This book presents a course in the geometry of convex polytopes in
arbitrary dimension, suitable for an advanced undergraduate or
beginning graduate student. The book starts with the basics of
polytope theory. Schlegel and Gale diagrams are introduced as
geometric tools to visualize polytopes in high dimension and to
unearth bizarre phenomena in polytopes. The heart of the book is a
treatment of the secondary polytope of a point configuration and
its connections to the state polytope of the toric ideal defined by
the configuration. These polytopes are relatively recent constructs
with numerous connections to discrete geometry, classical algebraic
geometry, symplectic geometry, and combinatorics.The connections
rely on Grobner bases of toric ideals and other methods from
commutative algebra. The book is self-contained and does not
require any background beyond basic linear algebra. With numerous
figures and exercises, it can be used as a textbook for courses on
geometric, combinatorial, and computational aspects of the theory
of polytopes.
General
Imprint: |
American Mathematical Society
|
Country of origin: |
United States |
Series: |
Student Mathematical Library |
Release date: |
July 2006 |
Authors: |
Rekha R. Thomas
|
Dimensions: |
214 x 133 x 8mm (L x W x T) |
Format: |
Paperback
|
Pages: |
143 |
Edition: |
illustrated Edition |
ISBN-13: |
978-0-8218-4140-2 |
Categories: |
Books >
Science & Mathematics >
Mathematics >
General
|
LSN: |
0-8218-4140-8 |
Barcode: |
9780821841402 |
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