Numbers, Groups and Codes

Content: 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 6.1 Introduction6.2 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
 Answers
 Chapter 1
 Chapter 2
 Chapter 3
 Chapter 4
 Chapter 5
 Chapter 6
 References and further reading
 Biography
 Name index
 Subject index