Author: Miklos Bona

Publisher: CRC Press

ISBN: 1482249103

Category: Computers

Page: 534

View: 7468

Introduction to Enumerative and Analytic Combinatorics fills the gap between introductory texts in discrete mathematics and advanced graduate texts in enumerative combinatorics. The book first deals with basic counting principles, compositions and partitions, and generating functions. It then focuses on the structure of permutations, graph enumeration, and extremal combinatorics. Lastly, the text discusses supplemental topics, including error-correcting codes, properties of sequences, and magic squares. Strengthening the analytic flavor of the book, this Second Edition: Features a new chapter on analytic combinatorics and new sections on advanced applications of generating functions Demonstrates powerful techniques that do not require the residue theorem or complex integration Adds new exercises to all chapters, significantly extending coverage of the given topics Introduction to Enumerative and Analytic Combinatorics, Second Edition makes combinatorics more accessible, increasing interest in this rapidly expanding field.
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Author: Walter D. Wallis,John C. George

Publisher: CRC Press

ISBN: 1498777627

Category: Mathematics

Page: 444

View: 922

What Is Combinatorics Anyway? Broadly speaking, combinatorics is the branch of mathematics dealing with different ways of selecting objects from a set or arranging objects. It tries to answer two major kinds of questions, namely, counting questions: how many ways can a selection or arrangement be chosen with a particular set of properties; and structural questions: does there exist a selection or arrangement of objects with a particular set of properties? The authors have presented a text for students at all levels of preparation. For some, this will be the first course where the students see several real proofs. Others will have a good background in linear algebra, will have completed the calculus stream, and will have started abstract algebra. The text starts by briefly discussing several examples of typical combinatorial problems to give the reader a better idea of what the subject covers. The next chapters explore enumerative ideas and also probability. It then moves on to enumerative functions and the relations between them, and generating functions and recurrences., Important families of functions, or numbers and then theorems are presented. Brief introductions to computer algebra and group theory come next. Structures of particular interest in combinatorics: posets, graphs, codes, Latin squares, and experimental designs follow. The authors conclude with further discussion of the interaction between linear algebra and combinatorics. Features Two new chapters on probability and posets. Numerous new illustrations, exercises, and problems. More examples on current technology use A thorough focus on accuracy Three appendices: sets, induction and proof techniques, vectors and matrices, and biographies with historical notes, Flexible use of MapleTM and MathematicaTM
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Author: Jurgen Bierbrauer

Publisher: CRC Press

ISBN: 148229981X

Category: Computers

Page: 538

View: 6428

This book is designed to be usable as a textbook for an undergraduate course or for an advanced graduate course in coding theory as well as a reference for researchers in discrete mathematics, engineering and theoretical computer science. This second edition has three parts: an elementary introduction to coding, theory and applications of codes, and algebraic curves. The latter part presents a brief introduction to the theory of algebraic curves and its most important applications to coding theory.
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Author: Kenneth H. Rosen

Publisher: CRC Press

ISBN: 135164405X

Category: Mathematics

Page: 1612

View: 423

Handbook of Discrete and Combinatorial Mathematics provides a comprehensive reference volume for mathematicians, computer scientists, engineers, as well as students and reference librarians. The material is presented so that key information can be located and used quickly and easily. Each chapter includes a glossary. Individual topics are covered in sections and subsections within chapters, each of which is organized into clearly identifiable parts: definitions, facts, and examples. Examples are provided to illustrate some of the key definitions, facts, and algorithms. Some curious and entertaining facts and puzzles are also included. Readers will also find an extensive collection of biographies. This second edition is a major revision. It includes extensive additions and updates. Since the first edition appeared in 1999, many new discoveries have been made and new areas have grown in importance, which are covered in this edition.
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Author: Herbert S. Wilf

