Discrete Mathematics and Its Applications, 7thEd, Kenneth H. Rosen, 2012

Discrete Mathematics and Its Applications,

Author: The McGraw-Hill Companies, Inc

Publisher: Bukupedia

ISBN: N.A

Category: Mathematics

Page: 1071

View: 8268

[1] The satisfiability problem is addressed in greater depth, with Sudoku modeled in terms of satisfiability. [1] Hilbert’s Grand Hotel is used to help explain uncountability. [1] Proofs throughout the book have been made more accessible by adding steps and reasons behind these steps. [1] A template for proofs by mathematical induction has been added. [1] The step that applies the inductive hypothesis in mathematical induction proof is now explicitly noted. Algorithms [1] The pseudocode used in the book has been updated. [1] Explicit coverage of algorithmic paradigms, including brute force, greedy algorithms, and dynamic programing, is now provided. [1] Useful rules for big-O estimates of logarithms, powers, and exponential functions have been added. Number Theory and Cryptography [1] Expanded coverage allows instructors to include just a little or a lot of number theory in their courses. [1] The relationship between the mod function and congruences has been explained more fully. [1] The sieve of Eratosthenes is now introduced earlier in the book. [1] Linear congruences and modular inverses are now covered in more detail. [1] Applications of number theory, including check digits and hash functions, are covered in great depth. [1] A new section on cryptography integrates previous coverage, and the notion of a cryptosystem has been introduced. [1] Cryptographic protocols, including digital signatures and key sharing, are now covered. x Preface Graph Theory [1] A structured introduction to graph theory applications has been added. [1] More coverage has been devoted to the notion of social networks. [1] Applications to the biological sciences and motivating applications for graph isomorphism and planarity have been added. [1] Matchings in bipartite graphs are now covered, including Hall’s theorem and its proof. [1] Coverage of vertex connectivity, edge connectivity, and n-connectedness has been added, providing more insight into the connectedness of graphs. Enrichment Material [1] Many biographies have been expanded and updated, and new biographies of Bellman, Bézout Bienyamé, Cardano, Catalan, Cocks, Cook, Dirac, Hall, Hilbert, Ore, and Tao have been added. [1] Historical information has been added throughout the text. [1] Numerous updates for latest discoveries have been made. Expanded Media [1] Extensive effort has been devoted to producing valuable web resources for this book. [1] Extra examples in key parts of the text have been provided on companion website. [1] Interactive algorithms have been developed, with tools for using them to explore topics and for classroom use. [1] A new online ancillary, The Virtual Discrete Mathematics Tutor, available in fall 2012, will help students overcome problems learning discrete mathematics. [1] A new homework delivery system, available in fall 2012, will provide automated homework for both numerical and conceptual exercises. [1] Student assessment modules are available for key concepts. [1] Powerpoint transparencies for instructor use have been developed. [1] Asupplement Exploring Discrete Mathematics has been developed, providing extensive support for using MapleTM or MathematicaTM in conjunction with the book. [1] An extensive collection of external web links is provided. Features of the Book ACCESSIBILITY This text has proved to be easily read and understood by beginning students. There are no mathematical prerequisites beyond college algebra for almost all the content of the text. Students needing extra help will find tools on the companion website for bringing their mathematical maturity up to the level of the text. The few places in the book where calculus is referred to are explicitly noted. Most students should easily understand the pseudocode used in the text to express algorithms, regardless of whether they have formally studied programming languages. There is no formal computer science prerequisite. Each chapter begins at an easily understood and accessible level. Once basic mathematical concepts have been carefully developed, more difficult material and applications to other areas of study are presented. Preface xi FLEXIBILITY This text has been carefully designed for flexible use. The dependence of chapters on previous material has been minimized. Each chapter is divided into sections of approximately the same length, and each section is divided into subsections that form natural blocks of material for teaching. Instructors can easily pace their lectures using these blocks. WRITING STYLE The writing style in this book is direct and pragmatic. Precise mathematical language is used without excessive formalism and abstraction. Care has