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.