球垛格点和群
2008-11
世界图书出版公司
康韦
703
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The main themes. This book is mainly concerned with the problem of packing spheres in Euclidean space of dimensions 1,2,3,4,5,.... Given a large number of equal spheres, what is the most efficient （or densest） way to pack them together？ We also study several closely related problems: the kissing number problem, which asks how many spheres can be arranged so that they all touch one central sphere of the same size; the covering problem, which asks for thc least dense way to cover n-dimensional space with equal overlapping spheres; and the quantizing problem, important for applications to analog-to-digital conversion （or data compression）, which asks how to place points in space so that the average second moment of their Voronoi cells is as small as possible. Attacks on these problems usually arrange the spheres so their centers form a lattice. Lattices are described by quadratic forms, and we study the classification of quadratic forms. Most of the book is devoted to these five problems.
本书为第三版，继前两版之后，接着探讨“如何最有效地将大量等球放入n维的欧氏空间中？”这一核心问题。同时，作者仍在思考一些相关的问题，如：吻接数问题，覆盖问题，量子化问题以及格分类与二次型。与前两版相同的是，第三版也描述了以上这些问题与数学或自然科学中其他一些领域的联系，这些领域包括：码理论，数字通信，数论，群论，模拟数字转换以及数据压缩与n维晶体。值得特别注意的是，本书收录了一篇介绍本领域的最新的一些研究成果的报告，并补充了1988-1998年间出版的超过800项的参考书目，相信这些珍贵的资料一定能够引起读者特殊的兴趣。本书适用于数学专业的高年级本科生或研究生以及需要相关知识的科研人员。
作者：(英国)康韦 (Conway.J.H)
Preface to First EditionPreface to Third EditionList of SymbolsChapter 1 Sphere Packings and Kissing NumbersChapter 2 Coverings,Lattices and QuantizersChapter 3 Codes,Designs and GroupsChapter 4 Certain Important Lattices and Their PropertiesChapter 5 Sphere Packing and Error-Correcting CodesChapter 6 Laminated LatticesChapter 7 Further Connections Betwwen Codes and LatticesChapter 8 Algebraic Constructions for LatticesChapter 9 Bounds for Codes and Sphere PackingsChapter 10 Three Lectures on Exceptional GroupsChapter 11 The Golay Codes and the Mathieu GroupsChapter 12 A Characterization of the Leech LatticeChapter 13 Bounds on Kissing NumbersChapter 14 Uniqueness of Certain Spherical CodesChapter 15 On the Classification of Integral Quadratic FormsChapter 16 Enumeration of Unimodular LatticesChapter 17 The 24-Dimensional Odd Unimodular LatticesChapter 18 Even Unimodular 24-Dimensional LatticesChapter 19 Enumeration of Extremal Self-Dual LatticesChapter 20 Finding the Closest Lattice PointChapter 21 Voronoi Cells of Lattices and Quantization ErrorsChapter 22 A Bound for the Covering Radius of the Leech LatticeChapter 23 The Covering Radius of the Leech LatticeChapter 24 Twenty-Three Constructions for the Leech LatticeChapter 25 The Cellular Structure of the Leech LatticeChapter 26 Lorentzian Forms for the Leech LatticeChapter 27 The Automorphism Group of the 26-Dimensional Even Unimodular Lorentzian LatticeChapter 28 Leech Roots and Vinberg GroupsChapter 29 The Monster Group and its 196884-Dimensional SpaceChapter 30 A Monster Lie Algebra?BibliographySupplementary BibliographyIndex
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《球垛格点和群(第3版)》由世界图书出版公司。
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里面涉及的数学分支太多了.内容丰富,不容易读啊.
双十一半价买的很不错数的封皮灰尘不少估计放了有段时间了纸张较薄毕竟是影印版可以接受
没心思，也就没怎么看，看着郁闷。
从事代数编码必备的参考书。