Various Topics In Comparison Geometry And Discrete Mathematics
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Various Topics In Comparison Geometry And Discrete Mathematics
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Author : Chris Goddard
language : en
Publisher:
Release Date : 2010
Various Topics In Comparison Geometry And Discrete Mathematics written by Chris Goddard and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Calculus of variations categories.
Classical Topics In Discrete Geometry
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Author : Károly Bezdek
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-06-23
Classical Topics In Discrete Geometry written by Károly Bezdek and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-06-23 with Mathematics categories.
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.
Comparison Theorems In Riemannian Geometry
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Author : Jeff Cheeger
language : en
Publisher: American Mathematical Soc.
Release Date : 2008-04-08
Comparison Theorems In Riemannian Geometry written by Jeff Cheeger and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-04-08 with Mathematics categories.
The central theme of this book is the interaction between the curvature of a complete Riemannian manifold and its topology and global geometry. The first five chapters are preparatory in nature. They begin with a very concise introduction to Riemannian geometry, followed by an exposition of Toponogov's theorem--the first such treatment in a book in English. Next comes a detailed presentation of homogeneous spaces in which the main goal is to find formulas for their curvature. A quick chapter of Morse theory is followed by one on the injectivity radius. Chapters 6-9 deal with many of the most relevant contributions to the subject in the years 1959 to 1974. These include the pinching (or sphere) theorem, Berger's theorem for symmetric spaces, the differentiable sphere theorem, the structure of complete manifolds of non-negative curvature, and finally, results about the structure of complete manifolds of non-positive curvature. Emphasis is given to the phenomenon of rigidity, namely, the fact that although the conclusions which hold under the assumption of some strict inequality on curvature can fail when the strict inequality on curvature can fail when the strict inequality is relaxed to a weak one, the failure can happen only in a restricted way, which can usually be classified up to isometry. Much of the material, particularly the last four chapters, was essentially state-of-the-art when the book first appeared in 1975. Since then, the subject has exploded, but the material covered in the book still represents an essential prerequisite for anyone who wants to work in the field.
Applied Geometry And Discrete Mathematics
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Author : Peter Gritzmann
language : en
Publisher: American Mathematical Soc.
Release Date : 1991
Applied Geometry And Discrete Mathematics written by Peter Gritzmann and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with Mathematics categories.
This volume, published jointly with the Association for Computing Machinery, comprises a collection of research articles celebrating the occasion of Victor Klee's 65th birthday in September 1990. During his long career, Klee has made contributions to a wide variety of areas, such as discrete and computational geometry, convexity, combinatorics, graph theory, functional analysis, mathematical programming and optimization, and theoretical computer science. In addition, Klee made important contributions to mathematics, education, mathematical methods in economics and the decision sciences, applications of discrete mathematics in the biological and social sciences, and the transfer of knowledge from applied mathematics to industry. In honour of Klee's achievements, this volume presents more than 40 papers on topics related to Klee's research. While the majority of the papers are research articles, a number of survey articles are also included. Mirroring the breadth of Klee's mathematical contributions, this book shows how different branches of mathematics interact. It is a fitting tribute to one of the leading figures in discrete mathematics.
Recent Topics In Differential Geometry And Its Related Fields Proceedings Of The 6th International Colloquium On Differential Geometry And Its Related Fields
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Author : Adachi Toshiaki
language : en
Publisher: World Scientific
Release Date : 2019-10-15
Recent Topics In Differential Geometry And Its Related Fields Proceedings Of The 6th International Colloquium On Differential Geometry And Its Related Fields written by Adachi Toshiaki and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-10-15 with Mathematics categories.
This volume contains papers by the main participants in the meeting of the 6th International Colloquium on Differential Geometry and its Related Fields (ICDG2018).The volume consists of papers devoted to the study of recent topics in geometric structures on manifolds — which are related to complex analysis, symmetric spaces and surface theory — and also in discrete mathematics.Thus, it presents a broad overview of differential geometry and provides up-to-date information to researchers and young scientists in this field, and also to those working in the wide spectrum of mathematics.
Research Problems In Discrete Geometry
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Author : Peter Brass
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-01-27
Research Problems In Discrete Geometry written by Peter Brass and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-01-27 with Mathematics categories.
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.
Conformal Geometry Of Discrete Groups And Manifolds
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Author : Boris Nikolaevich Apanasov
language : en
Publisher: Walter de Gruyter
Release Date : 2000
Conformal Geometry Of Discrete Groups And Manifolds written by Boris Nikolaevich Apanasov and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.
No detailed description available for "Conformal Geometry of Discrete Groups and Manifolds".
Number Theory And Discrete Mathematics
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Author : A.K. Agarwal
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Number Theory And Discrete Mathematics written by A.K. Agarwal and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
To mark the World Mathematical Year 2000 an International Conference on Number Theory and Discrete Mathematics in honour of the legendary Indian Mathematician Srinivasa Ramanuj~ was held at the centre for Advanced study in Mathematics, Panjab University, Chandigarh, India during October 2-6, 2000. This volume contains the proceedings of that conference. In all there were 82 participants including 14 overseas participants from Austria, France, Hungary, Italy, Japan, Korea, Singapore and the USA. The conference was inaugurated by Prof. K. N. Pathak, Hon. Vice-Chancellor, Panjab University, Chandigarh on October 2, 2000. Prof. Bruce C. Berndt of the University of Illinois, Urbana Chaimpaign, USA delivered the key note address entitled "The Life, Notebooks and Mathematical Contributions of Srinivasa Ramanujan". He described Ramanujan--as one of this century's most influential Mathematicians. Quoting Mark K. ac, Prof. George E. Andrews of the Pennsylvania State University, USA, in his message for the conference, described Ramanujan as a "magical genius". During the 5-day deliberations invited speakers gave talks on various topics in number theory and discrete mathematics. We mention here a few of them just as a sampling: • M. Waldschmidt, in his article, provides a very nice introduction to the topic of multiple poly logarithms and their special values. • C.
Forbidden Configurations In Discrete Geometry
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Author : David Eppstein
language : en
Publisher: Cambridge University Press
Release Date : 2018-05-17
Forbidden Configurations In Discrete Geometry written by David Eppstein and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-05-17 with Computers categories.
Unifies discrete and computational geometry by using forbidden patterns of points to characterize many of its problems.
Volumetric Discrete Geometry
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Author : Karoly Bezdek
language : en
Publisher: CRC Press
Release Date : 2019-04-24
Volumetric Discrete Geometry written by Karoly Bezdek and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-04-24 with Mathematics categories.
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