Mathematics May be elected as a departmental concentration program Prerequisites to Concentration. Most programs require completion of one of the sequences ending with Math 215-217, 285-217, or 395-396. A working knowledge of a high-level computer language such as FORTRAN or C or a computer algebra system (such as Maple or Mathematica), at a level equivalent to completion of a course of three or more credits; and eight credits of Physics, preferably Physics 140/141 and 240/241, are recommended for all programs and required for some. For detailed requirements consult the brochure Undergraduate Programs available from the Undergraduate Mathematics Program Office (UMPO), 2084 East Hall, (734) 763-4223, or the Department's website. Concentration Programs. A student considering concentration in mathematics should consult a mathematics concentration advisor in the UMPO as early as possible and certainly by the first term of the sophomore year. The Department offers many different concentration programs with varying requirements; failure to meet some of these at the intended time may delay completion of the program and graduation. A concentration plan must be designed with and approved by a concentration advisor. The departmental brochure Undergraduate Programs should be regarded as the most comprehensive and up-to-date guide to the options and requirements for concentration programs in mathematics. All the information in that brochure and much more is available online via the World Wide Web. From the department's home page at: http://www.math.lsa.umich.edu select the item "Undergraduate Concentration Programs" Pure Mathematics (Students should consult the pamphlet Undergraduate Programs of the Department of Mathematics for its program requirements which take precedence over the descriptions in this Bulletin.) Four basic courses (one course from each of the following four groups): Modern Algebra: Math 412 or 512 Differential Equations: Math 256, 286, or 316 Analysis: Math 451 Geometry/Topology: Math 432, 433, 490, 531, or 590   Four elective courses (mathematics) chosen from a list of approved electives and approved by a concentration advisor. One cognate course outside the Mathematics Department, but having advanced mathematical content. Mathematical Sciences Program (Students should consult the pamphlet Undergraduate Programs of the Department of Mathematics for its program requirements which take precedence over the descriptions in this Bulletin.) Additional prerequisite: one term of computer programming (EECS 183 or the equivalent), and for the Numerical and Applied Analysis option, 8 credits of physics. Four basic courses (one course from each of the following four groups): Differential Equations: Math 256, 286, or 316 Discrete Math/Modern Algebra: Math 312, 412, or 512 Analysis: Math 354, 450, or 451 Probability: Math 425 or 525   At least three courses from ONE of the Program Options listed below (the list of possible electives for each option is given in the Undergraduate Programs pamphlet described above): Discrete and Algorithmic Methods Numerical and Applied Analysis Operations Research and Modelling Probabilistic Methods Mathematics of Finance and Risk Management Mathematical Economics Mathematical Physics Control Systems   Two additional advanced mathematics (or related) courses, approved by a concentration advisor. Honors Concentration Outstanding students may elect an Honors concentration in Mathematics. The Honors Program is designed not only for students who expect to become mathematicians but also for students whose ultimate professional goal lies in the humanities, law, medicine, or the sciences. Students intending an Honors concentration are strongly advised to take one of the Honors introductory calculus sequences 156-256, (175 or 185)-286 or 295-396, or some combination of the two. Eight credits of physics and familiarity with a high-level computer language are strongly recommended. (Students should consult the pamphlet Undergraduate Programs of the Department of Mathematics for its program requirements which take precedence over the descriptions in this Bulletin.) Four basic courses (one course from each of the following four groups): Linear Algebra: Math 513 Modern Algebra: Math 512 Analysis: Math 451 Geometry/Topology: Math 433, 490, 590, or 531   Four elective (mathematics) courses, chosen with the approval of the Honors advisor. One cognate course from outside the Mathematics department, but containing significant mathematical content, chosen with the approval of the Honors advisor. Students who, in the judgment of the departmental Honors committee, have completed an Honors concentration with distinction are granted a citation upon graduating. Interested students should discuss their program and the specific requirements for obtaining the citation with a Mathematics Honors advisor (appointments scheduled in 2084 East Hall) no later than the second term of their sophomore year. Actuarial Mathematics (Students should consult the pamphlet Undergraduate Programs of the Department of Mathematics for its program requirements which take precedence over the descriptions in this Bulletin.) Additional prerequisite: At least one course in each of the following fields: Accounting (271, 272, 471), Computer Science (CS 183, CS 280, Math 403), and Economics (101, 102). Five basic courses (one from each of the following five groups): Differential Equations: Math 256, 286, or 316 Probability: Math 425 or 525 Analysis: Math 354, 450, or 451 Statistics: Stat 426 Numerical Analysis: Math 471 Three special actuarial courses, including Math 424 and 520, and one of Math 521 or 522. Two additional courses in areas relating to Actuarial Science, approved by an advisor. Teaching Certificate It is essential that students planning to obtain a teaching certificate consult a teaching certificate advisor, either Professor Krause (LS&A) or Professor Coxford (Education), prior to beginning their concentration program. Additional prerequisite: One term of computer programming, EECS 183 or the equivalent. (Students should consult the pamphlet Undergraduate Programs of the Department of Mathematics for its program requirements which take precedence over the descriptions in this Bulletin.) Four basic courses, one from each of the following four groups (chosen with the approval of a teaching certificate advisor): Discrete Math/Modern Algebra: Math 312, 412, or 512 Geometry: Math 431, 432, or 531 Probability: Math 425 or 525 Secondary Mathematics: Math 486 Seven specific Education courses, totaling 28 credits. Consult the Undergraduate Programs pamphlet for the list of courses. A teaching major or minor in a second academic area (normally requires 20-24 credits in a structured program other than Mathematics. Consult the Bulletin of the School of Education for acceptable programs). Two additional courses, which must include a course in the Psychology Department, and a minimum of one additional mathematics course. Students should consult with Professor Coxford in their sophomore year to be admitted to the certification program and to schedule practice teaching. Advising. Appointments are scheduled at the Undergraduate Mathematics Program Office, 2084 East Hall. Students are strongly urged to consult with a concentration advisor each term before selecting courses for the following term. Foreign Languages. The language requirement of the A.B. or B.S. degrees with concentration in mathematics may be satisfied in any of the languages acceptable to the College. However, students planning to do graduate work in mathematics should be aware that at most universities one of the requirements for a Ph.D. degree is a demonstration of the ability to read mathematical texts in two of the three languages French, German, and Russian. Special Departmental Policies. All prerequisite courses must be satisfied with a grade of C- or above. Students with lower grades in prerequisite courses must receive special permission of the instructor to enroll in subsequent courses. 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