2012)

    • Undergraduate

    • 18.400J

    • Automata, Computability, and Complexity
      (Spring 2011)

    • Undergraduate

    • 18.410J

    • Design and Analysis of Algorithms
      (Spring 2015)

    • Undergraduate

    • 18.410J

    • Introduction to Algorithms (SMA 5503)
      (Fall 2005)

    • Undergraduate

    • 18.410J

    • Design and Analysis of Algorithms
      (Spring 2012)

    • Undergraduate

    • 18.413

    • Error-Correcting Codes Laboratory
      (Spring 2004)

    • Undergraduate

    • 18.433

    • Combinatorial Optimization
      (Fall 2003)

    • Undergraduate

    • 18.440

    • Probability and Random Variables
      (Spring 2014)

    • Undergraduate

    • 18.650

    • Statistics for Applications
      (Fall 2016)

    • Undergraduate

    • 18.650

    • Statistics for Applications (formerly 18.443)
      (Spring 2015)

    • Undergraduate

    • 18.650

    • Statistics for Applications (formerly 18.443)
      (Fall 2006)

    • Undergraduate

    • 18.650

    • Statistics for Applications (formerly 18.443)
      (Fall 2003)

    • Undergraduate

    • 18.700

    • Linear Algebra
      (Fall 2013)

    • Undergraduate

    • 18.701

    • Algebra I
      (Fall 2010)

    • Undergraduate

    • 18.702

    • Algebra II
      (Spring 2011)

    • Undergraduate

    • 18.703

    • Modern Algebra
      (Spring 2013)

    • Undergraduate

    • 18.704

    • Seminar in Algebra and Number Theory: Computational Commutative Algebra and Algebraic Geometry
      (Fall 2008)

    • Undergraduate

    • 18.704

    • Seminar in Algebra and Number Theory: Rational Points on Elliptic Curves
      (Fall 2004)

    • Undergraduate

    • 18.712

    • Introduction to Representation Theory
      (Fall 2010)

    • Undergraduate

    • 18.781

    • Theory of Numbers
      (Spring 2012)

    • Undergraduate

    • 18.782

    • Introduction to Arithmetic Geometry
      (Fall 2013)

    • Undergraduate

    • 18.821

    • Project Laboratory in Mathematics
      (Spring 2013)

    • Undergraduate

    • 18.901

    • Introduction to Topology
      (Fall 2004)

    • Undergraduate

    • 18.904

    • Seminar in Topology
      (Spring 2011)

    • Undergraduate

    • 18.950

    • Differential Geometry
      (Fall 2008)

    • Undergraduate

    • 18.994

    • Seminar in Geometry
      (Fall 2004)

    • Undergraduate

    • 18.S096

    • Topics in Mathematics of Data Science
      (Fall 2015)

    • Undergraduate

    • 18.S096

    • Topics in Mathematics with Applications in Finance
      (Fall 2013)

    • Undergraduate

    • 18.S34

    • Problem Solving Seminar
      (Fall 2007)

    • Undergraduate

    • 18.S66

    • The Art of Counting
      (Spring 2003)

    • Undergraduate

    • 18.S997

    • Introduction To MATLAB Programming
      (Fall 2011)

    • Undergraduate

    • 18.075

    • Advanced Calculus for Engineers
      (Fall 2004)

    • Graduate

    • 18.085

    • Computational Science and Engineering I
      (Fall 2008)

    • Graduate

    • 18.086

    • Mathematical Methods for Engineers II
      (Spring 2006)

    • Graduate

    • 18.094J

    • Teaching College-Level Science and Engineering
      (Fall 2015)

    • Graduate

    • 18.094J

    • Teaching College-Level Science and Engineering
      (Spring 2009)

    • Graduate

    • 18.117

    • Topics in Several Complex Variables
      (Spring 2005)

    • Graduate

    • 18.125

    • Measure and Integration
      (Fall 2003)

    • Graduate

    • 18.155

    • Differential Analysis
      (Fall 2004)

