MATH 497 - Reading in Mathematics

3 units (fi 6)(EITHER, 3-0-0)

This course is designed to give credit to mature and able students for reading in areas not covered by courses, under the supervision of a staff member. A student, or group of students, wishing to use this course should find a staff member willing to supervise the proposed reading program. A detailed description of the material to be covered should be submitted to the Chair of the Department Honors Committee. (This should include a description of testing methods to be used.) The program will require the approval of both the Honors Committee, and the Chair of the Department. The students' mastery of the material of the course will be tested by a written or oral examination. This course may be taken in Fall or Winter and may be taken any number of times, subject always to the approval mentioned above. Prerequisite: Any 300-level MATH course.

MATH 327 - Algebra I

3 units (fi 6)(FIRST, 3-0-0)

Basic group theory: Groups, subgroups, normal subgroups, homomorphisms, quotient groups, coset decomposition, Example: Permutation group and general linear group; basic (commutative) ring theory: Rings, subrings, homomorphisms, ideals, quotient rings, modules over rings, submodules and quotient modules, fraction field; further group theory: Groups operating on a set, Sylow theorems. Prerequisite : One of MATH 226 or MATH 227. Note: Credit can be obtained in at most one of MATH 326 and MATH 327.

MATH 411 - Honors Complex Variables

3 units (fi 6)(FIRST, 3-0-0)

Complex number system. Analytic functions. Cauchy's Integral theorem and formula. Applications including the maximum modulus principle, Taylor expansion and Laurent expansion. Harmonic functions. The residue theorem with applications; calculus of residues, argument principle, and Rouche's theorem. Basics of analytic continuation. Additional topics at the instructor's discretion such as: Normal families, The Riemann mapping Theorem, Picard's Theorem. Prerequisite: MATH 314 or 317. Notes: (1) This course is primarily for Honors students in Mathematics or Physics. (2) Offered in alternate years. It may be offered in intervening years if demand is sufficient.