Sphere Packings, Lattices and Groups (Grundlehren der mathematischen Wissenschaften) (v. 290) [Hardcover]

John Horton Conway (Author), Neil J. A. Sloane (Author)

Book Description

ISBN-10: 0387985859 | ISBN-13: 978-0387985855 | Publication Date: December 7, 1998 | Edition: 3rd

The third edition of this definitive and popular book continues to pursue the question: what is the most efficient way to pack a large number of equal spheres in n-dimensional Euclidean space? The authors also examine such related issues as the kissing number problem, the covering problem, the quantizing problem, and the classification of lattices and quadratic forms. There is also a description of the applications of these questions to other areas of mathematics and science such as number theory, coding theory, group theory, analogue-to-digital conversion and data compression, n-dimensional crystallography, dual theory and superstring theory in physics. New and of special interest is a report on some recent developments in the field, and an updated and enlarged supplementary bibliography with over 800 items.

Editorial Reviews

Review

Third Edition J.H. Conway and N.J.A. Sloane Sphere Packings, Lattices and Groups "This is the third edition of this reference work in the literature on sphere packings and related subjects. In addition to the content of the preceding editions, the present edition provides in its preface a detailed survey on recent developments in the field, and an exhaustive supplementary bibliography for 1988-1998. A few chapters in the main text have also been revised."—MATHEMATICAL REVIEWS

Product Details

• Hardcover: 777 pages
• Publisher: Springer; 3rd edition (December 7, 1998)
• Language: English
• ISBN-10: 0387985859
• ISBN-13: 978-0387985855
• Product Dimensions: 9.4 x 1.3 x 0.1 inches
• Shipping Weight: 2.7 pounds (View shipping rates and policies)
• Average Customer Review: 4.5 out of 5 stars  See all reviews (2 customer reviews)
• Amazon Best Sellers Rank: #1,217,999 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

15 of 16 people found the following review helpful:

5.0 out of 5 stars The book on lattice, September 9, 2001

By 

Mathieu Dutour (Jerusalem) - See all my reviews

This review is from: Sphere Packings, Lattices and Groups (Grundlehren der mathematischen Wissenschaften) (v. 290) (Hardcover)

This book is devoted to the subject of lattice packings. It is an outstanding book with all pages interesting. It acts as a reference on the subjects of lattices. What you will find:
--Sphere packings, ie the problem of packing spheres in order to maximize density.
--The problem of Kissin numbers: maximize the number of adjacent sphere to a given sphere in a lattice
--Code, design, and Groups
--Error correcting codes
--Leech lattice
--Integral quadratic forms
--Voronoi cell
--many, many other subjects
What you WON'T find in this book:
--The study of Delaunay cells (or holes, L-polytopes) is quite limited
--The study of continuous families of lattice is not done, you won't find the Voronoi memoires here
--There is just one page on computational aspects of lattice

Nevertheless this book is excellent

1 of 1 people found the following review helpful:

4.0 out of 5 stars One of the Mathematics master works of the 20th century, March 5, 2009

By 

R. Bagula "Roger L. Bagula" (Lakeside, Ca United States) - See all my reviews
(VINE VOICE)    (REAL NAME)   

This review is from: Sphere Packings, Lattices and Groups (Grundlehren der mathematischen Wissenschaften) (v. 290) (Hardcover)

I have this checked out of the county library, but two weeks or two years,
I would still have trouble reading it all.
Dr. John Conway is one of the most important mathematicians of the 20th century and Dr. Sloane isn't very far behind that. With their friend John Leech,
they have published this landmark in the history of group theory that seems destined to be beside Coexter's work as the most influential work on
on the theory of higher Euclidean and hyperbolic n dimensional groups.
That these groups have been related to the practical area of error free coding in information theory has made this knowledge both interesting and useful as well. With some awe I realize how much thought and work
went into writing this book.
I you were Dr. Sloane or Dr. Conway, you would have to ask yourselves, how can you ever top this?
This book is not "easy" reading, it hasn't been dumbed down
and the results are real enough for anybody.