Abstract Algebra

This text seeks to generate interest in abstract algebra by introducing each new structure and topic via a real-world application. The down-to-earth presentation is accessible to a readership with no prior knowledge of abstract algebra. Students are led to algebraic concepts and questions in a natural way through their everyday experiences. Applications include: Identification numbers and modular arithmetic (linear) error-correcting codes, including cyclic codes ruler and compass constructions cryptography symmetry of patterns in the real plane Abstract Algebra: Structure and Application is suitable as a text for a first course on abstract algebra whose main purpose is to generate interest in the subject or as a supplementary text for more advanced courses. The material paves the way to subsequent courses that further develop the theory of abstract algebra and will appeal to students of mathematics, mathematics education, computer science, and engineering interested in applications of algebraic concepts.

Identification Numbers and Modular Arithmetic Pages 1-21 Error Correcting Codes Pages 23-40 Rings and Fields Pages 41-55 Linear Algebra and Linear Codes Pages 57-72 Quotient Rings and Field Extensions Pages 73-91 Ruler and Compass Constructions Pages 93-104 Cyclic Codes Pages 105-120 Groups and Cryptography Pages 121-134 The Structure of Groups Pages 135-144 Symmetry Pages 145-181

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