Undergraduate Program Honors Mathematics 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.  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 concentration GPA of at least 3.25 and an LS&A 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. I. Students intending an honors concentration in mathematics 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 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. The Honors concentration program must include at least nine courses: four basic courses (II.), four elective courses (III.), and one cognate course (IV.) as described below. II. 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-: 1. Analysis:  Math 451 2. Modern Algebra:  Math 493 3. Linear Algebra:  Math 420 or 494 4. Geometry/Topology:  Math 433, 490, or 590 5. Probability:Math 525 6. 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. III. 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 part II 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)   IV. 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 at http://www.math.lsa.umich.edu/undergrad/cognates.