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Numbers, groups, and codes /
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 fini...
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Otros Autores: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Cambridge, UK ; New York, NY :
Cambridge University Press,
©2004.
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| Edición: | 2nd ed. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- 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.