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.
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.
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)
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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