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Lectures on Polytopes : Graduate Texts in Mathematics - Gunter M. Ziegler

Lectures on Polytopes

Graduate Texts in Mathematics

Paperback Published: November 1994
ISBN: 9780387943657
Number Of Pages: 370

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Based on a graduate course given at the Technische Universitat, Berlin, these lectures present a wealth of material on the modern theory of convex polytopes. The clear and straightforward presentation features many illustrations, and provides complete proofs for most theorems. The material requires only linear algebra as a prerequisite, but takes the reader quickly from the basics to topics of recent research, including a number of unanswered questions. The lectures - introduce the basic facts about polytopes, with an emphasis on the methods that yield the results (Fourier-Motzkin elimination, Schlegel diagrams, shellability, Gale transforms, and oriented matroids) - discuss important examples and elegant constructions (cyclic and neighborly polytopes, zonotopes, Minkowski sums, permutahedra and associhedra, fiber polytopes, and the Lawrence construction) - show the excitement of current work in the field (Kalai's new diameter bounds, construction of non-rational polytopes, the Bohne-Dress tiling theorem, the upper-bound theorem), and nonextendable shellings) They should provide interesting and enjoyable reading for researchers as well as students.

Industry Reviews

From the reviews:

"This is an excellent book on convex polytopes written by a young and extremely active researcher." (Acta Scientiarum Mathematicarum)

"From the publication of the first printing, in 1994, this book became one of the most widely used textbooks in Discrete Geometry. The reviewer sees at least two reasons for that: the beautiful mathematics presented here, and the fact that the book can be used at a wide variety of levels, for several different courses. ... It is not only students who can benefits from the book. Researchers will find its updates notes and references very helpful." (Miklos Bona, MathDL, August, 2007)

Preface to the Second Printing
Introduction and Examples
Polytopes, Polyhedra, and Cones
Faces of Polytopes
Graphs for Polytopes
Steinitz' Theorem for 3-Polytopes
Schlegel Diagrams for 4-Polytopes
Duality, Gale Diagrams, and Applications
Fans, Arrangements, Zonotopes, and Tilings
Shellability and the Upper Bound Theorem
Fiber Polytopes, and Beyond
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780387943657
ISBN-10: 038794365X
Series: Graduate Texts in Mathematics
Audience: General
Format: Paperback
Language: English
Number Of Pages: 370
Published: November 1994
Publisher: Springer-Verlag New York Inc.
Country of Publication: US
Dimensions (cm): 23.42 x 15.62  x 1.83
Weight (kg): 0.54

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