| Edition |
2nd ed. |
| Description |
1 online resource (xvi, 338 pages) : illustrations |
|
data file |
| Physical Medium |
polychrome |
| Bibliography |
Includes bibliographical references (pages 323-325) and indexes. |
| Contents |
Cover; Half-title; Title; Copyright; Dedication; Contents; Preface to first edition; Preface to second edition; Introduction; Advice to the reader; 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 logic3.2 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. |
| Summary |
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 adde. |
| Local Note |
eBooks on EBSCOhost EBSCO eBook Subscription Academic Collection - North America |
| Subject |
Group theory.
|
|
Group theory. |
|
Number theory.
|
|
Number theory. |
| Genre/Form |
Electronic book.
|
|
Electronic books.
|
|
Electronic books.
|
| Added Author |
Prest, Mike.
|
| Other Form: |
Print version: Humphreys, J.F. Numbers, groups, and codes. 2nd ed. Cambridge, UK ; New York, NY : Cambridge University Press, ©2004 (DLC) 2004555450 |
| ISBN |
0511193467 |
|
9780511193460 |
|
052154050X (paperback) |
|
9780521540506 (paperback) |
|
9780511648168 (electronic book) |
|
0511648162 (electronic book) |
|
9780511812187 (electronic book) |
|
0511812183 (electronic book) |
|
9780511194207 |
|
051119420X |
|