been taken to balance the mix of notation and words in mathematical statements. MATHEMATICAL RIGORAND PRECISION All definitions and theorems in this text are stated extremely carefully so that students will appreciate the precision of language and rigor needed in mathematics. Proofs are motivated and developed slowly; their steps are all carefully justified. The axioms used in proofs and the basic properties that follow from them are explicitly described in an appendix, giving students a clear idea of what they can assume in a proof. Recursive definitions are explained and used extensively. WORKEDEXAMPLES Over 800 examples are used to illustrate concepts, relate different topics, and introduce applications. In most examples, a question is first posed, then its solution is presented with the appropriate amount of detail. APPLICATIONS The applications included in this text demonstrate the utility of discrete mathematics in the solution of real-world problems. This text includes applications to a wide variety of areas, including computer science, data networking, psychology, chemistry, engineering, linguistics, biology, business, and the Internet. ALGORITHMS Results in discrete mathematics are often expressed in terms of algorithms; hence, key algorithms are introduced in each chapter of the book. These algorithms are expressed in words and in an easily understood form of structured pseudocode, which is described and specified in Appendix 3. The computational complexity of the algorithms in the text is also analyzed at an elementary level. HISTORICAL INFORMATION The background of many topics is succinctly described in the text. Brief biographies of 83 mathematicians and computer scientists are included as footnotes. These biographies include information about the lives, careers, and accomplishments of these important contributors to discrete mathematics and images, when available, are displayed. In addition, numerous historical footnotes are included that supplement the historical information in the main body of the text. Efforts have been made to keep the book up-to-date by reflecting the latest discoveries. KEY TERMS AND RESULTS A list of key terms and results follows each chapter. The key terms include only the most important that students should learn, and not every term defined in the chapter. EXERCISES There are over 4000 exercises in the text, with many different types of questions posed. There is an ample supply of straightforward exercises that develop basic skills, a large number of intermediate exercises, and many challenging exercises. Exercises are stated clearly and unambiguously, and all are carefully graded for level of difficulty. Exercise sets contain special discussions that develop new concepts not covered in the text, enabling students to discover new ideas through their own work. Exercises that are somewhat more difficult than average are marked with a single star ∗; those that are much more challenging are marked with two stars ∗∗. Exercises whose solutions require calculus are explicitly noted. Exercises that develop results used in the text are clearly identified with the right pointing hand symbol . Answers or outlined solutions to all oddxii Preface numbered exercises are provided at the back of the text. The solutions include proofs in which most of the steps are clearly spelled out. REVIEW QUESTIONS A set of review questions is provided at the end of each chapter. These questions are designed to help students focus their study on the most important concepts and techniques of that chapter. To answer these questions students need to write long answers, rather than just perform calculations or give short replies. SUPPLEMENTARY EXERCISE SETS Each chapter is followed by a rich and varied set of supplementary exercises. These exercises are generally more difficult than those in the exercise sets following the sections. The supplementary exercises reinforce the concepts of the chapter and integrate different topics more effectively. COMPUTER PROJECTS Each chapter is followed by a set of computer projects. The approximately 150 computer projects tie together what students may have learned in computing and in discrete mathematics. Computer projects that are more difficult than average, from both a mathematical and a programming point of view, are marked with a star, and those that are extremely challenging are marked with two stars. COMPUTATIONS AND EXPLORATIONS A set of computations and explorations is included at the conclusion of each chapter. These exercises (approximately 120 in total) are designed to be completed using existing software tools, such as programs that students or instructors have written or mathematical computation packages such as MapleTM or MathematicaTM. Many of these exercises give students the opportunity to uncover new facts and ideas through computation. (Some of these exercises