From error-correcting codes through sphere packings to simple groups /
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Author / Creator: | Thompson, Thomas M., author. |
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Imprint: | [Washington] : Mathematical Association of America, ©1983. |
Description: | 1 online resource (xiv, 228 pages) : illustrations |
Language: | English |
Series: | The Carus mathematical monographs ; no. 21 Carus mathematical monographs ; no. 21. |
Subject: | Error-correcting codes (Information theory) Finite simple groups. Codes correcteurs d'erreurs (Théorie de l'information) Groupes simples finis MATHEMATICS -- Algebra -- Intermediate. Error-correcting codes (Information theory) Finite simple groups. Einfache Gruppe Fehlerkorrekturcode Geschichte Kugelpackung Electronic books. Electronic books |
Format: | E-Resource Book |
URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/11233081 |
Summary: | 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. |
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Physical Description: | 1 online resource (xiv, 228 pages) : illustrations |
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. |
Bibliography: | Includes bibliographical references (pages 217-223) and index. |
ISBN: | 9781614440215 1614440212 0883850230 9780883850237 0883850001 9780883850008 0883850370 9780883850374 9780883850282 |