Fall Quarter 2017, Math 220A, Modern Algebra I

Instructor:
A. Agboola
Lecture:
TuTh 9:30am-10:45am, LSB 1101
Office:
6724 South Hall
Office hours:
TuTh 11am--12:30pm
Textbooks:
The following two books are required texts for this course (as well as for Math 220B and Math 220C):

David S. Dummit, Richard M. Foote, Abstract algebra, (Third Edition), Wiley (2004).

Serge Lang, Algebra, (Revised Third Edition), Springer (2002).

The following book may also be helpful to you:

J. J. Rotman, An introduction to the theory of groups, Springer (1995).

For a superb account (perhaps somewhat sophisticated for a beginner), the following is highly recommended:

J.-P. Serre, Finite Groups: An Introduction, International Press (2016).

There will be one take-home midterm examination. It will be handed out in class on Thursday, November 2nd, and will be due in class on Tuesday, November 7th. There will also be one take-home final examination. Precise arrangements concerning the final examination will be made later.

Homework may be assigned, and some of it may be collected from time to time. Your work should be typed neatly (preferably in Tex) on 8 X 11 sized paper.

The final grade for the course will be determined as follows: midterm 40\%, final exam. 60\%. Homework will not count towards the final grade.

PLEASE NOTE THAT NO MAKEUP EXAMINATIONS WILL BE GIVEN IN THIS COURSE.

The following link might take you to some problems:

Problems

The following link will take you to the Course Log:

Course Log

Course Outline:

We shall aim to cover the following topics. Additional topics will be covered if time permits.

Groups: definitions and basic properties. Examples: permutation groups. Subgroups. Lagrange's theorem. Cyclic groups. Quotient groups. Isomorphism theorems.

Groups acting on sets. Sylow's theorems and applications. Composition series. The Jordan-Holder theorem and related results. Soluble and nilpotent groups. Finite p-groups. Finitely generated abelian groups.