Based on a graduate course at the Technische Universität, Berlin, these lectures present a wealth of material on the modern theory of convex polytopes. The straightforward exposition features many illustrations, and complete proofs for most theorems. With only linear algebra as a prerequisite, it takes the reader quickly from the basics to topics of recent research. The lectures introduce basic facts about polytopes, with an emphasis on methods that yield the results, discuss important examples and elegant constructions, and show the excitement of current work in the field. They will provide interesting and enjoyable reading for researchers as well as students.
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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." (Miklós Bóna, MathDL, August, 2007)
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10 of 11 people found the following review helpful:
5.0 out of 5 stars
Excellent!,
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This review is from: Lectures on Polytopes (Graduate Texts in Mathematics) (Paperback)
If you are browsing around for a recent advanced text on modern polytope theory, this is it. Ziegler is very clear, comprehensive, and provides hundreds of references.
2 of 2 people found the following review helpful:
4.0 out of 5 stars
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This review is from: Lectures on Polytopes (Graduate Texts in Mathematics) (Paperback)
This book is very clearly an introduction, and does not cover the more advanced topics (for that, see the books by Richter-Gebert, Sturmfels, Stanley). Nor does it cover the major application area of the field (linear programming), which is a shame, since much of the subject does not seem to be very motivated without it. Indeed, even the major connected area in pure mathematics (toric varieties) is not touched on. Even the in the subjects he does cover, he does not try to dive very deeply (for example, in the (excellent) section on Steinitz' theorem, he does not prove the contractibility of the realization space). So, the author picks his battles, and wins the ones he picks. As the other reviewer has mentioned, the bibliography is excellent. So, I would have given the book 4.5 stars if that were possible, with a penalty for motivation (or lack thereof).
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Inside This Book
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First Sentence:
Convex polytopes are fundamental geometric objects: to a large extent the geometry of polytopes is just that of Rd itself. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
zonotopal tilings, fiber polytope, polytopal complex, polytope pairs, same oriented matroid, signed cocircuits, planar point configuration, polytopal subdivision, partial shelling, neighborly polytopes, oriented matroid duality, simplicial regions, simplicial polytopes, sign vector sign, shelling order, irredundant description, isotopy property, topological representation theorem, oriented matroids, shellable complexes, secondary polytope, face poset, pseudoline arrangement, simple vertices, polar polytope Key Phrases - Capitalized Phrases (CAPs): (learn more)
Gil Kalai, Jurgen Richter-Gebert, Use Exercise New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Convex polytopes are fundamental geometric objects: to a large extent the geometry of polytopes is just that of Rd itself. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
zonotopal tilings, fiber polytope, polytopal complex, polytope pairs, same oriented matroid, signed cocircuits, planar point configuration, polytopal subdivision, partial shelling, neighborly polytopes, oriented matroid duality, simplicial regions, simplicial polytopes, sign vector sign, shelling order, irredundant description, isotopy property, topological representation theorem, oriented matroids, shellable complexes, secondary polytope, face poset, pseudoline arrangement, simple vertices, polar polytope Key Phrases - Capitalized Phrases (CAPs): (learn more)
Gil Kalai, Jurgen Richter-Gebert, Use Exercise New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 100
books:
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100
books
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- Discrete Mathematics by Wiley in Back Matter (1), Back Matter (2), and Back Matter (3)
- Cyclotomic Fields (Graduate Texts in Mathematics) by S. Lang in Front Matter, Back Matter (1), and Back Matter (2)
- Oriented Matroids (Encyclopedia of Mathematics and its Applications) by Anders Björner in Back Matter (1), Back Matter (2), and Back Matter (3)
- Finite Reflection Groups (Graduate Texts in Mathematics) by L.C. Grove in Back Matter (1), and Back Matter (2)
- An Introduction to Algebraic Topology (Graduate Texts in Mathematics) by Joseph J. Rotman in Back Matter (1), and Back Matter (2)
See all 100 books this book cites
- Polytopes - Combinatorics and Computation (Oberwolfach Seminars) by Gil Kalai on page 103, page 130, and page 198
- Discrete and Computational Geometry: The Goodman-Pollack Festschrift (Algorithms and Combinatorics) by Boris Aronov on page 698, page 736, and page 796
- Discrete Geometry (Chapman & Hall/CRC Pure and Applied Mathematics) by Andras Bezdek on page 278, page 386, and page 406
- Using Algebraic Geometry by David A. Cox in Back Matter (1), and Back Matter (2)
- Foundations of Computational Mathematics: Proceedings of Smalefest 2000 by Felipe Cucker on page 13, and page 324
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