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A Course in Convexity

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Barvinok, Alexander 作者
Amer Mathematical Society
译者
2002-11 出版日期
366 页数
502.00 元 价格
HRD
Graduate Studies in Mathematics 丛书系列
9780821829684 图书编码

A Course in Convexity 在线电子书 图书标签: Math  数理  MathTopology   


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发表于2024-12-23


A Course in Convexity 在线电子书 epub 下载 mobi 下载 pdf 下载 txt 下载 2024

A Course in Convexity 在线电子书 epub 下载 mobi 下载 pdf 下载 txt 下载 2024

A Course in Convexity 在线电子书 pdf 下载 txt下载 epub 下载 mobi 下载 2024



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Convexity is a simple idea that manifests itself in a surprising variety of places. This fertile field has an immensely rich structure and numerous applications. Barvinok demonstrates that simplicity, intuitive appeal, and the universality of applications make teaching (and learning) convexity a gratifying experience. The book will benefit both teacher and student: It is easy to understand, entertaining to the reader, and includes many exercises that vary in degree of difficulty. Overall, the author demonstrates the power of a few simple unifying principles in a variety of pure and applied problems. <P>The notion of convexity comes from geometry. Barvinok describes here its geometric aspects, yet he focuses on applications of convexity rather than on convexity for its own sake. Mathematical applications range from analysis and probability to algebra to combinatorics to number theory. Several important areas are covered, including topological vector spaces, linear programming, ellipsoids, and lattices. Specific topics of note are optimal control, sphere packings, rational approximations, numerical integration, graph theory, and more. And of course, there is much to say about applying convexity theory to the study of faces of polytopes, lattices and polyhedra, and lattices and convex bodies. <P>The prerequisites are minimal amounts of linear algebra, analysis, and elementary topology, plus basic computational skills. Portions of the book could be used by advanced undergraduates. As a whole, it is designed for graduate students interested in mathematical methods, computer science, electrical engineering, and operations research. The book will also be of interest to research mathematicians, who will find some results that are recent, some that are new, and many known results that are discussed from a new perspective.

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