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.
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"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 Chirtes, zbMATH, Vol. 1304, 2015)