The Pure Mathematics Program is designed to provide broad training in basic modern mathematics including an introduction to the methods of rigorous mathematical proof and exposure to the major branches of mathematics: Algebra, Analysis, and Geometry/Topology.

The prerequisite to major in Pure Mathematics is one of the sequences 215 & 217, 255 & 217, or 295 & 296. Note that Math 216 is not intended for Mathematics majors.

All Pure Mathematics majors are also strongly encouraged to take Physics 140-141 and 240-241 and to acquire a working knowledge of a high-level computer language (e.g. Fortran, C, or C++) at a level equivalent to the completion of EECS 183.

The major program must include at least nine courses: four basic courses, four elective courses, and one cognate course as described below.

Basic Courses

The basic courses consist of one from each of the following groups completed with a grade of at least C-.

  • Modern Algebra: Math 412 or 493
  • Differential Equations: Math 256, 286, or 316
  • Analysis: Math 351 or 451
  • Geometry/Topology: Math 433, 490, or 590

More advanced students, such as those who have completed Math 396, may substitute higher lever courses with the approval of an advisor.

Following Math 215 all students intending to major in Pure Mathematics should elect Math 217 (Linear Algebra) rather than Math 216 (Introduction to Differential Equations). Math 216 is not intended for Mathematics majors, who generally take Math 316 (Differential Equations) after completing Math 217.

Elective Courses

The four elective courses must be chosen in consultation with an advisor to provide a cohesive program that explores an area of mathematics in some depth. There is a good deal of freedom here, but a random selection of courses may not satisfy this requirement. The courses should be chosen from the following list or have a course number of 600 or above. Math 289 is repeatable 1-credit courses and can be used to satisfy the elective requirement only in combinations totaling 3 credits.

289 Problem Solving

354  Fourier Analysis and its App.

389  Explorations in Mathematics

416  Theory of Algorithms

420 Advanced Linear Algebra

425  Introduction to Probability

437  Intro to Differential Manifolds

452  Advanced Calculus II

462  Mathematical Models

464  Inverse Problems

471  Introduction to Numerical Methods

481  Introduction to Mathematical Logic

498  Topics in Modern Mathematics

526  Discrete State Stochastic Processes

555  Intro to Complex Variables

557  Methods in Applied Math II

559  Topics in Applied Mathematics

562  Continuous Optimization Methods

565  Combinatorics and Graph Theory

571  Numerical Methods for Sci Comput. I

575  Intro to the Theory of Numbers

590  Intro to Topology

592  Intro to Algebraic Topology

594  Algebra II

597  Analysis II (Real)

310 Elementary Topics

362  App of Calculus and Linear Algebra

404  Intermediate Differential Equations

423  Mathematics of Finance

433  Introduction to Differential Geometry

450  Advanced Mathematics for Engineers I

454  Boundary Value Problems for PDE

463  Mathematical Modeling in Biology

465  Introduction to Combinatorics

475  Elementary Number Theory

490  Introduction to Topology

525 Probability Theory

550  Introduction to Adaptive Systems

556  Methods of Applied Mathematics I

558  Ordinary Differential Equations

561  Linear Programming I

563  Advanced Mathematical Biology

567  Intro to Coding Theory

572  Numerical Methods for Sci. Comput. II

582  Introduction to Set Theory

591  General and Differential Topology

593  Algebra I

596  Analysis I (Complex)

Cognate Courses

One cognate course should be chosen from some field other than mathematics. Almost any field is acceptable, but the course must be at the 300+ level and should have significant mathematical content, at least at the level of Math 215. A list of suggested courses is available in the Undergraduate Program office, but in all cases approval of an advisor is required.

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