Customer Reviews

Sphere Packings, Lattices and Groups (Grundlehren der Mathematischen Wissenschaften (Springer))

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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

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.