Authors:
The authors write with flair and have chosen a unique set of topics
Places a strong emphasis on computational techniques
Contains more than 200 exercises and has been heavily classtested
Includes hints to selected exercises
Includes supplementary material: sn.pub/extras
Part of the book series: Undergraduate Texts in Mathematics (UTM)
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Table of contents (12 chapters)

Front Matter

Back Matter
About this book
Keywords
 Combinatorics
 Lattice
 calculus
 combinatorial geometry
 computational geometry
 discrete geometry
 number theory
Reviews
From the reviews:
"You owe it to yourself to pick up a copy … to read about a number of interesting problems in geometry, number theory, and combinatorics … . Even people who are familiar with the material would almost certainly learn something from the clear and engaging exposition … . It contains a large number of exercises … . Each chapter also ends with a series of relevant open problems … . it is also full of mathematics that is selfcontained and worth reading on its own." (Darren Glass, MathDL, February, 2007)
"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. … Most importantly the book gives a complete presentation of the use of generating functions of various kinds to enumerate lattice points, as well as an introduction to the theory of Erhart quasipolynomials. … This book provides many wellcrafted exercises, and even a list of open problems in each chapter." (Jesús A. De Loera, Mathematical Reviews, Issue 2007 h)
"All mathematics majors study the topics they will need to know, should they want to go to graduate school. But most will not, and 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 (San Francisco State Univ.) and Robins (Temple Univ.) have written the perfect text for such a course. … Summing Up: Highly recommended. General readers; lowerdivision undergraduates through faculty." (D. V. Feldman, CHOICE, Vol. 45 (2), 2007)
"This book is concerned with the mathematics of that connection between the discrete and the continuous, with significance for geometry, number theory and combinatorics. … 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." (Margaret M. Bayer, Zentralblatt MATH, Vol. 1114 (16), 2007)
"The main topic of the book is initiated by a theorem of Ehrhart … . This is a wonderful book for various readerships. Students, researchers, lecturers in enumeration, geometry and number theory all find it very pleasing and useful. The presentation is accessible for mature undergraduates. … it is a clear introduction to graduate students and researchers with many exercises and with a list of open problems at the end of each chapter." (Péter Hajnal, Acta Scientiarum Mathematicarum, Vol. 75, 2009)
“The theme of this textbook … is the relation between the continuous and the discrete, namely, the interplay between the volume of a polytope and the number of grid points contained in it. … The text contains many exercises, some of which present material needed later (for these exercises hints are provided), and lists also many open research problems. – The book can be recommended both for its style and for its interesting … content.” (P. Schmitt, Monatshefte für Mathematik, Vol. 155 (2), October, 2008)
Authors and Affiliations

Mathematics Department, San Francisco State University, San Francisco, USA
Matthias Beck

Department of Mathematics, Temple University, Philadelphia, USA
Sinai Robins
Bibliographic Information
Book Title: Computing the Continuous Discretely
Book Subtitle: Integerpoint Enumeration in Polyhedra
Authors: Matthias Beck, Sinai Robins
Series Title: Undergraduate Texts in Mathematics
DOI: https://doi.org/10.1007/9780387461120
Publisher: Springer New York, NY
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: SpringerVerlag New York 2007
Softcover ISBN: 9781441921192Published: 23 November 2010
eBook ISBN: 9780387461120Published: 27 November 2007
Series ISSN: 01726056
Series EISSN: 21975604
Edition Number: 1
Number of Pages: XVIII, 227
Topics: Combinatorics, Geometry, Discrete Mathematics, Number Theory, Convex and Discrete Geometry, Computational Science and Engineering