Authors:
- New edition extensively revised and updated
- Places a strong emphasis on computational techniques
- Contains more than 200 exercises, including 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 (14 chapters)
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Front Matter
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The Essentials of Discrete Volume Computations
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Front Matter
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Beyond the Basics
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Front Matter
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Back Matter
About this book
This richly illustrated textbook explores the amazing interaction between combinatorics, geometry, number theory, and analysis which arises in the interplay between polyhedra and lattices. Highly accessible to advanced undergraduates, as well as beginning graduate students, this second edition is perfect for a capstone course, and adds two new chapters, many new exercises, and updated open problems. For scientists, this text can be utilized as a self-contained tooling device.
The topics include a friendly invitation to Ehrhart’s theory of counting lattice points in polytopes, finite Fourier analysis, the Frobenius coin-exchange problem, Dedekind sums, solid angles, Euler–Maclaurin summation for polytopes, computational geometry, magic squares, zonotopes, and more.
With more than 300 exercises and open research problems, the reader is an active participant, carried through diverse but tightly woven mathematical fields that are inspired by an innocently elementary question: What are the relationships between the continuous volume of a polytope and its discrete volume?
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 mate
rial, 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 Robinshave written the perfect text for such a course.”— CHOICE
Reviews
“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
Authors and Affiliations
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Department of Mathematics, San Francisco State University, San Francisco, USA
Matthias Beck
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Department of Mathematics, Brown University, Providence, USA
Sinai Robins
About the authors
Bibliographic Information
Book Title: Computing the Continuous Discretely
Book Subtitle: Integer-Point Enumeration in Polyhedra
Authors: Matthias Beck, Sinai Robins
Series Title: Undergraduate Texts in Mathematics
DOI: https://doi.org/10.1007/978-1-4939-2969-6
Publisher: Springer New York, NY
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Matthias Beck and Sinai Robins 2015
Hardcover ISBN: 978-1-4939-2968-9Published: 14 November 2015
Softcover ISBN: 978-1-4939-3858-2Published: 23 August 2016
eBook ISBN: 978-1-4939-2969-6Published: 14 November 2015
Series ISSN: 0172-6056
Series E-ISSN: 2197-5604
Edition Number: 2
Number of Pages: XX, 285
Topics: Combinatorics, Number Theory, Convex and Discrete Geometry, Computational Science and Engineering