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.)


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 courses, supplementary mathematics resources are also available. Various MIT faculty are openly sharing these resources as a service to OCW users. The resources include calculus textbooks by Professors Gilbert Strang and Daniel Kleitman.


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 Undergraduate
18.014 Calculus with Theory 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 Undergraduate
18.024 Multivariable Calculus with Theory 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 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 Undergraduate
18.091 Mathematical Exposition Undergraduate
18.098 Street-Fighting Mathematics Undergraduate
18.100A Introduction to Analysis Undergraduate
18.100B Analysis I Undergraduate
18.100C Real Analysis Undergraduate
18.101 Analysis II Undergraduate
18.102 Introduction to Functional Analysis Undergraduate
18.103 Fourier Analysis Undergraduate
18.104 Seminar in Analysis: Applications to Number Theory Undergraduate
18.112 Functions of a Complex Variable 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 Undergraduate
18.303 Linear Partial Differential Equations: Analysis and Numerics Undergraduate
18.303 Linear Partial Differential Equations Undergraduate
18.304 Undergraduate Seminar in Discrete Mathematics Undergraduate
18.310 Principles of Discrete Applied Mathematics Undergraduate
18.311 Principles of Applied Mathematics Undergraduate
18.312 Algebraic Combinatorics Undergraduate
18.314 Combinatorial Analysis Undergraduate
18.330 Introduction to Numerical Analysis (Spring 2012) Undergraduate
18.330 Introduction to Numerical Analysis (Spring 2004) Undergraduate
18.352J Theoretical Environmental Analysis Undergraduate
18.353J Nonlinear Dynamics I: Chaos Undergraduate
18.361J Introduction to Modeling and Simulation Undergraduate
18.400J Automata, Computability, and Complexity Undergraduate
18.410J Design and Analysis of Algorithms (Spring 2015) Undergraduate
18.410J Introduction to Algorithms (SMA 5503) Undergraduate
18.410J Design and Analysis of Algorithms (Spring 2012) Undergraduate
18.413 Error-Correcting Codes Laboratory Undergraduate
18.433 Combinatorial Optimization Undergraduate
18.440 Probability and Random Variables Undergraduate
18.443 Statistics for Applications (Spring 2015) Undergraduate
18.443 Statistics for Applications (Fall 2006) Undergraduate
18.443 Statistics for Applications (Fall 2003) Undergraduate
18.700 Linear Algebra (Fall 2013) Undergraduate
18.701 Algebra I Undergraduate
18.702 Algebra II Undergraduate
18.703 Modern Algebra Undergraduate
18.704 Seminar in Algebra and Number Theory: Computational Commutative Algebra and Algebraic Geometry Undergraduate
18.704 Seminar in Algebra and Number Theory: Rational Points on Elliptic Curves Undergraduate
18.712 Introduction to Representation Theory Undergraduate
18.781 Theory of Numbers Undergraduate
18.782 Introduction to Arithmetic Geometry Undergraduate
18.821 Project Laboratory in Mathematics Undergraduate
18.901 Introduction to Topology Undergraduate
18.904 Seminar in Topology Undergraduate
18.950 Differential Geometry Undergraduate
18.994 Seminar in Geometry Undergraduate
18.S096 Topics in Mathematics of Data Science Undergraduate
18.S096 Topics in Mathematics with Applications in Finance Undergraduate
18.S34 Problem Solving Seminar Undergraduate
18.S66 The Art of Counting Undergraduate
18.S997 Introduction To MATLAB Programming Undergraduate
18.075 Advanced Calculus for Engineers Graduate
18.085 Computational Science and Engineering I Graduate
18.086 Mathematical Methods for Engineers II Graduate
18.094J Teaching College-Level Science and Engineering (Spring 2009) Graduate
