From error-correcting codes through sphere packings to simple groups /:
This book traces a remarkable path of mathematical connections through seemingly disparate topics. Frustrations with a 1940's electro-mechanical computer at a premier research laboratory begin this story. Subsequent mathematical methods of encoding messages to ensure correctness when transmitte...
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
[Washington] :
Mathematical Association of America,
©1983.
|
| Schriftenreihe: | Carus mathematical monographs ;
no. 21. |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | This book traces a remarkable path of mathematical connections through seemingly disparate topics. Frustrations with a 1940's electro-mechanical computer at a premier research laboratory begin this story. Subsequent mathematical methods of encoding messages to ensure correctness when transmitted over noisy channels led to discoveries of extremely efficient lattice packings of equal-radius balls, especially in 24-dimensional space. In turn, this highly symmetric lattice, with each point neighbouring exactly 196,560 other points, suggested the possible presence of new simple groups as groups of symmetries. Indeed, new groups were found and are now part of the 'Enormous Theorem' - the classification of all simple groups whose entire proof runs to some 10,000+ pages. And these connections, along with the fascinating history and the proof of the simplicity of one of those 'sporadic' simple groups, are presented at an undergraduate mathematical level. -- Amazon.com. |
| Beschreibung: | 1 online resource (xiv, 228 pages :) |
| Format: | Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002. |
| Bibliographie: | Includes bibliographical references (pages 217-223) and index. |
| ISBN: | 9781614440215 1614440212 |
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| 588 | 0 | |a Print version record. | |
| 505 | 0 | |a The origin of error-correcting codes -- From coding to sphere packing -- From sphere packing to new simple groups -- Appendix 1. Densest known sphere packings -- Appendix 2. Further properties of the (12, 24) Golay code and the related Steiner system S(5, 8, 24) -- Appendix 3. A calculation of the number of spheres with centers in [lambda]₂ adjacent to one, two, three and four adjacent spheres with centers in [lambda]₂ -- Appendix 4. The Mathieu group M₂₄ and the order of M₂₂ -- Appendix 5. The proof of Lemma 3.3 -- Appendix 6. The sporadic simple groups. | |
| 520 | |a This book traces a remarkable path of mathematical connections through seemingly disparate topics. Frustrations with a 1940's electro-mechanical computer at a premier research laboratory begin this story. Subsequent mathematical methods of encoding messages to ensure correctness when transmitted over noisy channels led to discoveries of extremely efficient lattice packings of equal-radius balls, especially in 24-dimensional space. In turn, this highly symmetric lattice, with each point neighbouring exactly 196,560 other points, suggested the possible presence of new simple groups as groups of symmetries. Indeed, new groups were found and are now part of the 'Enormous Theorem' - the classification of all simple groups whose entire proof runs to some 10,000+ pages. And these connections, along with the fascinating history and the proof of the simplicity of one of those 'sporadic' simple groups, are presented at an undergraduate mathematical level. -- Amazon.com. | ||
| 650 | 0 | |a Error-correcting codes (Information theory) |0 http://id.loc.gov/authorities/subjects/sh85044725 | |
| 650 | 0 | |a Finite simple groups. |0 http://id.loc.gov/authorities/subjects/sh85048356 | |
| 650 | 6 | |a Codes correcteurs d'erreurs (Théorie de l'information) | |
| 650 | 6 | |a Groupes simples finis. | |
