Customer Reviews

Lectures on Polytopes (Graduate Texts in Mathematics)

5 star:		(1)
4 star:		(1)
3 star:		(0)
2 star:		(0)
1 star:		(0)

 

 

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.

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).