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 UrbanaChampaign
 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 UrbanaChampaign
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 NUMBERSorg.com

References on the classification of finite simple groups:
 R. Solomon,
A brief history of the classification of the finite simple groups,
Bull. A.M.S. 38 (2001), 315352.
 R. Solomon,
On Finite Simple Groups and Their Classification,
Notices of the AMS 42, (1995), 231239.
 D. Gorenstein, Classifying the finite simple groups,
Bull. A.M.S. 14 (1986), 198.
 M. Aschbacher,
Finite group theory,
Cambridge Univ. Press, 1986, 249266.
 D. Gorenstein,
Finite simple groups: An introduction to their classification,
Plenum Press, New York, 1982.

ATLAS of Finite Group Representations

The Moonshine Page
History:

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

UIUC
Graduate study in algebra:
 At
NIU
and at the
University of Illinois
at UrbanaChampaign

Graduate courses at
Berkeley,
Michigan,
Michigan State,
Penn

Rankings
of programs, by US News and World Report
Back
to John Beachy's homepage