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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 |
|---|---|
| Autor principal: | |
| Otros Autores: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Cambridge, UK ; New York, NY :
Cambridge University Press,
©2004.
|
| Edición: | 2nd ed. |
| Temas: | |
| Acceso en línea: | Texto completo |
MARC
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| 100 | 1 | |a Humphreys, J. F. | |
| 245 | 1 | 0 | |a Numbers, groups, and codes / |c J.F. Humphreys, M.Y. Prest. |
| 250 | |a 2nd ed. | ||
| 260 | |a Cambridge, UK ; |a New York, NY : |b Cambridge University Press, |c ©2004. | ||
| 300 | |a 1 online resource (xvi, 338 pages) : |b illustrations | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
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| 504 | |a Includes bibliographical references (pages 323-325) and indexes. | ||
| 588 | 0 | |a Print version record. | |
| 505 | 0 | |a 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. | |
| 505 | 8 | |a 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. | |
| 520 | |a 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. | ||
| 546 | |a English. | ||
| 590 | |a ProQuest Ebook Central |b Ebook Central Academic Complete | ||
| 590 | |a eBooks on EBSCOhost |b EBSCO eBook Subscription Academic Collection - Worldwide | ||
| 650 | 0 | |a Group theory. | |
| 650 | 0 | |a Number theory. | |
| 650 | 6 | |a Théorie des groupes. | |
| 650 | 6 | |a Théorie des nombres. | |
| 650 | 7 | |a MATHEMATICS |x Group Theory. |2 bisacsh | |
| 650 | 7 | |a Group theory |2 fast | |
| 650 | 7 | |a Number theory |2 fast | |
| 650 | 7 | |a Codierungstheorie |2 gnd | |
| 650 | 7 | |a Gruppentheorie |2 gnd | |
| 650 | 7 | |a Zahlentheorie |2 gnd | |
| 700 | 1 | |a Prest, Mike. | |
| 758 | |i has work: |a Numbers, groups, and codes (Text) |1 https://id.oclc.org/worldcat/entity/E39PCGb4J3pFGhcdHFvmQtv9ym |4 https://id.oclc.org/worldcat/ontology/hasWork | ||
| 776 | 0 | 8 | |i Print version: |a Humphreys, J.F. |t Numbers, groups, and codes. |b 2nd ed. |d Cambridge, UK ; New York, NY : Cambridge University Press, ©2004 |w (DLC) 2004555450 |
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