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