Abstract algebra: structures and applications

by Lovett, Stephen, (Stephen T.)

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Title Statements

Full title :Abstract algebra : structures and applications / Stephen Lovett, Wheaton College, Wheaton, Illinois, USA.

Summary

A Discovery-Based Approach to Learning about Algebraic Structures. Lovett (Wheaton College) takes readers through the variegated landscape of algebra, from elementary modular arithmetic through groups, semigroups, and monoids, past rings and fields and group actions, beyond modules and algebras, to Galois Theory, multivariable polynomial rings, and Gröbner bases. Abstract Algebra: Structures and Applications helps students understand the abstraction of modern algebra. It emphasizes the more general concept of an algebraic structure while simultaneously covering applications. The text can be used in a variety of courses, from a one-semester introductory course to a full two-semester sequence. The book presents the core topics of structures in a consistent order: Definition of structure, Motivation, Examples, General properties, Important objects, Description, Subobjects, Morphisms, Subclasses, Quotient objects, Action structures, and Applications. The text uses the general concept of an algebraic structure as a unifying principle and introduces other algebraic structures besides the three standard ones (groups, rings, and fields). Examples, exercises, investigative projects, and entire sections illustrate how abstract algebra is applied to areas of science and other branches of mathematics.