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Home : Science : Math : Algebra
Algebra
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.
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.
Sites in Algebra
Abstract Algebra Online
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.
Intro to Abstract Algebra
Paul Garrett's detailed and comprehensive lecture notes in abstract algebra.
Octonions and Sedenions
Enter the world of 8 and 16 dimensional hypercomplex numbers and discover that the laws that we take as granted do not always hold.
IDA: Algebra Interactive
An HTML-based book by Arjeh M. Cohen, Hans Cuypers and Hans Sterk. It focuses on an algorithmic approach to algebraic structures. Many of these tools and examples use the computer algebra package GAP. Site has samples and errata.
Algebraic Areas of Mathematics
Topics include number theory, groups and sets, commutative rings, algebraic geometry, and linear algebra.
A Catalogue of Lattices
By Gabriele Nebe and Neil Sloane.
Abstract Algebra
Lecture notes by David Wilkins, Trinity College, Dublin. Topics in Number Theory; Group Theory; Galois Theory.
Macdonald Polynomials and the n! Conjecture
Manuscripts and Publications.
Robbins Algebras Are Boolean
A web text by William McCune describing the solution of this problem by a theorem-proving program, with input files and the proofs.
Center for Commutative Algebra
A site for the commutative algebra community, including news, conference and preprint announcements, and a huge list of algebraists.
Algebra Links
From Spartanburg County School District Two.
Dave's Short Course on Complex Numbers
An introduction with math and a little history intended for those having a familiarity with ordinary real numbers and algebra.
Homogeneous Transformation Matrices
Explicit n-dimensional homogeneous matrices for projection, dilation, reflection, shear, strain, rotation and other familiar transformations.
Algebra Universalis List of Researchers
Compiled by G. Gratzer.
Lecture Notes in Algebra and Number Theory
Andrew Baker, University of Glasgow.
Univalg Mailing List
Mailing list for use by the Universal Algebra community. Universal Algebra is a technical branch of mathematics related to algebra and model theory.
Cohomology of Modules over the Mod 2 Steenrod Algebra
Robert R. Bruner, Wayne State University. Tables in PS or GIF formats.
Catalogue of Algebraic Systems.
Summary of and links to online materials concerning algebraic systems: semigroups, groups, rings, algebras, groupoids, and categories.
Math Forum: Algebra Problem of the Week
A weekly interactive project for algebra on the Internet. Challenging problems are posted and solutions appear on the Web.
FDLIST
Information on representation theory of finite dimensional algebras. Papers, meetings, places, people, jobs, journals, software.
Real Reductive Lie Groups
Notes for lectures by Amer Habib at the Mehta Research Institute in 1997-98. DVI, PS.
Abstract and Linear Algebra
A forum for students on abstract algebra and linear algebra.
Macdonald Polynomial Page
Includes information about the Ribbon Rule, as well as link about symmetric functions and representation theory.
Home Page of J. S. Milne
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.
What is a Jordan-like Algebra?
Includes generalizations, and algebraic geometry. Notes and links by Tony Smith.
All About Circuits - Boolean Algebra
An introduction to boolean algebra from the perspective of electronic engineering.
A Web Resource in Mathematics
Tailored help for students in Algebra.
Groupoids
Notes by Ronald Brown.
Groupoid Home Page
Maintained by Birant Ramazan. Address book, open problems, meetings, pictures, other resources.
An Introduction to the Algebraic Specification of Abstract Data Types
Jean Baillie, Department of Computer Science, University of Hertfordshire. |
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