## Lecture Notes

### Group Theory

The intended purpose of these lecture notes is not in any way to attempt to provide in-depth discussions or any new insight on Group Theory but to provide beginners a quick crash course on basic ideas, compuational techniques, and applications of Group Theory so readers can advance more easily by filling in gaps with more in-depth knowledge from currently existing so many wonderful books on Group Theory.

These lecture notes should be accessible by undergraduate students of mathematics or physics who have taken Linear Algebra.

#### Lecture Notes

#### Homework

#### References and Further Reading

Click on linked topics to view lecture notes.

An Overview

Functions

Basic Number Theory

Examples of Groups

Subgroups

Laglange's Theorem

Congruence Modulo \(n\)

Homomorphisms

Normal Subgroups

Quotient Groups

The Isomorphism Theorems

Direct Products

Finitely Generated Abelian Groups

Click on the following links topics for homework.

Not in particular order. There are so many wonderful books on Functions of a Complex Variable. I have listed below only some of those books on Functions of a Complex Variable that I am familiar with.

A First Course in Abstract Algebra, John B. Fraleigh, 7th Edition, Pearson, 2002

Abstract Algebra, I. N. Herstein, 3rd Edition, Wiley, 1996

Topics in Algebra, I. N. Herstein, 2nd Edition, John Wiley & Sons, 1975

A Course in Universal Algebra, Stanley N. Burris and H. P. Shankappanavar, Graduate Texts in Mathematics, Springer-Verlag, 1981

This last book is not about group theory but if you are interested in studying general algebra beyond group theory (in the sense of Nicolas Bourbaki?), this is a wonderful book which can be downloaded for free from the website of Stanley N. Burris (linked above).