18.094J Teaching College-Level Science and Engineering (Fall 2012) Graduate
18.117 Topics in Several Complex Variables Graduate
18.125 Measure and Integration Graduate
18.155 Differential Analysis (Fall 2004) Graduate
18.156 Differential Analysis II: Partial Differential Equations and Fourier Analysis Graduate
18.156 Differential Analysis (Spring 2004) Graduate
18.175 Theory of Probability Graduate
18.177 Universal Random Structures in 2D Graduate
18.305 Advanced Analytic Methods in Science and Engineering Graduate
18.306 Advanced Partial Differential Equations with Applications Graduate
18.307 Integral Equations Graduate
18.315 Combinatorial Theory: Introduction to Graph Theory, Extremal and Enumerative Combinatorics Graduate
18.315 Combinatorial Theory: Hyperplane Arrangements Graduate
18.318 Topics in Algebraic Combinatorics Graduate
18.319 Geometric Combinatorics Graduate
18.325 Topics in Applied Mathematics: Waves and Imaging Graduate
18.327 Wavelets, Filter Banks and Applications 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 Graduate
18.337J Parallel Computing Graduate
18.338J Infinite Random Matrix Theory Graduate
18.354J Nonlinear Dynamics II: Continuum Systems Graduate
18.357 Interfacial Phenomena Graduate
18.366 Random Walks and Diffusion Graduate
18.369 Mathematical Methods in Nanophotonics Graduate
18.376J Wave Propagation Graduate
18.377J Nonlinear Dynamics and Waves Graduate
18.385J Nonlinear Dynamics and Chaos (Fall 2014) Graduate
18.385J Nonlinear Dynamics and Chaos (Fall 2004) Graduate
18.404J Theory of Computation Graduate
18.405J Advanced Complexity Theory Graduate
18.409 Algorithmic Aspects of Machine Learning Graduate
18.409 Topics in Theoretical Computer Science: An Algorithmist's Toolkit Graduate
18.409 Behavior of Algorithms Graduate
18.415J Advanced Algorithms (Fall 2008) Graduate
18.415J Advanced Algorithms (Fall 2005) Graduate
18.416J Randomized Algorithms Graduate
18.417 Introduction to Computational Molecular Biology Graduate
18.426J Advanced Topics in Cryptography Graduate
18.435J Quantum Computation Graduate
18.437J Distributed Algorithms Graduate
18.445 Introduction to Stochastic Processes Graduate
18.465 Topics in Statistics: Statistical Learning Theory Graduate
18.465 Topics in Statistics: Nonparametrics and Robustness Graduate
18.655 Mathematical Statistics Graduate
18.657 Mathematics of Machine Learning Graduate
18.705 Commutative Algebra 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 Graduate
18.727 Topics in Algebraic Geometry: Intersection Theory on Moduli Spaces Graduate
18.735 Double Affine Hecke Algebras in Representation Theory, Combinatorics, Geometry, and Mathematical Physics Graduate
18.755 Introduction to Lie Groups Graduate
18.769 Topics in Lie Theory: Tensor Categories Graduate
18.783 Elliptic Curves Graduate
18.785 Number Theory I 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 Graduate
18.906 Algebraic Topology II Graduate
18.915 Graduate Topology Seminar: Kan Seminar Graduate
18.917 Topics in Algebraic Topology: The Sullivan Conjecture Graduate
18.965 Geometry of Manifolds (Fall 2004) Graduate
18.966 Geometry of Manifolds (Spring 2007) Graduate
18.969 Topics in Geometry: Mirror Symmetry Graduate
18.969 Topics in Geometry: Dirac Geometry Graduate
18.996 Random Matrix Theory and Its Applications Graduate
18.996 Topics in Theoretical Computer Science : Internet Research Problems Graduate
18.996A Simplicity Theory Graduate
18.997 Topics in Combinatorial Optimization Graduate
18.S996 Category Theory for Scientists Graduate
18.S997 High-Dimensional Statistics Graduate
18.S997 The Polynomial Method Graduate

Archived Mathematics Courses

Some prior versions of courses listed above have been archived in OCW's DSpace@MIT 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.