are discussed in the Exploring Discrete Mathematics companion workbooks available online.) WRITING PROJECTS Each chapter is followed by a set of writing projects. To do these projects students need to consult the mathematical literature. Some of these projects are historical in nature and may involve looking up original sources. Others are designed to serve as gateways to new topics and ideas. All are designed to expose students to ideas not covered in depth in the text. These projects tie mathematical concepts together with the writing process and help expose students to possible areas for future study. (Suggested references for these projects can be found online or in the printed Student’s Solutions Guide.) APPENDIXES There are three appendixes to the text. The first introduces axioms for real numbers and the positive integers, and illustrates howfacts are proved directly from these axioms. The second covers exponential and logarithmic functions, reviewing some basic material used heavily in the course. The third specifies the pseudocode used to describe algorithms in this text. SUGGESTED READINGS A list of suggested readings for the overall book and for each chapter is provided after the appendices. These suggested readings include books at or below the level of this text, more difficult books, expository articles, and articles in which discoveries in discrete mathematics were originally published. Some of these publications are classics, published many years ago, while others have been published in the last few years. How to Use This Book This text has been carefully written and constructed to support discrete mathematics courses at several levels and with differing foci. The following table identifies the core and optional sections. An introductory one-term course in discrete mathematics at the sophomore level can be based on the core sections of the text, with other sections covered at the discretion of the Preface xiii instructor. A two-term introductory course can include all the optional mathematics sections in addition to the core sections. A course with a strong computer science emphasis can be taught by covering some or all of the optional computer science sections. Instructors can find sample syllabi for a wide range of discrete mathematics courses and teaching suggestions for using each section of the text can be found in the Instructor’s Resource Guide available on the website for this book. Chapter Core Optional CS Optional Math 1 1.1–1.8 (as needed) 2 2.1–2.4, 2.6 (as needed) 2.5 3 3.1–3.3 (as needed) 4 4.1–4.4 (as needed) 4.5, 4.6 5 5.1–5.3 5.4, 5.5 6 6.1–6.3 6.6 6.4, 6.5 7 7.1 7.4 7.2, 7.3 8 8.1, 8.5 8.3 8.2, 8.4, 8.6 9 9.1, 9.3, 9.5 9.2 9.4, 9.6 10 10.1–10.5 10.6–10.8 11 11.1 11.2, 11.3 11.4, 11.5 12 12.1–12.4 13 13.1–13.5 Instructors using this book can adjust the level of difficulty of their course by choosing either to cover or to omit the more challenging examples at the end of sections, as well as the more challenging exercises. The chapter dependency chart shown here displays the strong dependencies.A star indicates that only relevant sections of the chapter are needed for study of a later chapter.Weak dependencies have been ignored. More details can be found in the Instructor Resource Guide. Chapter 9* Chapter 10* Chapter 11 Chapter 13 Chapter 12 Chapter 2* Chapter 7 Chapter 8 Chapter 6* Chapter 3* Chapter 1 Chapter 4* Chapter 5* Ancillaries STUDENT’S SOLUTIONS GUIDE This student manual, available separately, contains full solutions to all odd-numbered problems in the exercise sets. These solutions explain why a particular method is used and why it works. For some exercises, one or two other possible approaches are described to show that a problem can be solved in several different ways. Suggested references for the writing projects found at the end of each chapter are also included in this volume. Also included are a guide to writing proofs and an extensive description of common xiv Preface mistakes students make in discrete mathematics, plus sample tests and a sample crib sheet for each chapter designed to help students prepare for exams. (ISBN-10: 0-07-735350-1) (ISBN-13: 978-0-07-735350-6) INSTRUCTOR’S RESOURCE GUIDE This manual, available on the website and in printed form by request for instructors, contains full solutions to even-numbered exercises in the text. Suggestions on how to teach the material in each chapter of the book are provided, including the points to stress in each section and how to put the material into perspective. It also offers sample tests for each chapter and a test bank containing over 1500 exam questions to choose from. Answers to all sample tests and test bank questions are included. Finally, several sample syllabi are presented for courses with differing emphases and student ability levels. (ISBN-10: 0-07-735349-8) (ISBN-13: 978-0-07-735349-0) Acknowledgments