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  2. Timeline of algebra - Wikipedia

    en.wikipedia.org/wiki/Timeline_of_algebra

    Al-Khwarizmi is often considered the "father of algebra", for founding algebra as an independent discipline and for introducing the methods of "reduction" and "balancing" (the transposition of subtracted terms to the other side of an equation, that is, the cancellation of like terms on opposite sides of the equation) which was what he ...

  3. Elementary algebra - Wikipedia

    en.wikipedia.org/wiki/Elementary_algebra

    [1] Elementary algebra, also known as high school algebra or college algebra, [2] encompasses the basic concepts of algebra. It is often contrasted with arithmetic : arithmetic deals with specified numbers , [ 3 ] whilst algebra introduces variables (quantities without fixed values).

  4. Abeka - Wikipedia

    en.wikipedia.org/wiki/Abeka

    Some Abeka textbooks have been criticized by educators as lacking academic rigor and taking contrary or reactive positions toward their subject matter. Experts from the University of Florida and University of Central Florida in 2018 criticized the content of Abeka textbooks as being markedly more simple and less challenging than the content of comparable textbooks used in public education.

  5. Algebra - Wikipedia

    en.wikipedia.org/wiki/Algebra

    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.

  6. Abstract algebra - Wikipedia

    en.wikipedia.org/wiki/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 , vector spaces , lattices , and algebras over a field .

  7. Elements of Algebra - Wikipedia

    en.wikipedia.org/wiki/Elements_of_Algebra

    The title page of Elements of Algebra. Elements of Algebra is an elementary mathematics textbook written by mathematician Leonhard Euler around 1765 in German. It was first published in Russian as "Universal Arithmetic" (Универсальная арифметика), two volumes appearing in 1768-9 [1] and in 1770 was printed from the original text.

  8. Tensor algebra - Wikipedia

    en.wikipedia.org/wiki/Tensor_algebra

    In mathematics, the tensor algebra of a vector space V, denoted T(V) or T • (V), is the algebra of tensors on V (of any rank) with multiplication being the tensor product.It is the free algebra on V, in the sense of being left adjoint to the forgetful functor from algebras to vector spaces: it is the "most general" algebra containing V, in the sense of the corresponding universal property ...

  9. F-algebra - Wikipedia

    en.wikipedia.org/wiki/F-algebra

    Therefore, a ring is an F-algebra of signature 1 + R×R over the category of abelian groups which satisfies two axioms (associativity and identity for the multiplication). When we come to vector spaces and modules , the signature functor includes a scalar multiplication k × E → E , and the signature F ( E ) = 1 + E + k × E is parametrized ...

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