Computing the Continuous Discretely: Integer-point Enumeration in Polyhedra (Undergraduate Texts in Mathematics) by Matthias Beck (PDF)

Description

This textbook illuminates the field of discrete mathematics with examples, theory, and applications of the discrete volume of a polytope. The authors have weaved a unifying thread through basic yet deep ideas in discrete geometry, combinatorics, and number theory. We encounter here a friendly invitation to the field of “counting integer points in polytopes”, and its various connections to elementary finite Fourier analysis, generating functions, the Frobenius coin-exchange problem, solid angles, magic squares, Dedekind sums, computational geometry, and more. With 250 exercises and open problems, the reader feels like an active participant.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐Item was delivered quickly and was just as described.

⭐Choppy exposition interrupts the flow of the topics.Too bad, the subject deserves another treatmentat this level.

⭐I wouldn’t have thought you could write a dull book on this subject but these authors have come perilously close! It is consciously designed as material for a “capstone course” allowing undergraduates to see different parts of their acquired knowledge working together. This is obviously a worthy aim, but it has lured the authors into adopting a heavy-handed, didactic approach at odds with the intrinsic elegance of the material. For example, more could have been said about the Diophantine Frobenius problem and less about counting lattice points in very simple examples of polyhedra; more about Dedekind-Rademacher sums and less about the tedious details of Euler-Maclaurin summation in many dimensions (just the result would suffice for non-specialist readers).I find odd, too, that the beautiful and inspiring work of Arnol’d, Vershik, Barany and others on convex lattice polygons doesn’t get so much as a mention.The production of the book is just about up to Springer’s recent standard, which is to say far below its historic best. It isn’t easy on the eye, but at least I’ve got through it without the binding coming apart.

⭐Very nice but the germans are printing too thin letters…Another t’en words..what could I Say..It was a gratis book for sales’library or other..I think , if my german is Ok. It’s Ok for me..

⭐Not found.

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