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Mathematics
Mathematics
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
Introduction to Probability and Statistics
Linear Algebra
Introduction to Analysis
Differential Analysis II: Partial Differential Equations and Fourier Analysis
Single Variable Calculus
Introduction to Topology
Street-Fighting Mathematics
Elliptic Curves
Algebraic Topology I
Number Theory I
Topics in Applied Mathematics: Waves and Imaging
Number Theory II: Class Field Theory
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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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