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**.

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