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【2015新书】Computing the Continuous Discretely: Integer-Point Enumeration in Polyhedra
Book 图书名称:Computing the Continuous Discretely: Integer-Point Enumeration in Polyhedra
Author 作者: Matthias Beck, Sinai Robins
Publisher 出版社:Springer
Page 页数:295
Publishing Date 出版时间: Nov 14, 2015
Language 语言: English
Size 大小: 3 MB
Format 格式: pdf 文字版
ISBN: 1493929682, 9781493929689
Edition: 第1版 搜索过论坛,没有该文档
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?
== Table of contents ==
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