Classical Topics In Discrete Geometry PDF Download
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Author | : Károly Bezdek |
Publisher | : Springer Science & Business Media |
Total Pages | : 171 |
Release | : 2010-06-23 |
Genre | : Mathematics |
ISBN | : 1441906002 |
Download Classical Topics in Discrete Geometry Book in PDF, ePub and Kindle
Geometry 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 | : K. Roly Bezdek |
Publisher | : |
Total Pages | : 180 |
Release | : 2010-06-25 |
Genre | : |
ISBN | : 9781441906014 |
Download Classical Topics in Discrete Geometry Book in PDF, ePub and Kindle
Author | : Jiri Matousek |
Publisher | : Springer Science & Business Media |
Total Pages | : 491 |
Release | : 2013-12-01 |
Genre | : Mathematics |
ISBN | : 1461300398 |
Download Lectures on Discrete Geometry Book in PDF, ePub and Kindle
The main topics in this introductory text to discrete geometry include basics on convex sets, convex polytopes and hyperplane arrangements, combinatorial complexity of geometric configurations, intersection patterns and transversals of convex sets, geometric Ramsey-type results, and embeddings of finite metric spaces into normed spaces. In each area, the text explains several key results and methods.
Author | : Andras Bezdek |
Publisher | : CRC Press |
Total Pages | : 500 |
Release | : 2003-02-04 |
Genre | : Mathematics |
ISBN | : 0824747615 |
Download Discrete Geometry Book in PDF, ePub and Kindle
Celebrating the work of Professor W. Kuperberg, this reference explores packing and covering theory, tilings, combinatorial and computational geometry, and convexity, featuring an extensive collection of problems compiled at the Discrete Geometry Special Session of the American Mathematical Society in New Orleans, Louisiana. Discrete Geometry analyzes packings and coverings with congruent convex bodies , arrangements on the sphere, line transversals, Euclidean and spherical tilings, geometric graphs, polygons and polyhedra, and fixing systems for convex figures. This text also offers research and contributions from more than 50 esteemed international authorities, making it a valuable addition to any mathematical library.
Author | : Peter M. Gruber |
Publisher | : Springer Science & Business Media |
Total Pages | : 590 |
Release | : 2007-05-17 |
Genre | : Mathematics |
ISBN | : 3540711333 |
Download Convex and Discrete Geometry Book in PDF, ePub and Kindle
Convex and Discrete Geometry is an area of mathematics situated between analysis, geometry and discrete mathematics with numerous relations to other subdisciplines. This book provides a comprehensive 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, and useful to people working in the applied fields.
Author | : Peter Brass |
Publisher | : Springer Science & Business Media |
Total Pages | : 507 |
Release | : 2006-01-27 |
Genre | : Mathematics |
ISBN | : 0387299297 |
Download Research Problems in Discrete Geometry Book in PDF, ePub and Kindle
This book is the result of a 25-year-old project and comprises a collection of more than 500 attractive open problems in the field. The largely self-contained chapters provide a broad overview of discrete geometry, along with historical details and the most important partial results related to these problems. This book is intended as a source book for both professional mathematicians and graduate students who love beautiful mathematical questions, are willing to spend sleepless nights thinking about them, and who would like to get involved in mathematical research.
Author | : Károly Bezdek |
Publisher | : Springer Science & Business Media |
Total Pages | : 186 |
Release | : 2013-08-04 |
Genre | : Mathematics |
ISBN | : 146148118X |
Download Lectures on Sphere Arrangements – the Discrete Geometric Side Book in PDF, ePub and Kindle
This monograph gives a short introduction to the relevant modern parts of discrete geometry, in addition to leading the reader to the frontiers of geometric research on sphere arrangements. The readership is aimed at advanced undergraduate and early graduate students, as well as interested researchers. It contains more than 40 open research problems ideal for graduate students and researchers in mathematics and computer science. Additionally, this book may be considered ideal for a one-semester advanced undergraduate or graduate level course. The core part of this book is based on three lectures given by the author at the Fields Institute during the thematic program on “Discrete Geometry and Applications” and contains four core topics. The first two topics surround active areas that have been outstanding from the birth of discrete geometry, namely dense sphere packings and tilings. Sphere packings and tilings have a very strong connection to number theory, coding, groups, and mathematical programming. Extending the tradition of studying packings of spheres, is the investigation of the monotonicity of volume under contractions of arbitrary arrangements of spheres. The third major topic of this book can be found under the sections on ball-polyhedra that study the possibility of extending the theory of convex polytopes to the family of intersections of congruent balls. This section of the text is connected in many ways to the above-mentioned major topics and it is also connected to some other important research areas as the one on coverings by planks (with close ties to geometric analysis). This fourth core topic is discussed under covering balls by cylinders.
Author | : Karoly Bezdek |
Publisher | : CRC Press |
Total Pages | : 199 |
Release | : 2019-04-24 |
Genre | : Mathematics |
ISBN | : 1000007162 |
Download Volumetric Discrete Geometry Book in PDF, ePub and Kindle
Volume of geometric objects plays an important role in applied and theoretical mathematics. This is particularly true in the relatively new branch of discrete geometry, where volume is often used to find new topics for research. Volumetric Discrete Geometry demonstrates the recent aspects of volume, introduces problems related to it, and presents methods to apply it to other geometric problems. Part I of the text consists of survey chapters of selected topics on volume and is suitable for advanced undergraduate students. Part II has chapters of selected proofs of theorems stated in Part I and is oriented for graduate level students wishing to learn about the latest research on the topic. Chapters can be studied independently from each other. Provides a list of 30 open problems to promote research Features more than 60 research exercises Ideally suited for researchers and students of combinatorics, geometry and discrete mathematics
Author | : Alexander Barg |
Publisher | : American Mathematical Society |
Total Pages | : 202 |
Release | : 2014-08-28 |
Genre | : Mathematics |
ISBN | : 1470409054 |
Download Discrete Geometry and Algebraic Combinatorics Book in PDF, ePub and Kindle
This volume contains the proceedings of the AMS Special Session on Discrete Geometry and Algebraic Combinatorics held on January 11, 2013, in San Diego, California. The collection of articles in this volume is devoted to packings of metric spaces and related questions, and contains new results as well as surveys of some areas of discrete geometry. This volume consists of papers on combinatorics of transportation polytopes, including results on the diameter of graphs of such polytopes; the generalized Steiner problem and related topics of the minimal fillings theory; a survey of distance graphs and graphs of diameters, and a group of papers on applications of algebraic combinatorics to packings of metric spaces including sphere packings and topics in coding theory. In particular, this volume presents a new approach to duality in sphere packing based on the Poisson summation formula, applications of semidefinite programming to spherical codes and equiangular lines, new results in list decoding of a family of algebraic codes, and constructions of bent and semi-bent functions.
Author | : Gergely Ambrus |
Publisher | : Springer |
Total Pages | : 458 |
Release | : 2018-11-03 |
Genre | : Mathematics |
ISBN | : 3662574136 |
Download New Trends in Intuitive Geometry Book in PDF, ePub and Kindle
This volume contains 17 surveys that cover many recent developments in Discrete Geometry and related fields. Besides presenting the state-of-the-art of classical research subjects like packing and covering, it also offers an introduction to new topological, algebraic and computational methods in this very active research field. The readers will find a variety of modern topics and many fascinating open problems that may serve as starting points for research.