    • Graduate

    • 18.156

    • Differential Analysis II: Partial Differential Equations and Fourier Analysis
      (Spring 2016)

    • Graduate

    • 18.156

    • Differential Analysis
      (Spring 2004)

    • Graduate

    • 18.175

    • Theory of Probability
      (Spring 2014)

    • Graduate

    • 18.177

    • Universal Random Structures in 2D
      (Fall 2015)

    • Graduate

    • 18.305

    • Advanced Analytic Methods in Science and Engineering
      (Fall 2004)

    • Graduate

    • 18.306

    • Advanced Partial Differential Equations with Applications
      (Fall 2009)

    • Graduate

    • 18.307

    • Integral Equations
      (Spring 2006)

    • Graduate

    • 18.315

    • Combinatorial Theory: Introduction to Graph Theory, Extremal and Enumerative Combinatorics
      (Spring 2005)

    • Graduate

    • 18.315

    • Combinatorial Theory: Hyperplane Arrangements
      (Fall 2004)

    • Graduate

    • 18.318

    • Topics in Algebraic Combinatorics
      (Spring 2006)

    • Graduate

    • 18.319

    • Geometric Combinatorics
      (Fall 2005)

    • Graduate

    • 18.325

    • Topics in Applied Mathematics: Waves and Imaging
      (Fall 2015)

    • Graduate

    • 18.327

    • Wavelets, Filter Banks and Applications
      (Spring 2003)

    • Graduate

    • 18.335J

    • Introduction to Numerical Methods
      (Fall 2010)

    • Graduate

    • 18.335J

    • Introduction to Numerical Methods
      (Fall 2004)

    • Graduate

    • 18.336

    • Numerical Methods for Partial Differential Equations
      (Spring 2009)

    • Graduate

    • 18.337J

    • Parallel Computing
      (Fall 2011)

    • Graduate

    • 18.338J

    • Infinite Random Matrix Theory
      (Fall 2004)

    • Graduate

    • 18.354J

    • Nonlinear Dynamics II: Continuum Systems
      (Spring 2015)

    • Graduate

    • 18.357

    • Interfacial Phenomena
      (Fall 2010)

    • Graduate

    • 18.366

    • Random Walks and Diffusion
      (Fall 2006)

    • Graduate

    • 18.369

    • Mathematical Methods in Nanophotonics
      (Spring 2008)

    • Graduate

    • 18.376J

    • Wave Propagation
      (Spring 2017)

    • Graduate

    • 18.377J

    • Nonlinear Dynamics and Waves
      (Spring 2007)

    • Graduate

    • 18.385J

    • Nonlinear Dynamics and Chaos
      (Fall 2014)

    • Graduate

    • 18.385J

    • Nonlinear Dynamics and Chaos
      (Fall 2004)

    • Graduate

    • 18.404J

    • Theory of Computation
      (Fall 2006)

    • Graduate

    • 18.405J

    • Advanced Complexity Theory
      (Spring 2016)

    • Graduate

    • 18.409

    • Algorithmic Aspects of Machine Learning
      (Spring 2015)

    • Graduate

    • 18.409

    • Topics in Theoretical Computer Science: An Algorithmist’s Toolkit
      (Fall 2009)

    • Graduate

    • 18.409

    • Behavior of Algorithms
      (Spring 2002)

    • Graduate

    • 18.415J

    • Advanced Algorithms
      (Fall 2008)

    • Graduate

    • 18.415J

    • Advanced Algorithms
      (Fall 2005)

    • Graduate

    • 18.416J

    • Randomized Algorithms
      (Fall 2002)

    • Graduate

    • 18.417

    • Introduction to Computational Molecular Biology
      (Fall 2004)

    • Graduate

    • 18.426J

    • Advanced Topics in Cryptography
      (Spring 2003)

    • Graduate

    • 18.435J

    • Quantum Computation
      (Fall 2003)

    • Graduate

    • 18.437J

    • Distributed Algorithms
      (Fall 2009)

    • Graduate

    • 18.445

    • Introduction to Stochastic Processes
      (Spring 2015)

