MATH 420 / 421: Algebra I, II

John Beachy, Department of Mathematical Sciences, Northern Illinois University

This is a personal page that I maintain even during semesters in which I do not teach the course. 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. If you need your own postscript viewer, you can obtain information from the Ghostview site.

Supplements to the textbook:

OnLine Study Guide (summaries of each section, with solved problems)

Overview / review of

• basic group theory (pdf), for 420
• factor groups and homomorphisms (pdf), for 421
• commutative rings (pdf), for 421

Some group multiplication tables (html) (text)

Preview of Galois theory (html) (ps)

History of Abstract Algebra:

Homepages of Abel | Emil Artin | Galois | Emmy Noether

Biographies (from St. Andrews University, Scotland)

History of Abstract Algebra, from St. Andrews University

Timeline for the use of symmetry in physics, chemistry, and mathematics

Timeline for associative algebras

Links to supplement the course:

Factor polynomials using Mathematica, from Vanderbilt University

Maple worksheets, developed by Mike May

Introduction to Logic, from Hofstra Univiversity

Essay on symmetry and group theory, from The Geometry Forum

Symmetry groups, from the Symmetry Web

Plane symmetry groups, from Clark University

Symmetry and Group Theory, from the University of California, Irvine

Rubik's cube

Lecture notes on Rubik's cube

Solving Cubic and Quartic Equations, from the University of Sydney

Solving the quintic and Quintic poster, from Wolfram Research

Abstract Algebra resources, from the University of Tennessee at Knoxville

Group theory resources (from Dave Rusin)

Algebraic systems (from Christer Blomqvist, Sweden)

Number Theory Web, maintained by Keith Matthews, at the University of Queensland

Online Books and Notes by E. Connell and L. Pomeroy

Links to applications:

Modular arithmetic pages, from Cal State, San Bernardino

Public Key Cryptography, from the AMS

Public Key Cryptography, from D. Wright at Oklahoma State

The Numeroscope, an interactive laboratory of numbers and cryptography

Number theory and public key cryptography, from Australia

Number theory and public key cryptography (2)

Digital Signatures, from S. Gao at Clemson University

Elliptic Curve Cryptosystems, from RSA Security

Cryptography links, from Cryptography Research, Inc.

Group theory and physics, from the Notices of the AMS, January, 1997

Group theory and crystallography, from Oak Ridge National Lab

Group theory in digital signal processing (see the Research Activities link)

Music and mod 12 arithmetic, by L. Solomon

Books on applications:

J.S.Lomont, Applications of Finite Groups, Dover Publications, Inc.

M.Hamermesh, Group Theory and its Application to Physical Problems, Dover Publications, Inc.

D.M.Bishop, Group Theory and Chemistry, Dover Publications, Inc.

George Perle, Serial Composition and Atonality: an Introduction to the Music of Schoenberg, Berg, and Webern. 1962; 6th edition, revised, 1991. University of California Press.

Previous semesters:

Final exams: 420 (pdf) | 420 (html) | 421

420 Syllabus: Spring 97 | Fall 95

421 Syllabus: Spring 96 | Summer 95

Graduate study in algebra:

At NIU and at the University of Illinois at Urbana-Champaign

Rankings of programs, by US News and World Report

Algebraic Structures, Math 520, at NIU

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