| 书目名称 | Computing the Continuous Discretely |
| 副标题 | Integer-point Enumer |
| 编辑 | Matthias Beck,Sinai Robins |
| 视频video | |
| 概述 | 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 class-tested.Includes hin |
| 丛书名称 | Undergraduate Texts in Mathematics |
| 图书封面 |  |
| 描述 | The world is continuous, but the mind is discrete. 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. Examples of polytopes in three dimensions include crystals, boxes, tetrahedra, and any convex object whose faces are all ?at. It is amusing to see how many problems in combinatorics, number theory, and many other mathematical areas can be recast in the language of polytopes that exist in some Euclidean space. Conversely, the versatile structure of polytopes gives us number-theoretic and combinatorial information that ?ows naturally from their geometry. Fig. 0. 1. Continuous and discrete volume. The discrete volume of a body P can be described intuitively as the number of grid points that lie inside P, given a ?xed grid in Euclidean space. The continuous volume of P has the usual intuitive meaning of volume that we attach to everyday objects we see in the real world. VIII Preface Indeed, the di?erence between the two realizations of volume can be thought of in physical terms as follows. On the one hand, the quant- level grid imposed by the molecular stru |
| 出版日期 | Textbook 20071st edition |
| 关键词 | Combinatorics; Lattice; calculus; combinatorial geometry; computational geometry; discrete geometry; numbe |
| 版次 | 1 |
| doi | https://doi.org/10.1007/978-0-387-46112-0 |
| isbn_softcover | 978-1-4419-2119-2 |
| isbn_ebook | 978-0-387-46112-0Series ISSN 0172-6056 Series E-ISSN 2197-5604 |
| issn_series | 0172-6056 |
| copyright | Springer-Verlag New York 2007 |
发表于 2025-3-21 18:26:33