| 650 | 7 | |a MATHEMATICS |x Algebra |x Intermediate. |2 bisacsh | |
| 650 | 7 | |a Error-correcting codes (Information theory) |2 fast | |
| 650 | 7 | |a Finite simple groups |2 fast | |
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| 650 | 1 | |a Finite simple groups. | |
| 650 | 7 | |a ALGEBRA. |2 nasat | |
| 650 | 7 | |a ERROR CORRECTING. |2 nasat | |
| 650 | 7 | |a COMBINATORIAL ANALYSIS. |2 nasat | |
| 650 | 7 | |a GROUP THEORY. |2 nasat | |
| 650 | 7 | |a HISTORIES. |2 nasat | |
| 650 | 7 | |a Group theory. |2 nli | |
| 650 | 7 | |a Coding theory. |2 nli | |
| 650 | 7 | |a Codes correcteurs d'erreurs (théorie de l'information) |2 ram | |
| 650 | 7 | |a Groupes simples finis. |2 ram | |
| 648 | 7 | |a Geschichte 1947-1949. |2 swd | |
| 648 | 7 | |a Geschichte 1950-1962. |2 swd | |
| 648 | 7 | |a Geschichte 1963-1980. |2 swd | |
| 758 | |i has work: |a From error-correcting codes through sphere packings to simple groups (Text) |1 https://id.oclc.org/worldcat/entity/E39PCYkpjxv8BJYwp9jHYPGDVP |4 https://id.oclc.org/worldcat/ontology/hasWork | ||
| 776 | 0 | 8 | |i Print version: |a Thompson, Thomas M. |t From error-correcting codes through sphere packings to simple groups. |d [Washington] : Mathematical Association of America, ©1983 |w (DLC) 82062784 |w (OCoLC)10565134 |
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Datensatz im Suchindex
| DE-BY-FWS_katkey | ZDB-4-EBA-ocn681278322 |
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| _version_ | 1813903388579987456 |
| adam_text | |
| any_adam_object | |
| author | Thompson, Thomas M. |
| author_GND | http://id.loc.gov/authorities/names/n85347771 |
| author_facet | Thompson, Thomas M. |
| author_role | aut |
| author_sort | Thompson, Thomas M. |
| author_variant | t m t tm tmt |
| building | Verbundindex |
| bvnumber | localFWS |
| callnumber-first | Q - Science |
| callnumber-label | QA268 |
| callnumber-raw | QA268 .T45 1983eb |
| callnumber-search | QA268 .T45 1983eb |
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| contents | The origin of error-correcting codes -- From coding to sphere packing -- From sphere packing to new simple groups -- Appendix 1. Densest known sphere packings -- Appendix 2. Further properties of the (12, 24) Golay code and the related Steiner system S(5, 8, 24) -- Appendix 3. A calculation of the number of spheres with centers in [lambda]₂ adjacent to one, two, three and four adjacent spheres with centers in [lambda]₂ -- Appendix 4. The Mathieu group M₂₄ and the order of M₂₂ -- Appendix 5. The proof of Lemma 3.3 -- Appendix 6. The sporadic simple groups. |
| ctrlnum | (OCoLC)681278322 |
| dewey-full | 005.7/2 |
| dewey-hundreds | 000 - Computer science, information, general works |
| dewey-ones | 005 - Computer programming, programs, data, security |
| dewey-raw | 005.7/2 |
| dewey-search | 005.7/2 |
| dewey-sort | 15.7 12 |
| dewey-tens | 000 - Computer science, information, general works |
| discipline | Informatik Mathematik |
| era | Geschichte 1947-1949. swd Geschichte 1950-1962. swd Geschichte 1963-1980. swd |
| era_facet | Geschichte 1947-1949. Geschichte 1950-1962. Geschichte 1963-1980. |
| format | Electronic eBook |
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| id | ZDB-4-EBA-ocn681278322 |
| illustrated | Illustrated |
| indexdate | 2024-10-25T16:17:54Z |
| institution | BVB |
| isbn | 9781614440215 1614440212 |
| language | English |
| oclc_num | 681278322 |
| open_access_boolean | |
| owner | MAIN |
| owner_facet | MAIN |
| physical | 1 online resource (xiv, 228 pages :) |
| psigel | ZDB-4-EBA |
| publishDate | 1983 |
| publishDateSearch | 1983 |
| publishDateSort | 1983 |
| publisher | Mathematical Association of America, |
| record_format | marc |
| series | Carus mathematical monographs ; |
| series2 | The Carus mathematical monographs ; |