Publisher: Elsevier

ISBN: 0080571514

Category: Mathematics

Page: 228

View: 7600

This is the Second Edition of the highly successful introduction to the use of generating functions and series in combinatorial mathematics. This new edition includes several new areas of application, including the cycle index of the symmetric group, permutations and square roots, counting polyominoes, and exact covering sequences. An appendix on using the computer algebra programs MAPLE(r) and Mathematica(r) to generate functions is also included. The book provides a clear, unified introduction to the basic enumerative applications of generating functions, and includes exercises and solutions, many new, at the end of each chapter. Key Features * Provides new applications on the cycle index of the symmetric group, permutations and square roots, counting polyominoes, and exact covering sequences * Features an Appendix on using MAPLE(r) and Mathematica (r) to generate functions * Includes many new exercises with complete solutions at the end of each chapter
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Author: Boyadzhiev Khristo N

Publisher: World Scientific

ISBN: 9813234997

Category: Mathematics

Page: 208

View: 1786

The binomial transform is a discrete transformation of one sequence into another with many interesting applications in combinatorics and analysis. This volume is helpful to researchers interested in enumerative combinatorics, special numbers, and classical analysis. A valuable reference, it can also be used as lecture notes for a course in binomial identities, binomial transforms and Euler series transformations. The binomial transform leads to various combinatorial and analytical identities involving binomial coefficients. In particular, we present here new binomial identities for Bernoulli, Fibonacci, and harmonic numbers. Many interesting identities can be written as binomial transforms and vice versa. The volume consists of two parts. In the first part, we present the theory of the binomial transform for sequences with a sufficient prerequisite of classical numbers and polynomials. The first part provides theorems and tools which help to compute binomial transforms of different sequences and also to generate new binomial identities from the old. These theoretical tools (formulas and theorems) can also be used for summation of series and various numerical computations. In the second part, we have compiled a list of binomial transform formulas for easy reference. In the Appendix, we present the definition of the Stirling sequence transform and a short table of transformation formulas. Contents: Theory of the Binomial Transform: Introduction Prerequisite: Special Numbers and Polynomials Euler's Transformation for Series Melzak's Formula and Related Formulas Special Properties. Creating New Identities Binomial Transforms of Products Special Formulas and Power Series with Binomial Sums Table of Binomial Transforms: Assorted Binomial Formulas Identities Involving Harmonic Numbers Transforms of Binomial Coefficients Transforms of Special Numbers and Polynomials Transforms of Trigonometric and Hyperbolic Functions and Applications to Some Trigonometric Integrals Transforms of Some Special Functions Appendix: The Stirling Transform of Sequences Readership: Graduate and researchers in the areas of number theory, discrete mathematics, combinatorics, statistics working with applications using the binomial transform. Keywords: Binomial Coefficients;Binomial Identities;Binomial Sums;Binomial Transform;Euler's Series Transformation;Discrete Mathematics;Finite Differences;Stirling Numbers of the First Kind;Stirling Numbers of the Second Kind;Stirling Transform;Special Numbers and Polynomials;Harmonic Numbers;Bernoulli Numbers;Fibonacci Numbers;Melzak's Formula;Exponential Polynomials;Geometric Polynomials;Laguerre Polynomials;Trigonometric IntegralsReview: Key Features: This is the first, long-overdue book on the subject. (At present, there are no competing books) The book provides interesting new material for researchers in discrete mathematics and will serve as a valuable reference for binomial identities, binomial transform formulas, and Euler series transformations
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vom Lösen mathematischer Probleme

Author: George Pólya

Publisher: N.A

ISBN: 9783772006081

Category:

Page: 266

View: 1538

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Mathematik im Spiel: Methoden, Ergebnisse und Grenzen

Author: Jörg Bewersdorff

Publisher: Springer-Verlag

ISBN: 9783834807755

Category:

