Computing the Continuous Discretely

Integer-point Enumeration in Polyhedra

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Author: Matthias Beck,Sinai Robins

Publisher: Springer Science & Business Media

ISBN: 0387461124

Category: Mathematics

Page: 227

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This textbook illuminates the field of discrete mathematics with examples, theory, and applications of the discrete volume of a polytope. The authors have weaved a unifying thread through basic yet deep ideas in discrete geometry, combinatorics, and number theory. We encounter here a friendly invitation to the field of "counting integer points in polytopes", and its various connections to elementary finite Fourier analysis, generating functions, the Frobenius coin-exchange problem, solid angles, magic squares, Dedekind sums, computational geometry, and more. With 250 exercises and open problems, the reader feels like an active participant.

Algorithmische Geometrie

Polyedrische und algebraische Methoden

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Author: Michael Joswig,Thorsten Theobald

Publisher: Springer-Verlag

ISBN: 3834894400

Category: Mathematics

Page: 266

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In dem Lehrbuch wird eine mathematisch orientierte Einführung in die algorithmische Geometrie gegeben. Im ersten Teil werden „klassische“ Probleme und Techniken behandelt, die sich auf polyedrische (= linear begrenzte) Objekte beziehen. Hierzu gehören beispielsweise Algorithmen zur Berechnung konvexer Hüllen und die Konstruktion von Voronoi-Diagrammen. Im zweiten Teil werden grundlegende Methoden der algorithmischen algebraischen Geometrie entwickelt und anhand von Anwendungen aus Computergrafik, Kurvenrekonstruktion und Robotik illustriert. Das Buch eignet sich für ein fortgeschrittenes Modul in den derzeit neu konzipierten Bachelor-Studiengängen in Mathematik und Informatik.

Handbook of Discrete and Computational Geometry, Third Edition

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Author: Csaba D. Toth,Joseph O'Rourke,Jacob E. Goodman

Publisher: CRC Press

ISBN: 1498711421

Category: Computers

Page: 1928

View: 6054

The Handbook of Discrete and Computational Geometry is intended as a reference book fully accessible to nonspecialists as well as specialists, covering all major aspects of both fields. The book offers the most important results and methods in discrete and computational geometry to those who use them in their work, both in the academic world—as researchers in mathematics and computer science—and in the professional world—as practitioners in ?elds as diverse as operations research, molecular biology, and robotics. Discrete geometry has contributed signi?cantly to the growth of discrete mathematics in recent years. This has been fueled partly by the advent of powerful computers and by the recent explosion of activity in the relatively young ?eld of computational geometry. This synthesis between discrete and computational geometry lies at the heart of this Handbook. A growing list of application fields includes combinatorial optimization, computer-aided design, computer graphics, crystallography, data analysis, error-correcting codes, geographic information systems, motion planning, operations research, pattern recognition, robotics, solid modeling, and tomography.

Discrete Geometry and Optimization

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Author: Károly Bezdek,Antoine Deza,Yinyu Ye

Publisher: Springer Science & Business Media

ISBN: 3319002007

Category: Mathematics

Page: 336

View: 7415

​Optimization has long been a source of both inspiration and applications for geometers, and conversely, discrete and convex geometry have provided the foundations for many optimization techniques, leading to a rich interplay between these subjects. The purpose of the Workshop on Discrete Geometry, the Conference on Discrete Geometry and Optimization, and the Workshop on Optimization, held in September 2011 at the Fields Institute, Toronto, was to further stimulate the interaction between geometers and optimizers. This volume reflects the interplay between these areas. The inspiring Fejes Tóth Lecture Series, delivered by Thomas Hales of the University of Pittsburgh, exemplified this approach. While these fields have recently witnessed a lot of activity and successes, many questions remain open. For example, Fields medalist Stephen Smale stated that the question of the existence of a strongly polynomial time algorithm for linear optimization is one of the most important unsolved problems at the beginning of the 21st century. The broad range of topics covered in this volume demonstrates the many recent and fruitful connections between different approaches, and features novel results and state-of-the-art surveys as well as open problems.

Trustworthy Global Computing

5th International Symposium, TGC 2010, Munich, Germany, February 24-26, 2010, Revised Selected Papers

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Author: Martin Wirsing,Martin Hofmann,Axel Rauschmayer

Publisher: Springer Science & Business Media

ISBN: 3642156398

Category: Business & Economics

Page: 380

View: 8084

This book constitutes the refereed proceedings of the 5th International Symposium on Trustworthly Global Computing, TGC 2010, held in Munich, Germany, in February 2010. The 17 revised full papers presented and the 7 invited papers were carefully reviewed and selected from 31 submissions. The papers are organized in topical sections on types and processes; games and concurrent systems; certification of correctness; tools and languages; and probabilistic aspects.