I would like to thank the many instructors and students at a variety of schools who have used this book and provided me with their valuable feedback and helpful suggestions. Their input has made this a much better book than it would have been otherwise. I especially want to thank Jerrold Grossman, Jean-Claude Evard, and Georgia Mederer for their technical reviews of the seventh edition and their “eagle eyes,” which have helped ensure the accuracy of this book. I also appreciate the help provided by all those who have submitted comments via the website. I thank the reviewers of this seventh and the six previous editions. These reviewers have provided much helpful criticism and encouragement to me. I hope this edition lives up to their high expectations. Reviewers for the Seventh Edition Philip Barry University of Minnesota, Minneapolis Miklos Bona University of Florida Kirby Brown Queens College John Carter University of Toronto Narendra Chaudhari Nanyang Technological University Allan Cochran University of Arkansas Daniel Cunningham Buffalo State College George Davis Georgia State University Andrzej Derdzinski The Ohio State University Ronald Dotzel University of Missouri-St. Louis T.J. Duda Columbus State Community College Bruce Elenbogen University of Michigan, Dearborn Norma Elias Purdue University, Calumet-Hammond Herbert Enderton University of California, Los Angeles Anthony Evans Wright State University Kim Factor Marquette University Margaret Fleck University of Illinois, Champaign Peter Gillespie Fayetteville State University Johannes Hattingh Georgia State University Ken Holladay University of New Orleans Jerry Ianni LaGuardia Community College Ravi Janardan University of Minnesota, Minneapolis Norliza Katuk University of Utara Malaysia William Klostermeyer University of North Florida Przemo Kranz University of Mississippi Jaromy Kuhl University of West Florida Loredana Lanzani University of Arkansas, Fayetteville Steven Leonhardi Winona State University Xu Liutong Beijing University of Posts and Telecommunications Vladimir Logvinenko De Anza Community College Preface xv Darrell Minor Columbus State Community College Keith Olson Utah Valley University Yongyuth Permpoontanalarp King Mongkut’s University of Technology, Thonburi Galin Piatniskaia University of Missouri, St. Louis Stefan Robila Montclair State University Chris Rodger Auburn University Sukhit Singh Texas State University, San Marcos David Snyder Texas State University, San Marcos Wasin So San Jose State University Bogdan Suceava California State University, Fullerton Christopher Swanson Ashland University Bon Sy Queens College MatthewWalsh Indiana-Purdue University, Fort Wayne GideonWeinstein Western Governors University DavidWilczynski University of Southern California I would like to thank Bill Stenquist, Executive Editor, for his advocacy, enthusiasm, and support. His assistance with this edition has been essential. I would also like to thank the original editor,WayneYuhasz, whose insights and skills helped ensure the book’s success, as well as all the many other previous editors of this book. I want to express my appreciation to the staff of RPK Editorial Services for their valuable work on this edition, including Rose Kernan, who served as both the developmental editor and the production editor, and the other members of the RPK team, Fred Dahl, Martha McMaster, ErinWagner, Harlan James, and Shelly Gerger-Knecthl. I thank Paul Mailhot of PreTeX, Inc., the compositor, for the tremendous amount to work he devoted to producing this edition, and for his intimate knowledge of LaTeX. Thanks also to Danny Meldung of Photo Affairs, Inc., who was resourceful obtaining images for the new biographical footnotes. The accuracy and quality of this new edition owe much to Jerry Grossman and Jean-Claude Evard, who checked the entire manuscript for technical accuracy and Georgia Mederer, who checked the accuracy of the answers at the end of the book and the solutions in the Student’s Solutions Guide and Instructor’s Resource Guide. As usual, I cannot thank Jerry Grossman enough for all his work authoring these two essential ancillaries. I would also express my appreciation the Science, Engineering, and Mathematics (SEM) Division of McGraw-Hill Higher Education for their valuable support for this new edition and the associated media content. In particular, thanks go to Kurt Strand: President, SEM, McGraw- Hill Higher Education, Marty Lange: Editor-in-Chief, SEM, Michael Lange: Editorial Director, Raghothaman Srinivasan: Global Publisher, Bill Stenquist: Executive Editor, Curt Reynolds: Executive Marketing Manager, Robin A. Reed: Project Manager, Sandy Ludovissey: Buyer, Lorraine Buczek: In-house Developmental Editor, Brenda Rowles: Design Coordinator, Carrie K. Burger: Lead Photo Research Coordinator, and Tammy Juran: Media Project Manager. Kenneth H. Rosen.

