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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.
Printable Pure Mathematics Subplan Checklist - Click Here
I. Prerequisites
The prerequisite to major in Pure Mathematics is one of the sequences 205 & 217, 215 & 217, 285 & 217, or 295 & 296. Note that Math 216 is not intended for Mathematics majors.
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-level 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 a repeatable 1-credit course and can be used to satisfy the elective requirement only when taken three times, totaling 3 credits.
| 289 Problem Solving | 310 Chance and Choice |
| 314 Math of Blockchains | 327 Evolution of Math Concepts |
| 354 Fourier Analysis and its App. | 404 Intermediate Differential Equations |
| 389 Explorations in Mathematics | 423 Mathematics of Finance |
| 416 Theory of Algorithms | 420 Advanced Linear Algebra |
| 425 Introduction to Probability | 431 Euclidean Geometry |
| 433 Introduction to Differential Geometry | 450 Advanced Mathematics for Engineers I |
| 440 Lab of Geometry - LoG(M) | 445 Entropy and Information: Concepts and Applications |
| 450 Advanced Math for Engineers | 452 Advanced Calculus II |
| 454 Boundary Value Problems for PDE | 460 Intr Stoch Processes |
| 462 Mathematical Models | 463 Mathematical Modeling in Biology |
| 464 Inverse Problems | 465 Introduction to Combinatorics |
| 472 Numerical Methods with Financial Applications | 471 Introduction to Numerical Methods |
| 475 Elementary Number Theory | 481 Introduction to Mathematical Logic |
| 490 Introduction to Topology | 498 Topics in Modern Mathematics |
| 511 Theory of Complex Systems | 525 Probability Theory |
| 526 Discrete State Stochastic Processes | 550 Introduction to Adaptive Systems |
| 551 Intro to Real Analysis | 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 a 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.
289 Problem Solving (only if 3 cr)
310 Chance and Choice
314 Math of Blockchains
327 Evolution of Math. Concepts
354 Fourier Anal. and its Applic.
389 Explorations in Mathematics
404 Inter. Diff. Equations
416 Theory of Algorithms
420 Advanced Linear Algebra
423 Mathematics of Finance
425 Introduction to Probability
431 Euclidean Geometry
433 Intro. to Differential Geom.
440 Lab of Geometry - LoG(M)
445 Intro to Info Theory
450 Adv. Math for Engineers I
452 Intro Analys: Multi Variable
454 Bound. Val. Prob. for PDE
460 Intr Stoch Processes
462 Mathematical Models
463 Math Modeling in Biology
464 Inverse Problems
465 Introduction to Combinatorics
471 Intro. to Numerical Methods
472 Numer. Methods w/Fin. Apps
475 Elementary Number Theory
481 Intro. to Mathematical Logic
490 Introduction to Topology
498 Topics in Modern Math
511 Theory of Complex Systems
525 Probability Theory
526 Discrete State Stoch Process
550 Intro. to Adaptive Systems
551 Intro Measure Theory
555 Intro. to Complex Variables
556 Applied Functional Analysis
557 Applied Asymptotic Analysis
558 Applied Nonlinear Dynamics
559 Topics in Applied Math
561 Linear Programming I
562 Cont. Optimization Meth.
563 Advanced Mathematical Bio
565 Combin. and Graph Theory
567 Intro. to Coding Theory
571 Numerical Linear Algebra
572 Num. Meth. for Diff. Equations
575 Intro. to Theory of Numbers
582 Introduction to Set Theory
590 Intro. to Topology
591 Differentiable Manifolds
592 Intro. to Algebraic Topology
593 Algebra I
594 Algebra II
596 Complex Analysis I
597 Real Analysis I
