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...
Gespeichert in:
| 1. Verfasser: | |
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| Weitere Verfasser: | |
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge, UK ; New York, NY :
Cambridge University Press,
©2004.
|
| Ausgabe: | 2nd ed. |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | 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. |
| Beschreibung: | 1 online resource (xvi, 338 pages) : illustrations |
| Bibliographie: | Includes bibliographical references (pages 323-325) and indexes. |
| ISBN: | 0511193467 9780511193460 052154050X 9780521540506 9780511648168 0511648162 9780511812187 0511812183 9780511194207 051119420X 1107141664 9781107141667 0511555652 9780511555657 |
Internformat
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| 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. | ||
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| 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. |
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| discipline | Informatik Mathematik |
| edition | 2nd ed. |
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| genre | Electronic book. Electronic books. |
| genre_facet | Electronic book. Electronic books. |
| id | ZDB-4-EBA-ocn439696987 |
| illustrated | Illustrated |
| indexdate | 2024-11-27T13:16:52Z |
| institution | BVB |
| isbn | 0511193467 9780511193460 052154050X 9780521540506 9780511648168 0511648162 9780511812187 0511812183 9780511194207 051119420X 1107141664 9781107141667 0511555652 9780511555657 |
| language | English |
| oclc_num | 439696987 |
| open_access_boolean | |
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| owner_facet | MAIN DE-863 DE-BY-FWS |
| physical | 1 online resource (xvi, 338 pages) : illustrations |
| psigel | ZDB-4-EBA |
| publishDate | 2004 |
| publishDateSearch | 2004 |
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| publisher | Cambridge University Press, |
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| spelling | Humphreys, J. F. http://id.loc.gov/authorities/names/n87851902 Numbers, groups, and codes / J.F. Humphreys, M.Y. Prest. 2nd ed. Cambridge, UK ; New York, NY : Cambridge University Press, ©2004. 1 online resource (xvi, 338 pages) : illustrations text txt rdacontent computer c rdamedia online resource cr rdacarrier data file Includes bibliographical references (pages 323-325) and indexes. Print version record. 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. 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. English. Group theory. http://id.loc.gov/authorities/subjects/sh85057512 Number theory. http://id.loc.gov/authorities/subjects/sh85093222 Théorie des groupes. Théorie des nombres. MATHEMATICS Group Theory. bisacsh Group theory fast Number theory fast Codierungstheorie gnd http://d-nb.info/gnd/4139405-7 Gruppentheorie gnd Zahlentheorie gnd Electronic book. Electronic books. Prest, Mike. http://id.loc.gov/authorities/names/n87851900 has work: Numbers, groups, and codes (Text) https://id.oclc.org/worldcat/entity/E39PCGb4J3pFGhcdHFvmQtv9ym https://id.oclc.org/worldcat/ontology/hasWork Print version: Humphreys, J.F. Numbers, groups, and codes. 2nd ed. Cambridge, UK ; New York, NY : Cambridge University Press, ©2004 (DLC) 2004555450 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=304475 Volltext |
| spellingShingle | Humphreys, J. F. Numbers, groups, and codes / 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. Group theory. http://id.loc.gov/authorities/subjects/sh85057512 Number theory. http://id.loc.gov/authorities/subjects/sh85093222 Théorie des groupes. Théorie des nombres. MATHEMATICS Group Theory. bisacsh Group theory fast Number theory fast Codierungstheorie gnd http://d-nb.info/gnd/4139405-7 Gruppentheorie gnd Zahlentheorie gnd |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85057512 http://id.loc.gov/authorities/subjects/sh85093222 http://d-nb.info/gnd/4139405-7 |
| title | Numbers, groups, and codes / |
| title_auth | Numbers, groups, and codes / |
| title_exact_search | Numbers, groups, and codes / |
| title_full | Numbers, groups, and codes / J.F. Humphreys, M.Y. Prest. |
| title_fullStr | Numbers, groups, and codes / J.F. Humphreys, M.Y. Prest. |
| title_full_unstemmed | Numbers, groups, and codes / J.F. Humphreys, M.Y. Prest. |
| title_short | Numbers, groups, and codes / |
| title_sort | numbers groups and codes |
| topic | Group theory. http://id.loc.gov/authorities/subjects/sh85057512 Number theory. http://id.loc.gov/authorities/subjects/sh85093222 Théorie des groupes. Théorie des nombres. MATHEMATICS Group Theory. bisacsh Group theory fast Number theory fast Codierungstheorie gnd http://d-nb.info/gnd/4139405-7 Gruppentheorie gnd Zahlentheorie gnd |
| topic_facet | Group theory. Number theory. Théorie des groupes. Théorie des nombres. MATHEMATICS Group Theory. Group theory Number theory Codierungstheorie Gruppentheorie Zahlentheorie Electronic book. Electronic books. |
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