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  2. Elementary algebra - Wikipedia

    en.wikipedia.org/wiki/Elementary_algebra

    Unlike abstract algebra, elementary algebra is not concerned with algebraic structures outside the realm of real and complex numbers. It is typically taught to secondary school students and at introductory college level in the United States, [4] and builds on their understanding of arithmetic. The use of variables to denote quantities allows ...

  3. Outline of algebra - Wikipedia

    en.wikipedia.org/wiki/Outline_of_algebra

    Outline of algebra. Algebra is one of the main branches of mathematics, covering the study of structure, relation and quantity. Algebra studies the effects of adding and multiplying numbers, variables, and polynomials, along with their factorization and determining their roots. In addition to working directly with numbers, algebra also covers ...

  4. Algebra - Wikipedia

    en.wikipedia.org/wiki/Algebra

    Algebra is the branch of mathematics that studies algebraic structuresand the operationsthey use.[1] An algebraic structure is a non-empty setof mathematical objects, such as the integers, together with algebraic operations defined on that set, like additionand multiplication. [2][a]Algebra explores the laws, general characteristics, and types ...

  5. Abstract algebra - Wikipedia

    en.wikipedia.org/wiki/Abstract_algebra

    The permutations of the Rubik's Cube form a group, a fundamental concept within abstract algebra. In mathematics, more specifically algebra, abstract algebra or modern algebra is the study of algebraic structures, which are sets with specific operations acting on their elements. [ 1 ] Algebraic structures include groups, rings, fields, modules ...

  6. Natural number - Wikipedia

    en.wikipedia.org/wiki/Natural_number

    Mathematicians have noted tendencies in which definition is used, such as algebra texts including 0, [22] [d] number theory and analysis texts excluding 0, [22] [29] [30] logic and set theory texts including 0, [31] [32] [33] dictionaries excluding 0, [22] [34] school books (through high-school level) excluding 0, and upper-division college ...

  7. Algebraic expression - Wikipedia

    en.wikipedia.org/wiki/Algebraic_expression

    In mathematics, an algebraic expression is an expression built up from constants (usually, algebraic numbers) variables, and the basic algebraic operations: addition (+), subtraction (-), multiplication (×), division (÷), whole number powers, and roots (fractional powers).

  8. Algebra of sets - Wikipedia

    en.wikipedia.org/wiki/Algebra_of_sets

    Fundamentals. The algebra of sets is the set-theoretic analogue of the algebra of numbers. Just as arithmetic addition and multiplication are associative and commutative, so are set union and intersection; just as the arithmetic relation "less than or equal" is reflexive, antisymmetric and transitive, so is the set relation of "subset".

  9. History of algebra - Wikipedia

    en.wikipedia.org/wiki/History_of_algebra

    Etymology. [] The word "algebra" is derived from the Arabic word الجبرal-jabr, and this comes from the treatise written in the year 830 by the medieval Persian mathematician, Al-Khwārizmī, whose Arabic title, Kitāb al-muḫtaṣar fī ḥisāb al-ğabr wa-l-muqābala, can be translated as The Compendious Book on Calculation by ...

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