Page: 369

View: 1289

Der Autor hat es in bewundernswerter Weise geschafft, anhand einer Vielzahl bekannter Spiele von Schach ber Poker bis Mastermind einen kleinen Einblick in mathematisch so anspruchsvolle Gebiete wie Wahrscheinlichkeitsrechnung, Optimierungstheorie, Kombinatorik und Spieltheorie zu geben. Hierbei werden so gut wie keine mathematischen Vorkenntnisse erwartet, so dass man das Buch auch interessierten Nichtmathematikern w rmstens empfehlen kann. Anspruchsvolle und unerschrockene Leserinnen und Leser werden in den sehr lesenswerten Anmerkungen am Schluss des Buches Hinweise auf weiterf hrende Literatur finden, anhand derer sie auch tiefer in mathematische Aspekte eindringen k nnen. Ein sch nes Buch, ohne wirkliche Konkurrenz auf dem deutschen Markt, und dies zu einem vern nftigen Preis. Zentralblatt MATH Database 1931 - 2002
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Author: Johannes Buchmann

Publisher: Springer-Verlag

ISBN: 3642980600

Category: Computers

Page: 234

View: 8323

Dieses Kryptographiebuch behandelt die grundlegenden Techniken der modernen Kryptographie. Es eignet sich hervorragend für Studierende der Mathematik und der Informatik ab dem dritten Semester. Das Buch setzt nur minimale Kenntnisse voraus und vermittelt auf elementare Weise die notwendigen mathematischen Kenntnisse, insbesondere die aus der Zahlentheorie. Die Leser werden durch diese Einführung in die Lage versetzt, fortgeschrittene Literatur zur Kryptographie zu verstehen.
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Author: W. Schwabhäuser,W. Szmielew,A. Tarski

Publisher: Springer-Verlag

ISBN: 3642694187

Category: Mathematics

Page: 484

View: 3825

Das vorliegende Buch besteht aus zwei Teilen. Teil I enthält einen axiomatischen Aufbau der euklidischen Geometrie auf Grund eines Axiomensystems von Tarski, das in einem gewissen Sinne (auch für die absolute Geometrie) gleichwertig ist mit dem Hilbertschen Axiomensystem, aber formalisiert ist in einer Sprache, die für die Betrachtungen in Teil II besonders geeignet ist. Mehrere solche Axio mensysteme wurden schon vor langer Zeit von Tarski veröffentlicht. Hier wird nun die Durchführung eines Aufbaus der Geometrie auf Grund eines solchen Axiomensystems - unter Benutzung von Resultaten von H. N. Gupta - allgemein zugänglich gemacht. Die vorliegende Darstel lung wurde vom zuerst genannten Autor allein geschrieben, aber sie beruht zum Teil auf unveröffentlichten Resultaten von Alfred Tarski und Wanda Szmielew; daher gebührt ihnen ein Teil der Autorschaft. Mehr über Entstehung und Inhalt von Teil I sowie über die Geschichte der Tarskischen Axiomensysteme wird in der Einleitung (Abschnitt I.O) gesagt. Teil II enthält metamathematische Untersuchungen und Ergebnisse über verschiedene Geometrien, was vielfac~ auf eine Anwendung von Methoden und Sätzen der mathematischen Logik auf Geometrien hinausläuft (vgl.
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Author: Werner Greub

Publisher: Springer-Verlag

ISBN: 3642663850

Category: Mathematics

Page: 222

View: 9553

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Author: Jakob Bernoulli

Publisher: Wentworth Press

ISBN: 9780270072112

Category:

Page: 170

View: 5336

This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
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Author: Cornell University

Publisher: N.A

ISBN: N.A

Category: Education

Page: N.A

View: 670

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auf den Spuren des größten Rätsels der Mathematik

Author: Marcus Du Sautoy

Publisher: C.H.Beck

ISBN: 9783406523205

Category: Primzahl

Page: 398

View: 4405

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Author: Ronald L. Graham,Martin Grötschel,László Lovász

Publisher: N.A

ISBN: N.A

Category: Combinatorial analysis

Page: 2198

View: 585

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