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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