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"Linglong method" (玲瓏 開方; línglóng kāifāng, roughly "method of harmoniously alternating evolution") for numerical solution of algebraic equations, 570 years before Horner's method [1] [2] Areas and volumes of geometric objects and
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.
In homological algebra, the relationship between currying and uncurrying is known as tensor-hom adjunction. Here, an interesting twist arises: the Hom functor and the tensor product functor might not lift to an exact sequence ; this leads to the definition of the Ext functor and the Tor functor .
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Al-Khwarizmi's algebra is regarded as the foundation and cornerstone of the sciences. In a sense, al-Khwarizmi is more entitled to be called "the father of algebra" than Diophantus because al-Khwarizmi is the first to teach algebra in an elementary form and for its own sake, Diophantus is primarily concerned with the theory of numbers. [52]
The quadratic formula, which concisely expresses the solutions of all quadratic equations The Rubik's Cube group is a concrete application of group theory. [26] Algebra is the art of manipulating equations and formulas. Diophantus (3rd century) and al-Khwarizmi (9th century) were the two main precursors of algebra.
The fundamental theorem of finitely generated abelian groups can be stated two ways, generalizing the two forms of the fundamental theorem of finite abelian groups.The theorem, in both forms, in turn generalizes to the structure theorem for finitely generated modules over a principal ideal domain, which in turn admits further generalizations.
The true solution to this linear system is = []. With Galerkin method, we can solve the system in a lower-dimensional space to obtain an approximate solution. Let us use the following basis for the subspace: = [].