**ISBN:** 0387291393

**Author:** Sinai Robins,Matthias Beck

**Language:** English

**Publisher:** Springer; F First Edition edition (July 1, 2007)

**Pages:** 227

**Category:** Mathematics

**Subcategory:** Science

**Rating:** 4.9

**Votes:** 985

**Size Fb2:** 1422 kb

**Size ePub:** 1787 kb

**Size Djvu:** 1897 kb

**Other formats:** docx txt lrf lrf

This book is an outstanding book on counting integer points of polytopes.

This book is an outstanding book on counting integer points of polytope. .The book contains lots of exercises with very helpful hints. Another essential feature of the book is a vast collection of open problems on different aspects of integer point counting and related areas. The book is reader-friendly written, self-contained and contains numerous beautiful illustrations. You owe it to yourself to pick up a copy of Computing the Continuous Discretely to read about a number of interesting problems in geometry, number theory, and combinatorics.

Matthias Beck, Sinai Robins. Because there is no other book that puts together all of these ideas in one place, this text is truly a service to the mathematical community. This much-anticipated textbook illuminates the field of discrete mathematics with examples, theory, and applications of the discrete volume of a polytope.

Matthias Beck & Sinai Robins. Computing the Continuous Discretely We seek to bridge some critical gaps between various elds of mathematics by studying the interplay between the continuous volume and the discrete vol-ume of polytopes. Computing the Continuous Discretely. Integer-Point Enumeration in Polyhedra. We seek to bridge some critical gaps between various elds of mathematics by studying the interplay between the continuous volume and the discrete vol-ume of polytopes.

The world is continuous, but the mind is discrete. The continuous volume of P has the usual intuitive meaning of volume that we attach to everyday objects we see in the real world. David Mumford We seek to bridge some critical gaps between various ?elds of mathematics by studying the interplay between the continuous volume and the discrete v- ume of polytopes. VIII Preface Indeed, the di?erence between the two realizations of volume can be thought of in physical terms as follows.

Undergraduate Texts in Mathematics (UTM) is a series of undergraduate-level textbooks in mathematics published by Springer-Verlag. The books in this series tend to be written at a more elementary level than the similar Graduate Texts in Mathematics series, although there is a fair amount of overlap between the two series in terms of material covered and difficulty level. ISBN 13: 9780387291390. Series: Undergraduate Texts in Mathematics. 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.

This chapter carries us through concrete instances of lattice-point enumeration in various integral and rational polytopes. Counting Lattice Points in Polytopes:The Ehrhart Theory.

Integer-point Enumeration in Polyhedra. Authors: Beck, Matthias, Robins, Sinai. This book is concerned with the mathematics of that connection between the discrete and the continuous, with significance for geometry, number theory and combinatorics

Integer-point Enumeration in Polyhedra. This book is concerned with the mathematics of that connection between the discrete and the continuous, with significance for geometry, number theory and combinatorics.

Undergraduate Texts in Mathematics. Sinai Robins, Matthias Beck. This book provides many well-crafted exercises, and even a list of open problems in each chapter.

Computing the Continuous Discretely : Integer-Point Enumeration in Polyhedra. by Sinai Robins and Matthias Beck. This richly illustrated textbook explores the amazing interaction between combinatorics, geometry, number theory, and analysis which arises in the interplay between polyhedra and lattices.

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.

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