John Beachy,
Department of Mathematical Sciences,
Northern Illinois University

MATH 520 / 521, Algebraic Structures I, II

I maintain this page as a general reference for NIU graduate students. Some of the following files are in postscript format (ps), which requires a postscript viewer. When using NETSCAPE on our departmental network, the viewer will come up automatically.

To download a file (for example, a .dvi file that you want to print, not just view) hold the shift key down while clicking on the link. Netscape will prompt you for a name under which the file is to be saved.

Material to supplement your textbook and lecture notes:

Introductory Lectures on Rings and Modules, Cambridge University Press
Abstract Algebra OnLine
OnLine Study Guide for Abstract Algebra, 2nd Ed.
Review Problems on Groups and Galois Theory
Lecture notes on nilpotent groups, semidirect products, and the classification of groups of small order
Undergraduate level review of
Lecture notes on canonical forms (ps) (dvi)

Lecture notes on fields by George Seelinger (in pdf format)
Lecture notes by Jeff Thunder on fields and rings (in ps format)

Texts or notes from other universities

Abstract Algebra: the Basic Graduate Year, by Robert Ash, University of Illinois at Urbana-Champaign
Elements of Abstract and Linear Algebra, by Edwin Connell, University of Miami
Notes on groups and Galois theory by Christopher Cooper, Macquarie University
Groups of small order, by John Pedersen, University of South Florida
Groups of small order, by John Sullivan, University of Illinois at Urbana-Champaign

Computer Algebra:

Groups 15 and Groups32, written by J. Wavrik, at UCSD
Mathematica Package for noncommutative algebra, from UCSD

General interest:

Abstract Algebra resources, from the University of Tennessee at Knoxville
Group theory resources (from Dave Rusin)
Algebra links, from

References on the classification of finite simple groups:
ATLAS of Finite Group Representations
The Moonshine Page


History of Abstract Algebra (from St. Andrews University)
Homepages of Abel | Emil Artin | Galois | Emmy Noether
On van der Waerden's textbook
Written by Saunders MacLane, the article gives an excellent historical background for the text that "served to transform the graduate teaching of algebra".
History of group representations I, II, written by T.Y.Lam (in pdf format)
Biographies (from St. Andrews University, Scotland)

Previous semesters:

Fall 92, Spring 93: 520 Syllabus (ps) || Exams (ps) ; 521 Exams (ps)
Summer 96: 520 Syllabus; assignments; review and exams; bibliography (html)
Fall 98, Spring 99: 520 Exams (ps) || (pdf) ; 521 Exams (ps)

Comprehensive exams


Graduate study in algebra:

At NIU and at the University of Illinois at Urbana-Champaign
Graduate courses at Berkeley, Michigan, Michigan State, Penn
Rankings of programs, by US News and World Report

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