Algebra

Algebra is the branch of mathematics which is concerned with the study of, properties of operations and structures and also analyzing the relation between the structures and operations. The word Algebra is derived from the concept of a book titled, Al-jebr w’ Al-muqabalah, written by an Arabic mathematician Muhammad bin Mu-sa- Al-Khwa-rizmi. The word when considered by splitting in to two parts, “Al-jebr w” means, “The reunion of parts” and “Al-Muqabalah” means, “to set equal” or “to balance something”. This book contained the solving of linear and quadratic equations. In the 16th century, Robert Recorde, invented the symbol “=”, which is called the “equality symbol” or operator and this symbol formed the basic criteria in solving equations. Algebra is one of the main concepts in mathematics that provides knowledge on solving equations, finding the roots of the equations, addition, subtraction, multiplication of constants and variables, substitution methods, factorization methods, finding out polynomials etc. by moving the equations and balancing them. Balancing is the most important criteria that make Algebra easy. Algebra is the introductory chapter in basic education standards, as it is the simple calculative and interesting chapter to deal in mathematics. Algebra is classified in to two categories.

1.   Elementary Algebra.

2.   Abstract Algebra (Modern Algebra).

Elementary Algebra deals with expressions and evaluations involving constants and variables whereas Abstract Algebra deals with groups and fields of algebraic structures like sets. Using Algebra, it is very easy to solve a load of problems in a few minutes, using formulas. Many typical problems in linear equations, quadratic equations etc. are solved using formulas with least effort. Algebra can also be used to solve problems in matrices, geometry, number theory etc. It just involves little time and effort to solve any sort of difficult problems using Algebra. Hence it is one of the major subjects in schools and colleges.


Categories

Computational Algebra

Linear Algebra

· Numerical Linear Algebra 

Basic Algebra

Geometric Algebra

Sponsored results

Links
  • An Introduction to the Algebraic Specification of Abstract Data Types
    Jean Baillie, Department of Computer Science, University of Hertfordshire.
    http://homepages.feis.herts.ac.uk/~comqejb/algspec/pr.html
  • Lecture Notes in Algebra and Number Theory
    Andrew Baker, University of Glasgow.
    http://www.maths.gla.ac.uk/~ajb/course-notes.html
  • Intro to Abstract Algebra
    Paul Garrett's detailed and comprehensive lecture notes in abstract algebra.
    http://www.math.umn.edu/~garrett/m/intro_algebra/index.shtml
  • 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.
    http://www.win.tue.nl/~ida/
  • 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.
    http://www.jmilne.org/math/
  • Homogeneous Transformation Matrices
    Explicit n-dimensional homogeneous matrices for projection, dilation, reflection, shear, strain, rotation and other familiar transformations.
    http://www.silcom.com/~barnowl/HTransf.htm
  • 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.
    http://mathforum.org/algpow/
  • 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.
    http://www.geocities.com/zerodivisor/
  • A Web Resource in Mathematics
    Tailored help for students in Algebra.
    http://www.mathshape.com/
  • What is a Jordan-like Algebra?
    Includes generalizations, and algebraic geometry. Notes and links by Tony Smith.
    http://www.valdostamuseum.org/hamsmith/Jordan.html
  • VectorLand
    An online course to get to grips with 3D vectors. Most of the material is about UK A-level difficulty.
    http://members.tripod.com/~Paul_Kirby/vector/VectorLand.html
  • 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.
    http://groups.yahoo.com/group/univalg/
  • 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.
    http://www.cs.unm.edu/~mccune/papers/robbins/
  • Harmonic Polynomials for the Symmetric Group and Macdonald Symmetric Polynomials
    Offers outline of the problem, bibliography, and math tables. Resources assembled by François Bergeron.
    http://bergeron.math.uqam.ca/conjecture_fact.html
  • FDLIST
    Information on representation theory of finite dimensional algebras. Papers, meetings, places, people, jobs, journals, software.
    http://www.mathematik.uni-bielefeld.de/birep/fdlist.html
  • Algebra Universalis List of Researchers
    Compiled by G. Gratzer.
    http://www.maths.umanitoba.ca/homepages/au/Researchers.html
  • Algebraic Areas of Mathematics
    Topics include number theory, groups and sets, commutative rings, algebraic geometry, and linear algebra.
    http://www.math.niu.edu/~rusin/known-math/index/tour_alg.html
  • Algebra Links
    From Spartanburg County School District Two.
    http://www.spartanburg2.k12.sc.us/links/algebra.htm
  • Abstract and Linear Algebra
    A forum for students on abstract algebra and linear algebra.
    http://www.math.miami.edu/forum/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.
    http://www.math.niu.edu/~beachy/aaol/
  • All About Circuits - Boolean Algebra
    An introduction to boolean algebra from the perspective of electronic engineering.
    http://www.allaboutcircuits.com/vol_4/chpt_7/index.html
  • Catalogue of Algebraic Systems.
    Summary of and links to online materials concerning algebraic systems: semigroups, groups, rings, algebras, groupoids, and categories.
    http://www.math.usf.edu/~eclark/algctlg/
  • 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.
    http://www.clarku.edu/~djoyce/complex/
  • Defining Boolean Algebra
    Defines and compares the postulates and use of symbols between Boolean and regular algebra.
    http://www.jairosoft.com/intro_math13.htm
  • Cohomology of Modules over the Mod 2 Steenrod Algebra
    Robert R. Bruner, Wayne State University. Tables in PS or GIF formats.
    http://www.math.wayne.edu/~rrb/cohom/
  • Center for Commutative Algebra
    A site for the commutative algebra community, including news, conference and preprint announcements, and a huge list of algebraists.
    http://www.commalg.org/
  • A Catalogue of Lattices
    By Gabriele Nebe and Neil Sloane.
    http://www.research.att.com/~njas/lattices/
  • Abstract Algebra
    Lecture notes by David Wilkins, Trinity College, Dublin. Topics in Number Theory; Group Theory; Galois Theory.
    http://www.maths.tcd.ie/~dwilkins/Courses/311/

 

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