Undergraduate Algebra I

Fall, 2008

Instructor: Jungkai Alfred Chen

Office: Old Math. Bldg. 108

I. Contents：

1. Prelimanary

a. Sets, equivalence relations

b. Integers, elementary number theory

2. Group theory

a. Examples

b. Definition

c. Subgroups, cosets

d. Homomorphism

e. Group actions on sets

f. Sylow’s theorems

g. Abelian groups

h. Group presentations

i. Groups representations

II. Course Goal：We would like introduce some basic notions and concepts of modern algebra for Math-majored students and those who are interesting in abstract algebra.

III. Course prerequisite： None

IV. Reference material ( textbook(s) )：

a. (Textbook) Fraleigh, J., A First Course in Abstract Algebra, Addison Wesley

b. (Reference) Hungerford, T., Abstract Algebra, an Introduction, Brooks Cole

c. (Reference) Lang, S., Undergraduate Algebra, UTM, Springer Verlag

V. Grading scheme：

a. Midterm 30%

b. Final examination 30%

c. Homework 20%

d. Quiz 20%