Abstract Algebra: Structures and Applications

Stephen Lovett

July 17, 2015 by Chapman and Hall/CRC
Textbook - 720 Pages - 152 B/W Illustrations
ISBN 9781482248906 - CAT# K23698

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Features

  • Emphasizes the general concept of an algebraic structure as a unifying principle instead of just focusing on groups, rings, and fields
  • Describes the application of algebra in numerous fields, such as cryptography and geometry
  • Includes brief introductions to other branches of algebra that encourage students to investigate further
  • Provides standard exercises as well as project ideas that challenge students to write investigative or expository mathematical papers
  • Contains many examples that illustrate useful strategies for solving the exercises

Solutions manual, lecture slides, and figure slides are available upon qualifying course adoption.

Summary

A Discovery-Based Approach to Learning about Algebraic Structures

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
  • 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.

 

 "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."

Choice Reviewed: Recommended

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