Abstract Algebra: Structure and Application

ISBN-13: 9783319044972 / Angielski / Twarda / 2014 / 187 str.

David Finston; Patrick Morandi

Opis

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.

Recenzje

"The essential characteristic of this book is the 'down-to-earth' presentation on the most fundamental aspects of modern algebra. This book is indeed accessible to a general audience without prior knowledge of modern algebra ... ." (Haohao Wang, Mathematical Reviews, April, 2017)

"Finston and Morandi intend to develop the structures and basic theorems of modern algebra through applications that have relevance to the students' daily lives. ... For the vast majority of their students this will be their final abstract algebra course. ... do an excellent job of introducing students to the theory of abstract algebra and its applications." (Ellen Ziliak, MAA Reviews, June, 2015)

"Finston (Brooklyn College) and Morandi (New Mexico State Univ.) have taken on the daunting task of writing an abstract algebra text for students who are majoring in math, math education, or computer science and emphasizing applications to cover in one semester. The well-written work is organized to meet the authors' stated goals. ... Summing Up: Recommended. Upper-division undergraduates and faculty." (J. R. Burke, Choice, Vol. 52 (9), May, 2015)

"This book can be used in various situations: for an applied algebra course, for courses designed for secondary mathematics teachers, for programs of Master' degree in middle school mathematics education or a Master of Arts in Teaching Mathematics. ... The book is structured in ten chapters." (Florentina Chirtes, zbMATH, Vol. 1304, 2015)

Spis treści

Identification Numbers and Modular Arithmetic.- Error Correcting Codes.- Rings and Fields.- Linear Algebra and Linear Codes.- Quotient Rings and Field Extensions.- Ruler and Compass Constructions.- Cyclic Codes.- Groups and Cryptography.- The Structure of Groups.- Symmetry.