Text: Algebra, A Graduate Course by I. M. Isaacs, AMS textbook series.

Other books for reference:
(i) Algebra by Serge Lang, GTM, Springer-Verlag.
(ii) Basic Algebra (two volumes) by Nathan Jacobson.
(iii) Algebra by T. W. Hungerford, GTM, Springer-Verlag.

Topics to be covered: (some of these will be covered in Graduate Algebra I and others in Graduate Algebra II)
(a) Group Theory
(b) Ring Theory
(c) Fields and Galois Theory
(d) Module Theory

Goals and objectives of the course: Math 5110 (together with its sequel) is a rigorous introduction to all those topics in basic algebra that every mathematician should know. They also form the syllabus for the Ph.D. Algebra comprehensive exam.


Tips on doing well:
(1) It is essential to keep up with what is being covered in class. A general principle to follow is to skim through up-coming section(s). This is extremely helpful.
(2) For every hour of class you should devote at least two hours of study time. Doing homework regularly is an easy way of staying with the class, and improving your grades.
(3) Work Hard and Be Happy!!


Homework:

Homework 1

Homework 2

Homework 3

Homework 4

Homework 5

Homework 6

Homework 7

Homework 8

Homework 9





Archive of homework from previous semester
Homework 1
Homework 2
Homework 3
Homework 4
Homework 5
Homework 6
Homework 7







Some useful articles to read:


What is Mathematics.


Axiom of choice and Zorn's Lemma .


Role of Algebra in Applied Mathematics .