Algebra

The word ''algebra'' comes from the title of [[al-Khwarizmi Algebra is the branch of mathematics that studies certain abstract systems, known as algebraic structures, and the manipulation of expressions within those systems. It is a generalization of arithmetic that introduces variables and algebraic operations other than the standard arithmetic operations, such as addition and multiplication.

Elementary algebra is the main form of algebra taught in schools. It examines mathematical statements using variables for unspecified values and seeks to determine for which values the statements are true. To do so, it uses different methods of transforming equations to isolate variables. Linear algebra is a closely related field that investigates linear equations and combinations of them called ''systems of linear equations''. It provides methods to find the values that solve all equations in the system at the same time, and to study the set of these solutions.

Abstract algebra studies algebraic structures, which consist of a set of mathematical objects together with one or several operations defined on that set. It is a generalization of elementary and linear algebra since it allows mathematical objects other than numbers and non-arithmetic operations. It distinguishes between different types of algebraic structures, such as groups, rings, and fields, based on the number of operations they use and the laws they follow, called axioms. Universal algebra and category theory provide general frameworks to investigate abstract patterns that characterize different classes of algebraic structures.

Algebraic methods were first studied in the ancient period to solve specific problems in fields like geometry. Subsequent mathematicians examined general techniques to solve equations independent of their specific applications. They described equations and their solutions using words and abbreviations until the 16th and 17th centuries when a rigorous symbolic formalism was developed. In the mid-19th century, the scope of algebra broadened beyond a theory of equations to cover diverse types of algebraic operations and structures. Algebra is relevant to many branches of mathematics, such as geometry, topology, number theory, and calculus, and other fields of inquiry, like logic and the empirical sciences. Provided by Wikipedia
Showing 1 - 20 results of 25 for search 'ALGEBRA', query time: 0.03s Refine Results
  1. 1
    by ALGEBRA
    Published 1975
    Other Authors: “…ALGEBRA…”
    Other
  2. 2
    Other Authors: “…RUIZ C. (Algebra)…”
    Other
  3. 3
    Published 2011
    “…Paul Drijvers -- Preface / Paul Drijvers -- Algebra Education: Exploring Topics and Themes / Paul Drijvers , Aad Goddijn and Martin Kindt -- Algebra from Ahmes to applet / Aad Goddijn -- From arithmetic to algebra / Truus Dekker and Maarten Dolk -- Patterns and formulas / Paul Drijvers , Truus Dekker and Monica Wijers -- Restrictions in algebra / David Webb and Mieke Abels -- Algebra in function / Michiel Doorman and Paul Drijvers -- Principles of practice / Martin Kindt -- Algebra and technology / Paul Drijvers , Peter Boon and Martin van Reeuwijk -- Algebra in science and engineering / Henk Van Der Kooij and Aad Goddijn -- Index / Paul Drijvers…”
    eBook
  4. 4
    Published 1988
    “…Conference on Computers in Algebra…”
    Book
  5. 5
    Other Authors:
    Other
  6. 6
    Published 2001
    “…Linear Algebra Modules Project…”
    Book
  7. 7
    Published 1984
    “…Colloquium on Trees in Algebra and Programming…”
    Book
  8. 8
    Published 1988
    “…SIAM Activity Group on Linear Algebra…”
    Book
  9. 9
    Published 1995
    “…IMA Workshop on Linear Algebra for Signal Processing…”
    Book
  10. 10
    Published 1994
    “…SIAM Conference on Applied Linear Algebra…”
    Book
  11. 11
  12. 12
    Published 1984
    “…Universidad de Granada. Departamento de Algebra y Fundamentos…”
    Journal
  13. 13
    Published 1969
    “…International Symposium on the Applications of Model Theory to Algebra, Analysis, and Probability…”
    Other
  14. 14
    by Barja Pérez, José María
    Published 1977
    “…Universidad de Santiago de Compostela. Departamento de Algebra y Fundamentos…”
    Book
  15. 15
    “…Universidad de Santiago de Compostela. Departamento de Algebra y Fundamentos…”
    Book
  16. 16
    by Blanco Ferro, Antonio
    Published 1984
    “…Universidad de Santiago de Compostela. Departamento de Algebra y Fundamentos…”
    Book
  17. 17
    by Gómez Pardo, J. L.
    Published 1972
    “…Universidad de Santiago de Compostela. Departamento de Algebra y Fundamentos…”
    Book
  18. 18
    “…Universidad de Santiago de Compostela. Departamento de Algebra y Fundamentos…”
    Book
  19. 19
    by Ladra González, Marcelino
    Published 1984
    “…Universidad de Santiago de Compostela. Departamento de Algebra y Fundamentos…”
    Thesis
  20. 20
    by Aznar García, E. R.
    Published 1982
    “…Universidad de Santiago de Compostela. Departamento de Algebra y Fundamentos…”
    Thesis