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Lectures in Geometric Combinatorics

Rekha R. Thomas
Publisher: 
American Mathematical Society/Institute for Advanced Study
Publication Date: 
2006
Number of Pages: 
143
Format: 
Paperback
Series: 
Student Mathematical Library 33
Price: 
29.00
ISBN: 
0-8218-4140-8
Category: 
Monograph
[Reviewed by
Miklós Bóna
, on
04/26/2007
]

This book can be a useful tool for a graduate student or researcher with no knowledge of the topics presented here and who wants to understand the main concepts quickly. No previous knowledge other than undergraduate-level linear algebra is required, and the chapters are ten pages long on average. This reviewer found the text easy to read.

Two main topics are discussed. The first two-thirds of the book is about polytopes and polyhedra. Readers who want to dig deeper into this field should continue their studies by consulting the book by Gunther Ziegler, Lectures on Polytopes , after reading the first nine chapters of this book.

The last third of the book is devoted to more algebraic aspects of geometric combinatorics. There are two chapters on Gröbner bases and two on Toric ideals. Readers who become interested in these two topics can learn more from the book by Bernd Sturmfels, Gröbner Bases and Convex Polytopes .


Miklós Bóna is Associate Professor of Mathematics at the University of Florida.

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