Abstract algebra.9781584886891 Abstract algebra
Abstract algebra is the subject area of mathematics that studies algebraic structures, such as groups, rings, fields, modules, . Garrett, Paul B. Chapman & Hall/CRC 2008 451 pages $89.95 Hardcover QA162 Garrett (mathematics, University of Minnesota (body, education) University of Minnesota - The home of Gopher. http://umn.edu/. Address: Minneapolis, Minnesota, USA. ) takes an example-oriented, less heavily symbolic approach to abstract algebra. He emphasizes specifics such as basic number theory, polynomials, and finite fields, as well as linear and multilinear algebra In mathematics, multilinear algebra extends the methods of linear algebra. Just as linear algebra is built on the concept of a vector and develops the theory of vector spaces, multilinear algebra builds on the concept of a tensor and develops the theory of 'tensor spaces'. . An unusual feature of the book is the systematic characterization of objects by universal mapping properties, rather than by constructions whose technical details are irrelevant. In addition to standard introductory material on the subject, such as Lagrange's and Sylow's theorems in group theory, the text provides specific illustrations of general theory, discussing in detail finite fields, cyclotomic polynomials, and cyclotomic fields. It also focuses on broader background, with brief but representative discussions of naive set theory and equivalents of the Axiom of Choice (mathematics) Axiom of Choice - (AC, or "Choice") An axiom of set theory: If X is a set of sets, and S is the union of all the elements of X, then there exists a function f:X -> S such that for all non-empty x in X, f(x) is an element of x. , quadratic reciprocity The law of quadratic reciprocity is a theorem from number theory which considers two distinct odd prime numbers, p and q, and the statements
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