From Error Correcting Codes Through Sphere Packings to Simple Groups

Thomas M. Thompson - Collection The Carus Mathematical Monographs

228 pages, parution le 01/10/2004

Ajouter à une liste

Indisponible

Résumé

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 lead 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 neighboring 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 some 10,000+ pages. And these connections, along with the fascinating history and the proof of the simplicity of one of those "sporatic" simple groups, are presented at an undergraduate mathematical level.

L'auteur - Thomas M. Thompson

Thomas M. Thompson received his Ph.D. from the University of California, Davis, under Sherman Stein. Before going to Davis, he began his teaching career at Walla Walla College in southeastern Washington State where he subsequently returned and has remained there to the present. His main mathematical interests are in algebra, history, and pedagogy, and for the past eleven years he has team-taught an interdisciplinary honors course combining science, mathematics, and the arts. This latter experience has also allowed him to pursue, without guilt, one of his many hobbies: amateur astronomy. While at Walla Walla College he has received The Thomas and Violet Zapara Excellence in Teaching Award in mathematics and science.

Sommaire

The origin of error-correcting codes
- An introduction to coding
- The work of Hamming
- The Hamming-Holbrook patent
- The Hamming codes are linear
- The work of Golay
- The priority controversy
From coding to sphere packing
- An introduction to sphere packing
- The Leech connection
- The origin of Leech's first packing in E²⁴
- The matrix for Leech's first packing
- The Leech lattice
From sphere packing to new simple groups
- Is there an interesting group in Leech's lattice?
- The hard sell of a simple group
- Twelve hours on Saturday, six on Wednesday
- The structure of 0
- New simple groups

Voir tout

Replier

Caractéristiques techniques

	PAPIER
Éditeur(s)	The Mathematical Association of America (MAA)
Auteur(s)	Thomas M. Thompson
Collection	The Carus Mathematical Monographs
Parution	01/10/2004
Nb. de pages	228
Format	12,5 x 19
Couverture	Broché
Poids	235g
Intérieur	Noir et Blanc
EAN13	9780883850374
ISBN13	978-0-88385-037-4