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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, 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 431, 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||597 Analysis II (Real)|
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 online, but in all cases approval of an advisor is required.