What is abstract algebra?

Abstract Algebra

Abstract algebra is the subject area of mathematics that studies algebraic structures such as groups, rings, fields, modules, vector spaces, and algebras. The phrase abstract algebra was coined at the turn of the 20th century to distinguish this area from what was normally referred to as algebra, the study of the rules for manipulating formulae and algebraic expressions involving unknowns and real or complex numbers, often now called elementary algebra. The distinction is rarely made in more recent writings.

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Some articles on abstract algebra:

Emmy Noether - Biography - Seminal Work in Abstract Algebra
... upon physics, among mathematicians she is best remembered for her seminal contributions to abstract algebra ... says in his Introduction to Noether's Collected Papers, The development of abstract algebra, which is one of the most distinctive innovations of twentieth ... Noether's groundbreaking work in algebra began in 1920 ...
History Of Elementary Algebra - Modern Algebra - Abstract Algebra
... The ability to do algebra is a skill cultivated in mathematics education ... Eventually mathematics was concerned completely with abstract polynomials, complex numbers, hypercomplex numbers and other concepts ... mathematics or mathematical physics, and the field of mathematics expanded to include abstract algebra ...
Abstract Algebra - Applications
... Because of its generality, abstract algebra is used in many fields of mathematics and science ... describe those symmetries are Lie groups, and the study of Lie groups and Lie algebras reveals much about the physical system for instance, the number of force carriers in a theory is equal to dimension of the Lie ...
... Algebra is related to mathematics, but for historical reasons, the word "algebra" has three meanings as a bare word, depending on the context ... As a single word, "algebra" can mean Use of letters and symbols to represent values and their relations, especially for solving equations ... This is also called "Elementary algebra" ...
Field With One Element
... and the notation F1 are only suggestive, as there is no field with one element in classical abstract algebra ... the traditional building blocks for abstract algebra, with other, more flexible objects ... Instead, most proposed theories of F1 replace abstract algebra entirely ...

Famous quotes containing the words algebra and/or abstract:

    Poetry has become the higher algebra of metaphors.
    José Ortega Y Gasset (1883–1955)

    Somebody once said that I am incapable of drawing a man, but that I draw abstract things like despair, disillusion, despondency, sorrow, lapse of memory, exile, and that these things are sometimes in a shape that might be called Man or Woman.
    James Thurber (1894–1961)