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From Error-Correcting Codes Through Sphere Packings to Simple Groups

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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.
Request Code : ZLIBIO4453867
Categories:
Year:
1983
Publisher:
The Mathematical Association of America
Language:
English
Pages:
228
ISBN 10:
0883850230
ISBN 13:
9780883850237
ISBN:
0883850230,9780883850237
Series:
The Carus Mathematical Monographs

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