Links to sites related to abstract algebra

Number theory:

Compute GCD's, by David Sumner, University of South Carolina
A calculator for the Euclidean algorithm
The Prime Machine, by Peter Alfeld, University of Utah
Explore prime numbers using a Java applet
Prime number generator, from Boise State University
Prime number generator, from Caltech
Generate lists of primes
About the proof of Fermat's last theorem, from NOVA Online
Includes an interview with Andrew Wiles

Cryptography:

Public Key Cryptography, from the American Mathematical Society
This seems like a reasonable place to start learning about how number theory is used in cryptography.
Digital Signatures, from S. Gao at Clemson University
New legislation has made it legal to use digital signatures. This site has some information about the background mathematics.
Cryptography A-Z, from SSH Communications Security
This company has a good introduction to some of the work they do.
Elliptic Curve Cryptosystems, from RSA Security
Understanding elliptic curves requires some graduate work, but you can get a general feel for the applications.
Cryptography links, from Cryptography Research, Inc.
This site has lots of links, but most are quite technical.

Group theory in geometry:

Symmetry and the Shape of Space, by C. Goodman-Strauss
Mathematics and Knots, from the University of Wales, Bangor
The KnotPlot Site, from the Pacific Institute for the Mathematical Sciences
Knot theory, by Bryson Payne

Group theory in the natural sciences:

Group theory and crystallography, from Oak Ridge National Lab
Symmetry in Chemistry - Group Theory, from Southern Illinois University
Group theory in digital signal processing (see the Research Activities link)
Group theory and physics, from the Notices of the AMS, January, 1997 (pdf format)

Other applications:

Music and mod 12 arithmetic, by L. Solomon

Reference sites with more links:

Group theory resources, from Dave Rusin, my colleague here at Northern Illinois University
Abstract Algebra resources, from the University of Tennessee at Knoxville
Symmetry and Group Theory, from David Eppstein, at the University of California, Irvine

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