Open Questions: Algebra
[Home] [Up]
[Glossary]
[Topic Index]
[Site Map]
See also: Symmetry 
Algebraic geometry
Introduction
Combinatorial group theory
The word problem
Algebraic Ktheory
Commutative algebra
Inverse Galois theory
Category theory
Topos theory

Site indexes

Math Forum Internet Mathematics Library: Modern Algebra
 Alphabetized list of links with extensive annotations.

The Math Forum: Modern Algebra
 Selected list of links with extensive annotations.

Mathematics Archives  Abstract Algebra
 Extensive annotated list of links.

Open Directory Project: Algebra
 Categorized and annotated algebra links. A version of this
list is at
Google, with entries sorted in "page rank" order.

Galaxy: Algebra
 Categorized site directory. Entries usually include
descriptive annotations.
There are also indexes for
group theory,
(more
here),
ring theory,
field theory, and
linear algebra
(more
here).
Sites with general resources

Abstract Algebra Online
 Contains a list of many links organized by topic, a glossary
of algebra terms, and an index of important theorems.
Site is maintained by John Beachy and is based on his abstract
algebtra textbooks.
Surveys, overviews, tutorials

Abstract algebra
 Article from
Wikipedia.

Wikibooks: Abstract Algebra
 Textbook in the
Wikibooks collection. A work in progress, but already contains
much useful information.
Topics covered include:
Groups,
Rings,
Category theory,
Finite fields.

Abstract algebra
 Elementary introduction to abstract algebra, by
Joseph Mileti.
Group theory

Group (mathematics)
 Article from
Wikipedia.
See also
Group theory.

Open Problems in Combinatorial Group Theory
 Collected by G.Baumslag, A.Miasnikov and V.Shpilrain.
Ring theory and commutative algebra

Ring (mathematics)
 Article from
Wikipedia.
See also
Ring theory,
Commutative algebra.
Field theory

Field (mathematics)
 Article from
Wikipedia.
See also
Field theory,
Galois theory,
Finite field.
Linear algebra and matrix theory

Linear algebra
 Article from
Wikipedia.
See also
Matrix theory.
Algebra over a field,
Associative algebra
Category theory

Galaxy: Category Theory
 Categorized site directory. Entries usually include
descriptive annotations.

Category theory
 Article from
Wikipedia.
See also
Universal algebra,
Topos.
Miscellaneous algebra topics

Homological algebra
 Article from
Wikipedia.

Ktheory
 Article from
Wikipedia.
 The Octonions
John C. Baez
Bulletin of the AMS, April 2002, pp. 145205
 There are only four normed divisions algebras: the real numbers,
the complex numbers, the quaternions, and the octonions. The latter
bridge many areas of mathematics, such as Clifford algebras and
spinors, Bott periodicity, projective and Lorentzian geometry,
Jordan algebras, and exceptional Lie groups. The also appear in
theoretical physics in connectin with quantum logic, special
relativity, and supersymmetry.
[Abstract, references, downloadable text]
 Recent Developments in the Cohomology of Finite Groups
Alejandro Adem
Notices of the AMS, August 1997, pp. 806812
 Cohomology of finite groups can be described completely
algebraically, but it can also be described in topological
terms. It forms an important bridge between algebra and topology
and touches a number of areas of mathematics. There are now a
number of ways to compute group cohomology.
[Article in PDF format]
 An Introduction to Computational Group Theory
Ákos Seress
Notices of the AMS, June/July 1997, pp. 671679
 Computational group theory is one of the oldest and most
developed branches of computational algebra. Different techniques
and problems are associated with specific types, of groups,
such as finitely presented groups, polycyclic groups, permutation
groups, and matrix groups.
[Article in PDF format]
 On Finite Simple Groups and Their Classification
Ron Solomon
Notices of the AMS, February 1995, pp. 231239
 Although the classification theorem for finite simple groups
was felt to be complete in 1983, and in spite of about 15,000
pages devoted to the proof, not all details had been
published, and loose ends remained. Since then, efforts have
continued to clean up the classification and address new problems
that it suggested. Interesting questions remain, especially
with respect to the sporadic simple groups, and the "Monster"
in particular.
[Article in PDF format]
Home
Copyright © 200204 by Charles Daney, All Rights Reserved