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Author: Peter Gritzmann Publisher: American Mathematical Soc. ISBN: 9780821870839 Category : Mathematics Languages : en Pages : 660
Book Description
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.
Author: Peter Gritzmann Publisher: American Mathematical Soc. ISBN: 9780821870839 Category : Mathematics Languages : en Pages : 660
Book Description
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.
Author: Andras Bezdek Publisher: CRC Press ISBN: 0824747615 Category : Mathematics Languages : en Pages : 500
Book Description
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: Heather A. Harrington Publisher: American Mathematical Soc. ISBN: 1470423219 Category : Commutative algebra -- Computational aspects and applications -- Applications of commutative algebra (e.g., to statistics, control theory, optimization, etc.) Languages : en Pages : 277
Book Description
This volume contains the proceedings of the AMS Special Session on Algebraic and Geometric Methods in Applied Discrete Mathematics, held on January 11, 2015, in San Antonio, Texas. The papers present connections between techniques from “pure” mathematics and various applications amenable to the analysis of discrete models, encompassing applications of combinatorics, topology, algebra, geometry, optimization, and representation theory. Papers not only present novel results, but also survey the current state of knowledge of important topics in applied discrete mathematics. Particular highlights include: a new computational framework, based on geometric combinatorics, for structure prediction from RNA sequences; a new method for approximating the optimal solution of a sum of squares problem; a survey of recent Helly-type geometric theorems; applications of representation theory to voting theory and game theory; a study of fixed points of tensors; and exponential random graph models from the perspective of algebraic statistics with applications to networks. This volume was written for those trained in areas such as algebra, topology, geometry, and combinatorics who are interested in tackling problems in fields such as biology, the social sciences, data analysis, and optimization. It may be useful not only for experts, but also for students who wish to gain an applied or interdisciplinary perspective.
Author: Peter M. Gruber Publisher: Springer Science & Business Media ISBN: 3540711333 Category : Mathematics Languages : en Pages : 580
Book Description
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: Karoly Bezdek Publisher: CRC Press ISBN: 1000000338 Category : Mathematics Languages : en Pages : 307
Book Description
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: Vladimir Rovenski Publisher: Springer ISBN: 3319046756 Category : Mathematics Languages : en Pages : 243
Book Description
This volume has been divided into two parts: Geometry and Applications. The geometry portion of the book relates primarily to geometric flows, laminations, integral formulae, geometry of vector fields on Lie groups and osculation; the articles in the applications portion concern some particular problems of the theory of dynamical systems, including mathematical problems of liquid flows and a study of cycles for non-dynamical systems. This Work is based on the second international workshop entitled "Geometry and Symbolic Computations," held on May 15-18, 2013 at the University of Haifa and is dedicated to modeling (using symbolic calculations) in differential geometry and its applications in fields such as computer science, tomography and mechanics. It is intended to create a forum for students and researchers in pure and applied geometry to promote discussion of modern state-of-the-art in geometric modeling using symbolic programs such as MapleTM and Mathematica® , as well as presentation of new results.
Author: Peter Gruber Publisher: Springer ISBN: 9783540835905 Category : Mathematics Languages : en Pages : 580
Book Description
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: Károly Bezdek Publisher: Springer Science & Business Media ISBN: 1441906002 Category : Mathematics Languages : en Pages : 166
Book Description
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: John Forbes Nash, Jr. Publisher: Springer ISBN: 3319321625 Category : Mathematics Languages : en Pages : 543
Book Description
The goal in putting together this unique compilation was to present the current status of the solutions to some of the most essential open problems in pure and applied mathematics. Emphasis is also given to problems in interdisciplinary research for which mathematics plays a key role. This volume comprises highly selected contributions by some of the most eminent mathematicians in the international mathematical community on longstanding problems in very active domains of mathematical research. A joint preface by the two volume editors is followed by a personal farewell to John F. Nash, Jr. written by Michael Th. Rassias. An introduction by Mikhail Gromov highlights some of Nash’s legendary mathematical achievements. The treatment in this book includes open problems in the following fields: algebraic geometry, number theory, analysis, discrete mathematics, PDEs, differential geometry, topology, K-theory, game theory, fluid mechanics, dynamical systems and ergodic theory, cryptography, theoretical computer science, and more. Extensive discussions surrounding the progress made for each problem are designed to reach a wide community of readers, from graduate students and established research mathematicians to physicists, computer scientists, economists, and research scientists who are looking to develop essential and modern new methods and theories to solve a variety of open problems.
Author: Peter Gritzmann
Author: Peter Gritzmann
Author: 
Author: Andras Bezdek
Author: Heather A. Harrington
Author: Peter M. Gruber
Author: Karoly Bezdek
Author: Vladimir Rovenski
Author: Peter Gruber
Author: Károly Bezdek
Author: John Forbes Nash, Jr.