UM Mathematics-UG Honors

A student who is either in the LS&A Honors Program or is approved by the Departmental Honors Committee may declare an honors concentration in mathematics. The honors concentrator will acquire a greater command of abstractions and of the subtleties of mathematical rigor, and will enhance their problem-solving abilities. Members of the Honors Committee of the Department of Mathematics counsel honors concentrators.

Honors students who complete an honors concentration with distinction may receive on their diplomas the designations "with honors," "with high honors," or "with highest honors." However, these designations are not restricted to students officially enrolled in the Honors Program; any student whose course selection has followed the pattern of an honors concentrator may ask the Chair of the Honors Committee to be considered for an honors designation. An honors citation will be awarded to any student who completes the honors concentration requirements with a GPA of at least 3.25 in these courses. 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.

Honors Concentrators are urged to participate regularly in the undergraduate problem-solving seminar, which meets once a week throughout the year. Participants may obtain one hour of course credit per term by registering for Math 289. By participating in this seminar the student learns to think like a mathematician and will develop an understanding of what it is like to do creative mathematics.

Students intending an honors concentration in mathematics are advised to take one of the Honors introductory calculus sequences 156-256, (174, 175 or 185)-286, or 295-396, or some combination of these two. Please note that the sequence 295-396 is very theoretical.

All Honors Mathematics concentrators 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, or of a computer algebra system (Maple or Mathematica) at a level equivalent to completion of Math 403.

The Honors concentration program must include at least nine courses: (a) four basic courses, (b) four elective courses, and (c) one cognate course as described below.

a. The basic courses consist of one from each of groups 1, 2, 3, and 4 or groups 1, 2, 5, and 6 below:

1. Linear Algebra: Math 513
2. Analysis: Math 451
3. Modern Algebra: Math 512
4. Geometry/Topology: Math 433, 490, 531, 532, or 590
5. Probability: Math 525
6. Differential Equations: Math 404, 454, 556, 557, 558

Students who complete MATH 295-296, with a grade of at least a C- are exempt from MATH 451. If you complete MATH 295-395, with a grade of at least a C- you are exempt from MATH 513.

b. The four elective courses must be chosen in consultation with an honors advisor to provide a cohesive program which 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 600 or above. Math 289 is a repeatable 1-credit course and can be used to satisfy the elective requirement only if taken for a total of 3 credits. 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.

289 Problem Solving	416 Theory of Algorithms
433 Intro. to Differential Geom.	452 Advanced Calculus II
462 Mathematical Models	463 Math Modeling in Biology
464 Inverse Problems	471 Intro. to Numerical Methods
481 Intro. to Mathematical Logic	490 Introduction to Topology
525 Probability Theory	526 Disc. State Stochastic Processes
531 Transformation Groups in Geom.	532 Disc. & Applied Geometry
535 Intro. to Algebraic Curves	537 Intro. to Diff. Manifolds
555 Complex Variables	556 Methods of Applied Math. I
557 Methods of Applied Math. II	558 Ordinary Differential Equations
559 Topics in Applied Mathematics	561 Linear Programming I
563 Adv. Mathematical Biology	565 Combinatorics and Graph Theory
566 Combinatorial Theory	567 Coding Theory
571 Num. Meth. for Sci. Comput. I	572 Num. Meth. for Sci. Comput. II
575 Intro. to Theory of Numbers	582 Introduction to Set Theory
590 An Introduction to Topology	591 General and Diff. Topology
592 Intro. to Algebraic Topology	593 Algebra I
594 Algebra II	596 Analysis I (Complex)
597 Analysis II (Real)

c. 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 or from the Undergraduate Office, but in all cases approval of a concentration advisor is required.