Computing the Continuous Discretely

Integer-Point Enumeration in Polyhedra

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Author: Matthias Beck,Sinai Robins

Publisher: Springer

ISBN: 1493929690

Category: Mathematics

Page: 285

View: 1295

This richly illustrated textbook explores the amazing interaction between combinatorics, geometry, number theory, and analysis which arises in the interplay between polyhedra and lattices. Highly accessible to advanced undergraduates, as well as beginning graduate students, this second edition is perfect for a capstone course, and adds two new chapters, many new exercises, and updated open problems. For scientists, this text can be utilized as a self-contained tooling device. The topics include a friendly invitation to Ehrhart’s theory of counting lattice points in polytopes, finite Fourier analysis, the Frobenius coin-exchange problem, Dedekind sums, solid angles, Euler–Maclaurin summation for polytopes, computational geometry, magic squares, zonotopes, and more. With more than 300 exercises and open research problems, the reader is an active participant, carried through diverse but tightly woven mathematical fields that are inspired by an innocently elementary question: What are the relationships between the continuous volume of a polytope and its discrete volume? Reviews of the first edition: “You owe it to yourself to pick up a copy of Computing the Continuous Discretely to read about a number of interesting problems in geometry, number theory, and combinatorics.” — MAA Reviews “The book is written as an accessible and engaging textbook, with many examples, historical notes, pithy quotes, commentary integrating the mate rial, exercises, open problems and an extensive bibliography.” — Zentralblatt MATH “This beautiful book presents, at a level suitable for advanced undergraduates, a fairly complete introduction to the problem of counting lattice points inside a convex polyhedron.” — Mathematical Reviews “Many departments recognize the need for capstone courses in which graduating students can see the tools they have acquired come together in some satisfying way. Beck and Robins have written the perfect text for such a course.” — CHOICE

Handbook of Discrete and Computational Geometry

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

Publisher: CRC Press

ISBN: 1498711421

Category: Computers

Page: 1928

View: 5333

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 fields as diverse as operations research, molecular biology, and robotics. Discrete geometry has contributed significantly 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 field 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: 4494

​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.

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

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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: 7470

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.

Algorithmische Geometrie

Polyedrische und algebraische Methoden

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Author: Michael Joswig,Thorsten Theobald

Publisher: Springer-Verlag

ISBN: 3834894400

Category: Mathematics

Page: 266

View: 4999

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.

Maß und Integral

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Author: Martin Brokate,Götz Kersting

Publisher: Springer-Verlag

ISBN: 303460646X

Category: Mathematics

Page: 160

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Der Integralbegriff in seiner Ausprägung durch Henri Lebesgue ist ein grundlegendes Werkzeug in der modernen Analysis, Numerik und Stochastik. Für Lehrveranstaltungen zu diesen Gebieten der Mathematik bereiten die Autoren wesentliche Sachverhalte in kompakter Weise auf. Das Buch liefert Orientierung und Material für verschiedene Varianten zwei- oder vierstündiger Lehrveranstaltungen. In einem ergänzenden Abschnitt werden um den Begriff der Konvexität herum Verbünde zur Funktionalanalysis hergestellt.

Choice

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Author: N.A

Publisher: N.A

ISBN: N.A

Category: Best books

Page: N.A

View: 5944

Proceedings of the Fifth Workshop on Algorithm Engineering and Experiments

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Author: Richard E. Ladner

Publisher: SIAM

ISBN: 9780898715422

Category: Mathematics

Page: 141

View: 3519

The ALENEX workshop provides a forum for the presentation of original research in the implementation and experimental evaluation of algorithms and data structures. This volume collects extended versions of the 12 papers that were selected for presentation.

Introduction to Geometric Probability

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Author: Daniel A. Klain,Gian-Carlo Rota

Publisher: Cambridge University Press

ISBN: 9780521596541

Category: Mathematics

Page: 178

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The basic ideas of the subject and the analogues with enumerative combinatorics are described and exploited.

Wavelets and Signal Processing

An Application-Based Introduction

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Author: Hans-Georg Stark

Publisher: Springer Science & Business Media

ISBN: 3540274812

Category: Technology & Engineering

Page: 150

View: 9910

Professor Noubari's recommendation: "Professor Starks book provides an effective entry into the field for engineering students who have little or no prior knowledge of this important subject. Avaibility of collection of computer codes and mfiles in combination with topics of the book, makes the book highly valuable to enhance student learning of the subject matter."

Arnold's Problems

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Author: Vladimir I. Arnold

Publisher: Springer Science & Business Media

ISBN: 9783540206149

Category: Mathematics

Page: 640

View: 2293

Vladimir Arnold is one of the most outstanding mathematicians of our time Many of these problems are at the front line of current research

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: 2737

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(...)

Transportation Systems Engineering

Theory and Methods

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Author: Ennio Cascetta

Publisher: Springer Science & Business Media

ISBN: 9780792367925

Category: Technology & Engineering

Page: 710

View: 3541

"This book provides a rigorous and comprehensive coverage of transportation models and planning methods and is a must-have to anyone in the transportation community, including students, teachers, and practitioners." Moshe Ben-Akiva, Massachusetts Institute of Technology.

A Course on Rough Paths

With an Introduction to Regularity Structures

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Author: Peter K. Friz,Martin Hairer

Publisher: N.A

ISBN: 9783319083339

Category:

Page: 268

View: 7868