Description 
1 online resource (XI, 301 pages 7 illustrations) 
Series 
Springer Undergraduate Mathematics Series, 16152085 

Springer undergraduate mathematics series. 16152085

Contents 
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 
Summary 
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 
Subject 
Algebra.


Associative rings.


Field theory (Physics)


Group theory.


Mathematics.


Rings (Algebra)


Algebra.


Associative rings.


Field theory (Physics)


Group theory.


Mathematics.


Rings (Algebra)

Form 
Electronic book

ISBN 
3319776487 

3319776495 

9783319776484 

9783319776491 
