**SYLLABUS MATH 690G in Spring 2006**

**Topics in Algebra and Number Theory**

**Instructor:**Ling Long (Office: 452 Carver Hall & Phone: 4-8150)**Meeting time:**MWF 2:10-3:00p.m.**Location:**290 Carver Hall**Office hours: 12-1p.m. MW & 3-4p.m.MW &10-11a.m. F****Textbook:**Selected topics from several references. Notes will be distributed.**Objective:**This is a topic course giving students a general introduction to several topics in algebra and number theory with emphasis on training students to give proper presentation and to do topic searching.**Grading:**The grade is based on either homework or a finial presentation.**Topics considered to be covered:**

1. Representation of finite and compact groups.

2. Quadratic forms, Lattices, and sphere packing problem.

3. Knots, links, and invariance.

4. Hypergeometric differential equations and hypergeometric series.

5. Classical problems: partition functions, congruence number problems, etc.

Tentative Course schedule

Week 1-4: Representation theory

Week 5-6: Hypergeometric differential equations and hypergeometric series

Week 7-8: Modular group and its subgroups

Week 9-12: Zeta functions and L-functions