 Directory of Algebra Resources

Algebra is a branch of mathematics that uses letters or other symbols to represent unknown quantities, called variables. These variables and number values are combined to form equations. The rules of these equations follow the exact same rules as arithmetic, such as the commutative and associative laws for addition and multiplication. Functions are a special type of equation, where one variable can be uniquely defined in terms of the other. Another part of this topic is graphing of equations and functions using the Cartesian coordinate graph or polar coordinates. Also, covered in this topic is set theory or what constitutes a grouping of numbers.

Resources in This Category

• A Catalogue of Lattices

http://www.math.rwth-aachen.de/~Gabriele.Nebe/LATTICES/
By Gabriele Nebe and Neil Sloane.

• Abstract Algebra

http://www.maths.tcd.ie/~dwilkins/Courses/311/
Lecture notes by David Wilkins, Trinity College, Dublin. Topics in Number Theory; Group Theory; Galois Theory.

• Abstract Algebra Online

http://www.math.niu.edu/~beachy/aaol/
Contains many of the definitions and theorems from the area of mathematics generally called abstract algebra. Intended for undergraduate students taking an abstract algebra class at the junior/senior level, as well as for students taking their first graduate algebra course.

• All About Circuits - Boolean Algebra

An introduction to boolean algebra from the perspective of electronic engineering.

• Center for Commutative Algebra

http://www.commalg.org/
A site for the commutative algebra community, including news, conference and preprint announcements, and a huge list of algebraists.

• Cohomology of Modules over the Mod 2 Steenrod Algebra

http://www.math.wayne.edu/~rrb/cohom/
Robert R. Bruner, Wayne State University. Tables in PS or GIF formats.

• Dave's Short Course on Complex Numbers

http://www.clarku.edu/~djoyce/complex/
An introduction with math and a little history intended for those having a familiarity with ordinary real numbers and algebra.

• FDLIST

http://www.math.uni-bielefeld.de/~fdlist/
Information on representation theory of finite dimensional algebras. Papers, meetings, places, people, jobs, journals, software.

http://www.jmilne.org/math/
Includes preprints and course notes on Group Theory, Fields and Galois Theory, Algebraic Geometry, Algebraic Number Theory,Modular Functions and Modular Forms, Elliptic Curves, Abelian Varieties, Etale Cohomology, and Class Field Theory.

• Homogeneous Transformation Matrices

http://www.silcom.com/~barnowl/HTransf.htm
Explicit n-dimensional homogeneous matrices for projection, dilation, reflection, shear, strain, rotation and other familiar transformations.

• Intro to Abstract Algebra

http://www.math.umn.edu/~garrett/m/intro_algebra/
Paul Garrett's detailed and comprehensive lecture notes in abstract algebra.

• Lecture Notes in Algebra and Number Theory

http://www.maths.gla.ac.uk/~ajb/course-notes.html
Andrew Baker, University of Glasgow.

• Macdonald Polynomials

http://garsia.math.yorku.ca/MPWP/

• Math Forum: Algebra Problem of the Week

http://mathforum.org/algpow/
A weekly interactive project for algebra on the Internet. Challenging problems are posted and solutions appear on the Web.

• Mileski Theorem

http://mileski-theorem.tripod.com/
A new mathematical theorem proposed by Robert Mileski.

• Octonions and Sedenions

http://octonions-sedenions.tripod.com/
Enter the world of 8 and 16 dimensional hypercomplex numbers and discover that the laws that are taken for granted, but do not always hold true.

• Robbins Algebras Are Boolean

http://www.cs.unm.edu/~mccune/papers/robbins/
A web text by William McCune describing the solution of this problem by a theorem-proving program, with input files and the proofs.

• Univalg Mailing List

http://groups.yahoo.com/group/univalg/
Mailing list for use by the Universal Algebra community. Universal Algebra is a technical branch of mathematics related to algebra and model theory.

• VectorLand

http://members.tripod.com/~Paul_Kirby/vector/VectorLand.html
An online course to get to grips with 3D vectors. Most of the material is about UK A-level difficulty.

• What is a Jordan-like Algebra?

http://www.tony5m17h.net/Jordan.html
Includes generalizations, and algebraic geometry. Notes and links by Tony Smith.

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