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Abstract Algebra : An Introductory Course

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概要 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 pro...perties 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.続きを見る
目次 Part I Preliminaries
1 Relations and Functions
2 The Integers and Modular Arithmetic
Part II Groups
3 Introduction to Groups
4 Factor Groups and Homomorphisms
5 Direct Products and the Classification of Finite Abelian Groups
6 Symmetric and Alternating Groups
7 The Sylow Theorems
Part III Rings
8 Introduction to Rings
9 Ideals, Factor Rings and Homomorphisms
10 Special Types of Domains
Part IV Fields and Polynomials
11 Irreducible Polynomials
12 Vector Spaces and Field Extensions
Part V Applications
13 Public Key Cryptography
14 Straightedge and Compass Constructions
A The Complex Numbers
B Matrix Algebra
Solutions
Index.
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本文を見る Full text available from SpringerLINK ebooks - Mathematics and Statistics (2018)

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登録日 2018.06.06
更新日 2018.06.06