Numbers groups and codes 2nd Edition by Humphreys, Prest 0511648162 9780511648168

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Product details:

ISBN 10: 0511648162 

ISBN 13: 9780511648168

Author: J. F. Humphreys; M. Y. Prest

This textbook is an introduction to algebra via examples. The book moves from properties of integers, through other examples, to the beginnings of group theory. Applications to public key codes and to error correcting codes are emphasised. These applications, together with sections on logic and finite state machines, make the text suitable for students of computer science as well as mathematics students. Attention is paid to historical development of the mathematical ideas. This second edition contains new material on mathematical reasoning skills and a new chapter on polynomials has been added. The book was developed from first-level courses taught in the UK and USA. These courses proved successful in developing not only a theoretical understanding but also algorithmic skills. This book can be used at a wide range of levels: it is suitable for first- or second-level university students, and could be used as enrichment material for upper-level school students.

Table of contents:

1 Number theory

1.1 The division algorithm and greatest common divisors

1.2 Mathematical induction

1.3 Primes and the Unique Factorisation Theorem

1.4 Congruence classes

1.5 Solving linear congruences

1.6 Euler’s Theorem and public key codes

Summary of Chapter 1

2 Sets, functions and relations

2.1 Elementary set theory

2.2 Functions

2.3 Relations

2.4 Finite state machines

Summary of Chapter 2

3 Logic and mathematical argument

3.1 Propositional logic

3.2 Quantifiers

3.3 Some proof strategies

Summary of Chapter 3

4 Examples of groups

4.1 Permutations

4.2 The order and sign of a permutation

4.3 Definition and examples of groups

4.3.1 Groups of numbers

4.3.2 Groups of permutations

4.3.3 Groups of matrices

4.3.4 Groups of symmetries of geometric figures

4.4 Algebraic structures

Summary of Chapter 4

5 Group theory and error-correcting codes

5.1 Preliminaries

5.2 Cosets and Lagrange’s Theorem

5.3 Groups of small order

5.4 Error-detecting and error-correcting codes

Summary of Chapter 5

6 Polynomials

6.1 Introduction

6.2 The division algorithm for polynomials

6.3 Factorisation

6.4 Polynomial congruence classes

6.5 Cyclic codes

Summary of Chapter 6

Appendix on complex numbers

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Tags: Humphreys, Prest, Numbers, groups, codes