Convex and Discrete Geometry is an area of mathematics situated between analysis, geometry and discrete mathematics with numerous relations to other areas. The book gives an overview of major results, methods and ideas of convex and discrete geometry and its applications. Besides being a graduate-level introduction to the field, it is a practical source of information and orientation for convex geometers. It should also be of use to people working in other areas of mathematics and in the applied fields.
Convex Functions.- Convex Bodies.- Convex Polytopes.- Geometry of Numbers and Aspects of Discrete Geometry.
From the reviews:
The aim of the present book is to give an overview of basic methods and results of convex analysis and discrete geometry and their applications. & A large bibliography of 1052 titles, each of them being referred to in the text, tries to cover all the facets of the subject, from its origins to the present day state. & the clear and pleasant style of presentation, make the book accessible to a large audience, including graduate students, teachers and researchers in various areas of mathematics. (S. Cobzas, Studia Universitatis Babes-Bolyai, Vol. LII (4), 2007)
Convex geometry is a classical area of mathematics that dates back to antiquity. & the authors main goal is to expose applications of convex geometry to other areas of mathematics and science, in particular number theory, mathematical physics, crystallography, tomography, optimization, and computational geometry. & The book can be used for graduate courses in convex, discrete geometry and geometry of numbers. For experts and people working on applications, the book is a very valuable source of open problems, new directions and references. (Aleksandr Koldobsky, Mathematical Reviews, Issue 2008 f)
This excellent book presents a complete and coherent overview of principal ideas, results and methods lcā
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