Kombinatorische Optimierung

Theorie und Algorithmen

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Author: Bernhard Korte,Jens Vygen

Publisher: Springer-Verlag

ISBN: 3540769196

Category: Mathematics

Page: 675

View: 8438

Das Lehrbuch ist die deutsche Übersetzung der 4., wesentlich erweiterten Auflage des Titels „Combinatorial Optimization – Theory and Algorithms". Es gibt den neuesten Stand der kombinatorischen Optimierung wieder und liefert vornehmlich theoretische Resultate und Algorithmen mit beweisbar guten Laufzeiten und Ergebnissen, jedoch keine Heuristiken. Enthalten sind vollständige Beweise, auch für viele tiefe und neue Resultate, von denen einige bisher in der Lehrbuchliteratur noch nicht erschienen sind. Mit Übungen und umfassendem Literaturverzeichnis.

Topologie

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Author: K. Jänich

Publisher: Springer-Verlag

ISBN: 3662225549

Category: Mathematics

Page: 215

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The Art of Proof

Basic Training for Deeper Mathematics

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Author: Matthias Beck,Ross Geoghegan

Publisher: Springer Science & Business Media

ISBN: 9781441970237

Category: Mathematics

Page: 182

View: 6314

The Art of Proof is designed for a one-semester or two-quarter course. A typical student will have studied calculus (perhaps also linear algebra) with reasonable success. With an artful mixture of chatty style and interesting examples, the student's previous intuitive knowledge is placed on solid intellectual ground. The topics covered include: integers, induction, algorithms, real numbers, rational numbers, modular arithmetic, limits, and uncountable sets. Methods, such as axiom, theorem and proof, are taught while discussing the mathematics rather than in abstract isolation. The book ends with short essays on further topics suitable for seminar-style presentation by small teams of students, either in class or in a mathematics club setting. These include: continuity, cryptography, groups, complex numbers, ordinal number, and generating functions.

Introduction to Calculus and Classical Analysis

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Author: Omar Hijab

Publisher: Springer Science & Business Media

ISBN: 0387693165

Category: Mathematics

Page: 342

View: 2492

Intended for an honors calculus course or for an introduction to analysis, this is an ideal text for undergraduate majors since it covers rigorous analysis, computational dexterity, and a breadth of applications. The book contains many remarkable features: * complete avoidance of /epsilon-/delta arguments by using sequences instead * definition of the integral as the area under the graph, while area is defined for every subset of the plane * complete avoidance of complex numbers * heavy emphasis on computational problems * applications from many parts of analysis, e.g. convex conjugates, Cantor set, continued fractions, Bessel functions, the zeta functions, and many more * 344 problems with solutions in the back of the book.

Grundlagen zur Neuroinformatik und Neurobiologie

The Computational Brain in deutscher Sprache

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Author: Patricia S. Churchland,Terrence J. Sejnowski

Publisher: Springer-Verlag

ISBN: 3322868214

Category: Technology & Engineering

Page: 702

View: 2344

The Computational Brain, das außergewöhnliche Buch über vergleichende Forschung in den Bereichen von menschlichem Gehirn und neuesten Möglichkeiten der Computertechnologie, liegt hiermit erstmals in deutscher Sprache vor. Geschrieben von einem führenden Forscherteam in den USA, ist es eine Fundgrube für alle, die wissen wollen, was der Stand der Wissenschaft auf diesem Gebiet ist. Die Autoren führen die Bereiche der Neuroinformatik und Neurobiologie mit gut ausgesuchten Beispielen und der gebotenen Hintergrundinformation gekonnt zusammen. Das Buch wird somit nicht nur dem Fachwissenschaftler sondern auch dem interdisziplinären Interesse des Informatikers und des Biologen auf eine hervorragende Weise gerecht. Übersetzt wurde das Buch von Prof. Dr. Steffen Hölldobler und Dipl.-Biol. Claudia Hölldobler, einem Informatiker und einer Biologin. Rezension in Spektrum der Wissenschaft nr. 10, S. 122 f. im Oktober 1997 (...) Die 1992 erschienene amerikanische Originalausgabe des vorliegenden Werkes ist so erfolgreich, daß man bereits von einem Klassiker reden kann. (...) (...) ....ist das Buch sehr zu empfehlen. In Verbindung von Neurobiologie und Neuroinformatik konkurrenzlos, vermittelt es einiges von der Faszination theoretischer Hirnforschung, die auch in Deutschland zunehmend mehr Wissenschaftler in ihren Bann schlägt. Rezension erschienen in: Computer Spektrum 3/1997, S. 2 (...)Das Buch wird somit nicht nur dem Fachwissenschaftler, sondern auch den interdisziplinären Interesse des Informatikers und des Biologen auf eine hervorragende Weise gerecht(...)

Mathematische Edelsteine

der elementaren Kombinatorik, Zahlentheorie und Geometrie

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Author: Ross Honsberger

Publisher: Springer-Verlag

ISBN: 3322859304

Category: Mathematics

Page: 179

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