Abstract Algebra : an Introductory Course / by Gregory T. Lee.

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Abstract Algebra : an Introductory Course / by Gregory T. Lee.

9783319776491
3319776495
9783319776484
3319776487

Cham : Springer International Publishing : Imprint : Springer, 2018.

English

1 online resource (xi, 301 pages) : illustrations.

10.1007/978-3-319-77649-1 doi

QA174-183

512/.02

This carefully written textbook offers a thorough introduction to abstract algebra, covering the fundamentals of groups, rings and fields. The first two chapters present preliminary topics such as properties of the integers and equivalence relations. The author then explores the first major algebraic structure, the group, progressing as far as the Sylow theorems and the classification of finite abelian groups. An introduction to ring theory follows, leading to a discussion of fields and polynomials that includes sections on splitting fields and the construction of finite fields. The final part contains applications to public key cryptography as well as classical straightedge and compass constructions. Explaining key topics at a gentle pace, this book is aimed at undergraduate students. It assumes no prior knowledge of the subject and contains over 500 exercises, half of which have detailed solutions provided.

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Springer undergraduate mathematics series.

Print version: 9783319776484

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