| spelling | Thompson, Thomas M., author. http://id.loc.gov/authorities/names/n85347771 From error-correcting codes through sphere packings to simple groups / by Thomas M. Thompson. [Washington] : Mathematical Association of America, ©1983. 1 online resource (xiv, 228 pages :) text txt rdacontent computer c rdamedia online resource cr rdacarrier The Carus mathematical monographs ; no. 21 Includes bibliographical references (pages 217-223) and index. Use copy Restrictions unspecified star MiAaHDL Electronic reproduction. [Place of publication not identified] : HathiTrust Digital Library, 2010. MiAaHDL Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002. http://purl.oclc.org/DLF/benchrepro0212 MiAaHDL digitized 2010 HathiTrust Digital Library committed to preserve pda MiAaHDL Print version record. The origin of error-correcting codes -- From coding to sphere packing -- From sphere packing to new simple groups -- Appendix 1. Densest known sphere packings -- Appendix 2. Further properties of the (12, 24) Golay code and the related Steiner system S(5, 8, 24) -- Appendix 3. A calculation of the number of spheres with centers in [lambda]₂ adjacent to one, two, three and four adjacent spheres with centers in [lambda]₂ -- Appendix 4. The Mathieu group M₂₄ and the order of M₂₂ -- Appendix 5. The proof of Lemma 3.3 -- Appendix 6. The sporadic simple groups. This book traces a remarkable path of mathematical connections through seemingly disparate topics. Frustrations with a 1940's electro-mechanical computer at a premier research laboratory begin this story. Subsequent mathematical methods of encoding messages to ensure correctness when transmitted over noisy channels led to discoveries of extremely efficient lattice packings of equal-radius balls, especially in 24-dimensional space. In turn, this highly symmetric lattice, with each point neighbouring exactly 196,560 other points, suggested the possible presence of new simple groups as groups of symmetries. Indeed, new groups were found and are now part of the 'Enormous Theorem' - the classification of all simple groups whose entire proof runs to some 10,000+ pages. And these connections, along with the fascinating history and the proof of the simplicity of one of those 'sporadic' simple groups, are presented at an undergraduate mathematical level. -- Amazon.com. Error-correcting codes (Information theory) http://id.loc.gov/authorities/subjects/sh85044725 Finite simple groups. http://id.loc.gov/authorities/subjects/sh85048356 Codes correcteurs d'erreurs (Théorie de l'information) Groupes simples finis. MATHEMATICS Algebra Intermediate. bisacsh Error-correcting codes (Information theory) fast Finite simple groups fast Einfache Gruppe gnd http://d-nb.info/gnd/4123107-7 Fehlerkorrekturcode gnd http://d-nb.info/gnd/4124917-3 Geschichte gnd Kugelpackung gnd http://d-nb.info/gnd/4165929-6 Finite simple groups. ALGEBRA. nasat ERROR CORRECTING. nasat COMBINATORIAL ANALYSIS. nasat GROUP THEORY. nasat HISTORIES. nasat Group theory. nli Coding theory. nli Codes correcteurs d'erreurs (théorie de l'information) ram Groupes simples finis. ram Geschichte 1947-1949. swd Geschichte 1950-1962. swd Geschichte 1963-1980. swd has work: From error-correcting codes through sphere packings to simple groups (Text) https://id.oclc.org/worldcat/entity/E39PCYkpjxv8BJYwp9jHYPGDVP https://id.oclc.org/worldcat/ontology/hasWork Print version: Thompson, Thomas M. From error-correcting codes through sphere packings to simple groups. [Washington] : Mathematical Association of America, ©1983 (DLC) 82062784 (OCoLC)10565134 Carus mathematical monographs ; no. 21. http://id.loc.gov/authorities/names/n86717982 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=760878 Volltext CBO01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=760878 Volltext |
