Read and Download eBook Full
Author: Chuanming Zong
Publisher: Cambridge University Press
Published: 2006-02-02
Total Pages: 196
ISBN-13: 9780521855358
DOWNLOAD EBOOKAnalysis, Algebra, Combinatorics, Graph Theory, Hyperbolic Geometry, Number Theory.
Author: Károly Bezdek
Publisher: Springer Science & Business Media
Published: 2010-06-23
Total Pages: 171
ISBN-13: 1441906002
DOWNLOAD EBOOKGeometry is a classical core part of mathematics which, with its birth, marked the beginning of the mathematical sciences. Thus, not surprisingly, geometry has played a key role in many important developments of mathematics in the past, as well as in present times. While focusing on modern mathematics, one has to emphasize the increasing role of discrete mathematics, or equivalently, the broad movement to establish discrete analogues of major components of mathematics. In this way, the works of a number of outstanding mathema- cians including H. S. M. Coxeter (Canada), C. A. Rogers (United Kingdom), and L. Fejes-T oth (Hungary) led to the new and fast developing eld called discrete geometry. One can brie y describe this branch of geometry as the study of discrete arrangements of geometric objects in Euclidean, as well as in non-Euclidean spaces. This, as a classical core part, also includes the theory of polytopes and tilings in addition to the theory of packing and covering. D- crete geometry is driven by problems often featuring a very clear visual and applied character. The solutions use a variety of methods of modern mat- matics, including convex and combinatorial geometry, coding theory, calculus of variations, di erential geometry, group theory, and topology, as well as geometric analysis and number theory.
Author: Vitor Balestro
Publisher: Springer Nature
Published:
Total Pages: 1195
ISBN-13: 3031505077
DOWNLOAD EBOOKAuthor: Hiroshi Maehara
Publisher: Springer Nature
Published:
Total Pages: 342
ISBN-13: 3031627768
DOWNLOAD EBOOKAuthor: Daniel Hug
Publisher: Springer Nature
Published: 2020-08-27
Total Pages: 287
ISBN-13: 3030501809
DOWNLOAD EBOOKThis book provides a self-contained introduction to convex geometry in Euclidean space. After covering the basic concepts and results, it develops Brunn–Minkowski theory, with an exposition of mixed volumes, the Brunn–Minkowski inequality, and some of its consequences, including the isoperimetric inequality. Further central topics are then treated, such as surface area measures, projection functions, zonoids, and geometric valuations. Finally, an introduction to integral-geometric formulas in Euclidean space is provided. The numerous exercises and the supplementary material at the end of each section form an essential part of the book. Convexity is an elementary and natural concept. It plays a key role in many mathematical fields, including functional analysis, optimization, probability theory, and stochastic geometry. Paving the way to the more advanced and specialized literature, the material will be accessible to students in the third year and can be covered in one semester.
Author: Rolf Schneider
Publisher: Cambridge University Press
Published: 2014
Total Pages: 759
ISBN-13: 1107601010
DOWNLOAD EBOOKA complete presentation of a central part of convex geometry, from basics for beginners, to the exposition of current research.
Author: Barry Simon
Publisher: Cambridge University Press
Published: 2011-05-19
Total Pages: 357
ISBN-13: 1139497596
DOWNLOAD EBOOKConvexity is important in theoretical aspects of mathematics and also for economists and physicists. In this monograph the author provides a comprehensive insight into convex sets and functions including the infinite-dimensional case and emphasizing the analytic point of view. Chapter one introduces the reader to the basic definitions and ideas that play central roles throughout the book. The rest of the book is divided into four parts: convexity and topology on infinite-dimensional spaces; Loewner's theorem; extreme points of convex sets and related issues, including the Krein–Milman theorem and Choquet theory; and a discussion of convexity and inequalities. The connections between disparate topics are clearly explained, giving the reader a thorough understanding of how convexity is useful as an analytic tool. A final chapter overviews the subject's history and explores further some of the themes mentioned earlier. This is an excellent resource for anyone interested in this central topic.
Author: R. J. Hans-Gill
Publisher: Springer Nature
Published:
Total Pages: 212
ISBN-13: 9819996023
DOWNLOAD EBOOKAuthor: Cho-Ho Chu
Publisher: Cambridge University Press
Published: 2011-11-17
Total Pages: 273
ISBN-13: 1139505432
DOWNLOAD EBOOKJordan theory has developed rapidly in the last three decades, but very few books describe its diverse applications. Here, the author discusses some recent advances of Jordan theory in differential geometry, complex and functional analysis, with the aid of numerous examples and concise historical notes. These include: the connection between Jordan and Lie theory via the Tits–Kantor–Koecher construction of Lie algebras; a Jordan algebraic approach to infinite dimensional symmetric manifolds including Riemannian symmetric spaces; the one-to-one correspondence between bounded symmetric domains and JB*-triples; and applications of Jordan methods in complex function theory. The basic structures and some functional analytic properties of JB*-triples are also discussed. The book is a convenient reference for experts in complex geometry or functional analysis, as well as an introduction to these areas for beginning researchers. The recent applications of Jordan theory discussed in the book should also appeal to algebraists.
Author: Sinai Robins
Publisher: American Mathematical Society
Published: 2024-04-24
Total Pages: 352
ISBN-13: 1470470330
DOWNLOAD EBOOKThis book offers a gentle introduction to the geometry of numbers from a modern Fourier-analytic point of view. One of the main themes is the transfer of geometric knowledge of a polytope to analytic knowledge of its Fourier transform. The Fourier transform preserves all of the information of a polytope, and turns its geometry into analysis. The approach is unique, and streamlines this emerging field by presenting new simple proofs of some basic results of the field. In addition, each chapter is fitted with many exercises, some of which have solutions and hints in an appendix. Thus, an individual learner will have an easier time absorbing the material on their own, or as part of a class. Overall, this book provides an introduction appropriate for an advanced undergraduate, a beginning graduate student, or researcher interested in exploring this important expanding field.