    • Graduate

    • 18.465

    • Topics in Statistics: Statistical Learning Theory
      (Spring 2007)

    • Graduate

    • 18.465

    • Topics in Statistics: Nonparametrics and Robustness
      (Spring 2005)

    • Graduate

    • 18.6501

    • Statistics for Applications
      (Fall 2016)

    • Graduate

    • 18.655

    • Mathematical Statistics
      (Spring 2016)

    • Graduate

    • 18.657

    • Mathematics of Machine Learning
      (Fall 2015)

    • Graduate

    • 18.705

    • Commutative Algebra
      (Fall 2008)

    • Graduate

    • 18.725

    • Algebraic Geometry
      (Fall 2015)

    • Graduate

    • 18.725

    • Algebraic Geometry
      (Fall 2003)

    • Graduate

    • 18.726

    • Algebraic Geometry
      (Spring 2009)

    • Graduate

    • 18.727

    • Topics in Algebraic Geometry: Algebraic Surfaces
      (Spring 2008)

    • Graduate

    • 18.727

    • Topics in Algebraic Geometry: Intersection Theory on Moduli Spaces
      (Spring 2006)

    • Graduate

    • 18.735

    • Double Affine Hecke Algebras in Representation Theory, Combinatorics, Geometry, and Mathematical Physics
      (Fall 2009)

    • Graduate

    • 18.755

    • Introduction to Lie Groups
      (Fall 2004)

    • Graduate

    • 18.769

    • Topics in Lie Theory: Tensor Categories
      (Spring 2009)

    • Graduate

    • 18.783

    • Elliptic Curves
      (Spring 2017)

    • Graduate

    • 18.785

    • Number Theory I
      (Fall 2017)

    • Graduate

    • 18.786

    • Number Theory II: Class Field Theory
      (Spring 2016)

    • Graduate

    • 18.786

    • Topics in Algebraic Number Theory
      (Spring 2010)

    • Graduate

    • 18.786

    • Topics in Algebraic Number Theory
      (Spring 2006)

    • Graduate

    • 18.905

    • Algebraic Topology I
      (Fall 2016)

    • Graduate

    • 18.906

    • Algebraic Topology II
      (Spring 2006)

    • Graduate

    • 18.915

    • Graduate Topology Seminar: Kan Seminar
      (Fall 2014)

    • Graduate

    • 18.917

    • Topics in Algebraic Topology: The Sullivan Conjecture
      (Fall 2007)

    • Graduate

    • 18.965

    • Geometry of Manifolds
      (Fall 2004)

    • Graduate

    • 18.966

    • Geometry of Manifolds
      (Spring 2007)

    • Graduate

    • 18.969

    • Topics in Geometry: Mirror Symmetry
      (Spring 2009)

    • Graduate

    • 18.969

    • Topics in Geometry: Dirac Geometry
      (Fall 2006)

    • Graduate

    • 18.996

    • Random Matrix Theory and Its Applications
      (Spring 2004)

    • Graduate

    • 18.996

    • Topics in Theoretical Computer Science : Internet Research Problems
      (Spring 2002)

    • Graduate

    • 18.996A

    • Simplicity Theory
      (Spring 2004)

    • Graduate

    • 18.997

    • Topics in Combinatorial Optimization
      (Spring 2004)

    • Graduate

    • 18.S996

    • Category Theory for Scientists
      (Spring 2013)

    • Graduate

    • 18.S997

    • High-Dimensional Statistics
      (Spring 2015)

    • Graduate

    • 18.S997

    • The Polynomial Method
      (Fall 2012)

    • Graduate

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Welcome!

This page lists OCW courses from just one of over 30 MIT departments.

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Archived Mathematics Courses

Some prior versions of courses listed above have been archived in OCW’s [email protected] repository for long-term access and preservation. Links to archived prior versions of a course may be found on that course’s "Other Versions" tab.

Additionally, the Archived Mathematics Courses page has links to every archived course from this department.

Mathematics Links

  • Department Website
  • Department Curriculum
  • Supplemental Resources