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From Error-Correcting Codes through Sphere Packings to Simple Groups (Carus Mathematical Monographs, Series Number 21) - Softcover
Synopsis
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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Book Description
Mathematical methods of encoding messages to ensure correctness when transmitted over noisy channels led to discoveries of extremely efficient sphere lattice packings. In turn, this suggested the possible presence of new groups of symmetries. These connections, along with the fascinating history, are presented at an undergraduate mathematical level.
About the Author
Thomas M. Thompson recieved his Ph.D. from the University of California. He teaches at Walla Walla College in southeastern Washington State where he has received The Thomas and Violet Zapara Excellence in Teaching Award in mathematics and science.
"About this title" may belong to another edition of this title.
- PublisherThe Mathematical Association of America
- Publication date2004
- ISBN 10 0883850370
- ISBN 13 9780883850374
- BindingPaperback
- LanguageEnglish
- Number of pages244
- Rating
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