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Pure Mathematics

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.

I. Prerequisites

The prerequisite to major in Pure Mathematics is one of the sequences 215 & 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 (II.), four elective courses (III.), and one cognate course (IV.) as described below.

II. 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 312, 412 or 493
  • Differential Equations: Math 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.

III. 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 310 Chance and Choice
354  Fourier Analysis and its App. 362  App of Calculus and Linear Algebra
389  Explorations in Mathematics 404  Intermediate Differential Equations
416  Theory of Algorithms 423  Mathematics of Finance
420 Advanced Linear Algebra 433  Introduction to Differential Geometry
425  Introduction to Probability 450  Advanced Mathematics for Engineers I
437  Intro to Differential Manifolds 454  Boundary Value Problems for PDE
452  Advanced Calculus II 463  Mathematical Modeling in Biology
462  Mathematical Models 465  Introduction to Combinatorics
464  Inverse Problems 475  Elementary Number Theory
471  Introduction to Numerical Methods 490  Introduction to Topology
481  Introduction to Mathematical Logic 525 Probability Theory
498  Topics in Modern Mathematics 550  Introduction to Adaptive Systems
526  Discrete State Stochastic Processes 556  Methods of Applied Mathematics I
555  Intro to Complex Variables 558  Ordinary Differential Equations
557  Methods in Applied Math II 561  Linear Programming I
559  Topics in Applied Mathematics 563  Advanced Mathematical Biology
562  Continuous Optimization Methods 567  Intro to Coding Theory
565  Combinatorics and Graph Theory 572  Numerical Methods for Sci. Comput. II
571  Numerical Methods for Sci Comput. I 582  Introduction to Set Theory
575  Intro to the Theory of Numbers 591  General and Differential Topology
590  Intro to Topology 593  Algebra I
592  Intro to Algebraic Topology 596  Analysis I (Complex)
594  Algebra II  

IV. 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.

Print a Pure Mathematics Worksheet