| spellingShingle | Thompson, Thomas M. From error-correcting codes through sphere packings to simple groups / Carus mathematical monographs ; The origin of error-correcting codes -- From coding to sphere packing -- From sphere packing to new simple groups -- Appendix 1. Densest known sphere packings -- Appendix 2. Further properties of the (12, 24) Golay code and the related Steiner system S(5, 8, 24) -- Appendix 3. A calculation of the number of spheres with centers in [lambda]₂ adjacent to one, two, three and four adjacent spheres with centers in [lambda]₂ -- Appendix 4. The Mathieu group M₂₄ and the order of M₂₂ -- Appendix 5. The proof of Lemma 3.3 -- Appendix 6. The sporadic simple groups. Error-correcting codes (Information theory) http://id.loc.gov/authorities/subjects/sh85044725 Finite simple groups. http://id.loc.gov/authorities/subjects/sh85048356 Codes correcteurs d'erreurs (Théorie de l'information) Groupes simples finis. MATHEMATICS Algebra Intermediate. bisacsh Error-correcting codes (Information theory) fast Finite simple groups fast Einfache Gruppe gnd http://d-nb.info/gnd/4123107-7 Fehlerkorrekturcode gnd http://d-nb.info/gnd/4124917-3 Geschichte gnd Kugelpackung gnd http://d-nb.info/gnd/4165929-6 Finite simple groups. ALGEBRA. nasat ERROR CORRECTING. nasat COMBINATORIAL ANALYSIS. nasat GROUP THEORY. nasat HISTORIES. nasat Group theory. nli Coding theory. nli Codes correcteurs d'erreurs (théorie de l'information) ram Groupes simples finis. ram |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85044725 http://id.loc.gov/authorities/subjects/sh85048356 http://d-nb.info/gnd/4123107-7 http://d-nb.info/gnd/4124917-3 http://d-nb.info/gnd/4165929-6 |
| title | From error-correcting codes through sphere packings to simple groups / |
| title_auth | From error-correcting codes through sphere packings to simple groups / |
| title_exact_search | From error-correcting codes through sphere packings to simple groups / |
| title_full | From error-correcting codes through sphere packings to simple groups / by Thomas M. Thompson. |
| title_fullStr | From error-correcting codes through sphere packings to simple groups / by Thomas M. Thompson. |
| title_full_unstemmed | From error-correcting codes through sphere packings to simple groups / by Thomas M. Thompson. |
| title_short | From error-correcting codes through sphere packings to simple groups / |
| title_sort | from error correcting codes through sphere packings to simple groups |
| topic | Error-correcting codes (Information theory) http://id.loc.gov/authorities/subjects/sh85044725 Finite simple groups. http://id.loc.gov/authorities/subjects/sh85048356 Codes correcteurs d'erreurs (Théorie de l'information) Groupes simples finis. MATHEMATICS Algebra Intermediate. bisacsh Error-correcting codes (Information theory) fast Finite simple groups fast Einfache Gruppe gnd http://d-nb.info/gnd/4123107-7 Fehlerkorrekturcode gnd http://d-nb.info/gnd/4124917-3 Geschichte gnd Kugelpackung gnd http://d-nb.info/gnd/4165929-6 Finite simple groups. ALGEBRA. nasat ERROR CORRECTING. nasat COMBINATORIAL ANALYSIS. nasat GROUP THEORY. nasat HISTORIES. nasat Group theory. nli Coding theory. nli Codes correcteurs d'erreurs (théorie de l'information) ram Groupes simples finis. ram |
| topic_facet | Error-correcting codes (Information theory) Finite simple groups. Codes correcteurs d'erreurs (Théorie de l'information) Groupes simples finis. MATHEMATICS Algebra Intermediate. Finite simple groups Einfache Gruppe Fehlerkorrekturcode Geschichte Kugelpackung ALGEBRA. ERROR CORRECTING. COMBINATORIAL ANALYSIS. GROUP THEORY. HISTORIES. Group theory. Coding theory. Codes correcteurs d'erreurs (théorie de l'information) |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=760878 |
| work_keys_str_mv | AT thompsonthomasm fromerrorcorrectingcodesthroughspherepackingstosimplegroups |