Math 360 - Abstract Algebra I

Credits: 3

Course Description: Review of set theory and introduction to mathematical proof. Introduction to concepts and techniques of group theory, including but not limited to: symmetric groups, axiomatic definitions of groups, important classes of groups, subgroups, group homomorphisms, coset theory, normal subgroups, quotient groups, direct products, Sylow theorems. Possible applications include number theory, geometry, physics and combinatorics.

Pre-Requisites: MATH 260.

Frequency: Course offered in the fall only.

Current Textbook: A First Course in Abstract Algebra, 7th Edition, by John Fraleigh, published by Addison-Wesley, 2002. ISBN: 0-201-76390-7. Check with your instructor to make sure this is the textbook used for your section.

Chapter 0:

Sets and Relations.

Chapter 2:

Permutations, Cosets and Direct Products

Chapter 3:

Homomorphisms and Factor Groups [sections 13-16]

Chapter 4:

Rings and Fields [sections 18-23]

Chapter 5:

Ideals and Factor Rings [sections 26-27]

Chapter 6:

Extension Fields [sections 29-32]

Chapter 7:

Advanced Group Theory