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    STUDIA MATHEMATICA - Issue no. 4 / 2007  
         
  Article:   BOOK REVIEWS - PETER M. GRUBER, CONVEX AND DISCRETE GEOMETRY, SPRINGER-VERLAG, BERLIN-HEIDELBERG, 2007, GRUNDLEHREN DER MATHEMATISCHEN WISSENSCHAFTEN, VOLUME 336, XIII+578 PP..

Authors:  ŞTEFAN COBZAŞ. 		 
       
         
  Abstract:  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. The general idea of the book is that there are a plenty of beautiful and deep classical results and challenging problems in the domain, which are still in the focus of current research. Some of the problems as, for instance, the isoperimetric problems, the Platonic solids, the volumes of pyramids, have their roots in antiquity, while the modern research in convex geometry concerns local theory of Banach spaces, best and random approximation, surfaces and curvature measures, tilings and packings. Their solution requires tools and methods from various fields of mathematics, as Fourier analysis, probability theory, combinatorics, topology, and, in turn, the results from convex and discrete geometry are very useful in many domain of mathematics.  
         
     
         
         
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