**SYLLABUS MATH 690G in Spring 2005**

**Topics in Algebra and Number Theory**

**Instructor:**Ling Long (Office: 452 Carver Hall & Phone: 4-8150)**Meeting time:**Tuesday and Thursday 2:10-3:30p.m.**Location:****Office hours:****Textbook:**Selected topics from several references**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 a finial presentation.**Topics considered to be covered:**

1. Representation of finite groups.

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

3. Knots, links, and invariance.

4. Hypergeometricdifferential equations and hypergeometric series.

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