Lectures on Polytopes (Springer Series in Operations Research) [Hardcover]

Gunter M. Ziegler (Author)

Book Description

Publication Date: January 1995 | ISBN-10: 0387943293 | ISBN-13: 978-0387943299

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.

--This text refers to the Paperback edition.

Editorial Reviews

Review

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) --This text refers to the Paperback edition.

Product Details

• Hardcover: 370 pages
• Publisher: Springer (January 1995)
• Language: English
• ISBN-10: 0387943293
• ISBN-13: 978-0387943299
• Product Dimensions: 9.8 x 6.5 x 1 inches
• Shipping Weight: 1.5 pounds
• Average Customer Review: 4.5 out of 5 stars  See all reviews (2 customer reviews)
• Amazon Best Sellers Rank: #10,928,477 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

10 of 11 people found the following review helpful:

5.0 out of 5 stars Excellent!, March 23, 2000

By A Customer

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 Clear and modern, May 19, 2010

By 

Narada "the wondering jew" (Princeton, NJ, USA) - See all my reviews
(VINE VOICE)   

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).