Overview
- Accessible to students with no prior knowledge of abstract algebra
- Focuses on a wide variety of daily applications
- Numerous sample problems and exercises
- Includes supplementary material: sn.pub/extras
Part of the book series: Springer Undergraduate Texts in Mathematics and Technology (SUMAT)
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Table of contents (11 chapters)
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Front Matter
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Back Matter
Keywords
About this book
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.
Reviews
“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 meetthe 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 Chirteş, zbMATH, Vol. 1304, 2015)
Authors and Affiliations
Bibliographic Information
Book Title: Abstract Algebra
Book Subtitle: Structure and Application
Authors: David R. Finston, Patrick J. Morandi
Series Title: Springer Undergraduate Texts in Mathematics and Technology
DOI: https://doi.org/10.1007/978-3-319-04498-9
Publisher: Birkhäuser Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing Switzerland 2014
Hardcover ISBN: 978-3-319-04497-2Published: 11 September 2014
Softcover ISBN: 978-3-319-34395-2Published: 30 April 2017
eBook ISBN: 978-3-319-04498-9Published: 29 August 2014
Series ISSN: 1867-5506
Series E-ISSN: 1867-5514
Edition Number: 1
Number of Pages: IX, 187
Number of Illustrations: 45 b/w illustrations
Topics: Algebra, Mathematical Applications in Computer Science, Linear and Multilinear Algebras, Matrix Theory