Introduction to Algebra / Edition 2

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Overview

Developed to meet the needs of modern students, this Second Edition of the classic algebra text by Peter Cameron covers all the abstract algebra an undergraduate student is likely to need. Starting with an introductory overview of numbers, sets and functions, matrices, polynomials, and modular arithmetic, the text then introduces the most important algebraic structures: groups, rings and fields, and their properties. This is followed by coverage of vector spaces and modules with applications to abelian groups and canonical forms before returning to the construction of the number systems, including the existence of transcendental numbers. The final chapters take the reader further into the theory of groups, rings and fields, coding theory, and Galois theory. With over 300 exercises, and web-based solutions, this is an ideal introductory text for Year 1 and 2 undergraduate students in mathematics.
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Editorial Reviews

From the Publisher

"Cameron goes somewhat against conventional wisdom by choosing rings over groups as the primary algebraic structure of study. This choice allows an introduction to the ideas of abstract algebra in a setting most students will find a bit more familiar and comfortable. After the obligatory chapter reviewing some of the basics of sets, functions, and logic, Cameron introduces the essentials of rings and fields and then the standard first topics in group theory. . . . Subsequent chapters provide ample opportunity to delve into less traditional and/or more advanced topics. . . . This book will support a very rigorous first course in abstract algebra and contains more than enough material to fill up a two-semester course. Upper-division undergraduate and graduate students."--Choice

"This book contains more information than can be covered in a year-long algebra course, which allows for flexibility in its use. . . . Cameron's writing style is very enjoyable and reader-friendly. He uses entertaining verbs such as 'whittle' and 'blur' and gives many examples throughout the book. Modern and up-to-date analogies help students relate to concepts . . . Connections between concepts are emphasized. The use of certain terminology and notation is explained, and differences in notation are pointed out. . . . Even though the text is reader-friendly, a high level of rigor is maintained. Kernels are first defined as equivalence relations, polynomials are defined as infinite sequences, and three different proofs of the existence of transcendental numbers are given. . . . Cameron's book also includes some interesting mathematical folklore, which piques the interest of many students."--American Mathematical Monthly

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Product Details

  • ISBN-13: 9780198569138
  • Publisher: Oxford University Press, USA
  • Publication date: 2/9/2008
  • Edition number: 2
  • Pages: 350
  • Product dimensions: 9.30 (w) x 6.20 (h) x 1.00 (d)

Meet the Author

Peter Cameron has taught mathematics at Oxford University and Queen Mary, University of London, with shorter spells at other institutions. He has received the Junior Whitehead Prize of the London Mathematical Society, and the Euler Medal of the Institute of Combinatorics and its Applications, and is currently chair of the British Combinatorial Committee.

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Table of Contents

1 Introduction 1
2 Rings 25
3 Groups 65
4 Vector spaces 103
5 Modules 135
6 The number systems 159
7 Further topics 181
8 Applications 235
Further reading 269
Solutions to selected exercises 271
Index 287
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