Computing the Continuous Discretely

Matthias Beck is Professor of Mathematics at San Francisco State University. Sinai Robins is Associate Professor of Mathematics at Nanyang Technological University, Singapore.

• The Coin-Exchange Problem of Frobenius.- A Gallery of Discrete Volumes.- Counting Lattice Points in Polytopes: The Ehrhart Theory.- Reciprocity.- Face Numbers and the Dehn–Sommerville Relations in Ehrhartian Terms.- Magic Squares.- Finite Fourier Analysis.- Dedekind Sums.- Zonotopes.- h-Polynomials and h*-Polynomials.- The Decomposition of a Polytope Into Its Cones.- Euler–Maclaurin Summation in Rd.- Solid Angles.- A Discrete Version of Green's Theorem Using Elliptic Functions.

“This book is an outstanding book on counting integer points of polytopes … . 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. The reader is always accompanied with deep research jokes by famous researchers and valuable historical notes.” (Oleg Karpenkov, zbMATH 1339.52002, 2016)Reviews of the first edition:“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.”— MAA Reviews“The book is written as an accessible and engaging textbook, with many examples, historical notes, pithy quotes, commentary integrating the material, exercises, open problems and an extensive bibliography.”— Zentralblatt MATH“This beautiful book presents, at a level suitable for advanced undergraduates, a fairly complete introduction to the problem of counting lattice points inside a convex polyhedron.”— Mathematical Reviews“Many departments recognize the need for capstone courses in which graduating students can see the tools they have acquired come together in some satisfying way. Beck and Robins have written the perfect text for such a course.”— CHOICE