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.
Amy has always loved cats and is thrilled when she spots a tiny little black kitten in her garden. Although she has no collar, she looks too well cared for to be a stray. Misty the kitten starts to spend more and more time with Amy, and they become best friends but just as Amy starts to think of the kitten as hers, the real owners show up...…
Identification numbers and modular arithmetic
(linear) error-correcting codes, including cyclic codes
ruler and compass constructions
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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