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# Honors Mathematics

Our honors program is ideal for students open to the challenges of higher mathematics. State-of-the-art courses are taught in small classes by leading faculty and cover a broad range of material in both pure and applied mathematics. Beyond the standard curriculum, we routinely offer courses on recent developments in cutting edge fields such as algorithms, biomathematics, cryptography, and financial mathematics. Our honors students also often take advantage of our top-ranked graduate program; qualified students are welcome to take graduate courses. All in all, the honors mathematics program at the University of Michigan will prepare you well for the challenge of a graduate or professional school at the finest universities in the country or a rewarding career in a variety of fields (see our Careers page for a discussion of career options for mathematicians).

The technical requirements of the honors program, such as required courses, follow below.

### Technical Requirements for the Honors Mathematics Program

A student who is either in the LSA Honors Program or is approved by the Departmental Honors Committee may declare an Honors Major in mathematics. The Honors major will acquire a greater command of abstractions and of the subtleties of mathematical rigor. Honors students who complete an honors major with distinction may receive on their diplomas the designations “with honors,” “with high honors,” or “with highest honors.” An honors citation will be awarded to any Honors major who completes the honors major requirements with a major GPA of at least 3.25 and an LSA cumulative GPA of at least 3.4 at the time of graduation. Honors will automatically remove students without a 3.4 GPA. Citations of high and highest honors are awarded at the discretion of the Honors Committee on the basis of superior performance in advanced courses as attested by grades and individual faculty evaluations.

Students intending to pursue an Honors major are advised to take one of the Honors introductory sequences 156-256, 175-286, 185-286, 295-396, or some combination of these four. Please note that the sequence 295-396 is very theoretical. It is recommended that students in the 156-256, 175-286, and 185-286 tracks also complete Math 217.

All Honors 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 completion of EECS 183.

The Honors program must include at least nine courses: four basic courses, four elective courses, and one cognate course as described below.

### Basic Courses

The basic courses consist of one from each of groups 1, 2, 3 and 4 or groups 1, 3, 5 and 6 below **completed with a grade of at least C-:**

**Analysis:**Math 451**Modern Algebra:**Math 493**Linear Algebra:**Math 420 or 494**Geometry/Topology:**Math 433, 490, or 590**Probability:**Math 525**Differential Equations:**Math 404, 454, 556, 557, or 558

A student who has completed Math 295-296, with a grade of at least a C- is exempt from Math 451. A student who completed Math 295-395, with a grade of at least a C- is exempt from Math 420.

### Elective Courses

The four elective courses must be chosen in consultation with an honors advisor to provide a cohesive program that explores an area of mathematics in some depth. There is a good deal of freedom allowed here, but a random selection of courses will 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 if taken three times. An honors counselor may approve another mathematics course or a course from another department with advanced mathematical content as one of these elective courses. The honors counselor may ask that the student arrange supplemental work in a given class not listed below to conform to expectations for an honors elective.** A student who completes the requirements for the Basic Courses by choosing courses from groups 1, 3, 5 and 6 must complete a course in Complex Analysis.**

289 Problem Solving |
310 Elementary Topics |

389 Explorations in Mathematics |
416 Theory of Algorithms |

433 Intro. to Differential Geom. |
452 Advanced Calculus II |

462 Mathematical Models |
463 Math Modeling in Biology |

464 Inverse Problems |
465 Introduction to Combinatorics |

471 Intro. to Numerical Methods |
481 Intro. to Mathematical Logic |

490 Introduction to Topology |
525 Probability Theory |

526 Disc. Stochastic Processes |
537 Differentiable Manifolds |

555 Intro. to Complex Variables |
556 Methods of Applied Math I |

557 Methods of Applied Math II |
558 Ordinary Diff. Equations |

559 Topics in Applied Math |
561 Linear Programming I |

563 Adv. Mathematical Biology |
565 Combin. and Graph Theory |

566 Combinatorial Theory |
567 Intro. to Coding Theory |

571 Num. Meth. for Sci. Comp. I |
572 Num. Meth. for Sci. Comp. II |

575 Intro. to Theory of Numbers |
582 Introduction to Set Theory |

590 An Intro. to Topology |
591 General and Diff. Topology |

592 An Intro. to Algebraic Topology |
593 Algebra I |

594 Algebra II |
596 Analysis I (Complex) |

597 Analysis II (Real) |

### 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 or higher and should have significant mathematical content, at least at the level of Math 215.

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