From Error- correcting Codes through Sphere Packings to Simple Groups.

THOMPSON, Thomas M.

ISBN 10: 0883850230 / ISBN 13: 9780883850237

Published by The Mathematical Association of America, 1983

About this Item

228pp, first printing, number 21 of Carus Mathematical Monographs, covers bright and clean, name and name stamp on half-title page otherwise unmarked.

Seller Inventory # 4445147

Bibliographic Details

• Title: From Error- correcting Codes through Sphere Packings to Simple Groups.
• Publisher: The Mathematical Association of America
• Publication Date: 1983
• Language: English
• ISBN 10: 0883850230
• ISBN 13: 9780883850237
• Binding: Hardcover
• Edition: 1st Edition
• Condition: Very Good
• Seller catalogs:
  • Science - Mathematics - Physics

About this title

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.

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.