Quantitative Analysis of Dependency Structures

Author: Jingyang Jiang,Haitao Liu

Publisher: Walter de Gruyter GmbH & Co KG

ISBN: 3110573563

Category: Language Arts & Disciplines

Page: 380

View: 7611

Dependency analysis is increasingly used in computational linguistics and cognitive science. Surprisingly, compared with studies based on phrase structures, quantitative methods and dependency structure are rarely integrated in research.This is the first book that collects original contributions which quantitatively analyze dependency structures across different languages and text genres.

Handbook of Discrete and Combinatorial Mathematics

Author: Kenneth H. Rosen

Publisher: CRC Press

ISBN: 135164405X

Category: Mathematics

Page: 1612

View: 848

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.

Basiswissen Archäologie

Theorien, Methoden, Praxis

Author: Colin Renfrew,Paul G. Bahn

Publisher: Philipp Von Zabern Verlag Gmbh

ISBN: 9783805339483

Category: History

Page: 304

View: 5353

Mit mehr als 150.000 verkauften Exemplaren gilt der Band Archaeology: Theories, Methods and Practice im englischsprachigen Raum bereits jetzt als Standardwerk im Fach Archaologie. Diese jetzt erstmals auf Deutsch vorliegende sorgfaltig uberarbeitete und zum Teil vollig neu geschriebene Fassung ist eine ausserst gut lesbare Einfuhrung fur alle, die sich fur Archaologie interessieren und eine kompakte Darstellung der Methoden und Praxis archaologischer Arbeit suchen. Beruhmte Archaologen und Ausgrabungsstatten passieren Revue. Inhaltlich ist das Buch auf der Hohe der Forschung, auch die neuesten technischen Methoden und Technologien werden behandelt. (Philipp von Zabern 2009)

Der tägliche Stoiker

366 nachdenkliche Betrachtungen über Weisheit, Beharrlichkeit und Lebensstil

Author: Ryan Holiday,Stephen Hanselman

Publisher: FinanzBuch Verlag

ISBN: 3960920717

Category: Self-Help

Page: 432

View: 9147

Wie findet man das wahre Glück? Wie lässt sich Erfolg wirklich bemessen? Und wie geht man mit den Herausforderungen des Alltags wie Wut, Trauer und der Frage nach dem Sinn des Ganzen um? Was große Geister wie George Washington, Friedrich der Große, Weltklassesportler oder Top-Performer längst für sich entdeckt haben, liegt mit "Der tägliche Stoiker" erstmals gesammelt vor. New York Times-Bestsellerautor Ryan Holiday und Stephen Hanselman haben das Wissen der Stoiker in 366 zeitlose Lektionen verpackt und zeigen, dass die Philosophie des Stoizismus nicht nur zeitlos, sondern gerade für unsere hektische und unsichere Zeit ein Segen ist. Weisheit, Mut, Gerechtigkeitssinn und Selbstbeherrschung sowie Gelassenheit lassen sich erlernen und helfen uns, in der zunehmenden Komplexität unserer Welt zu bestehen. Die uralten Weisheiten der Stoiker, gesammelt und kommentiert, unterstützen bei diesen alltäglichen Herausforderungen.

Das BUCH der Beweise

Author: Martin Aigner,Günter M. Ziegler

Publisher: Springer-Verlag

ISBN: 3662064545

Category: Mathematics

Page: 247

View: 7845

Die elegantesten mathematischen Beweise, spannend und für jeden Interessierten verständlich. "Der Beweis selbst, seine Ästhetik, seine Pointe geht ins Geschichtsbuch der Königin der Wissenschaften ein. Ihre Anmut offenbart sich in dem gelungenen und geschickt illustrierten Buch." Die Zeit

Rechnerorganisation und Rechnerentwurf

Die Hardware/Software-Schnittstelle

Author: David Patterson,John LeRoy Hennessy

Publisher: Walter de Gruyter GmbH & Co KG

ISBN: 3110446065

Category: Computers

Page: 833

View: 7491

Mit der deutschen Übersetzung zur fünfter Auflage des amerikanischen Klassikers Computer Organization and Design - The Hardware/Software Interface ist das Standardwerk zur Rechnerorganisation wieder auf dem neusten Stand - David A. Patterson und John L. Hennessy gewähren die gewohnten Einblicke in das Zusammenwirken von Hard- und Software, Leistungseinschätzungen und zahlreicher Rechnerkonzepte in einer Tiefe, die zusammen mit klarer Didaktik und einer eher lockeren Sprache den Erfolg dieses weltweit anerkannten Standardwerks begründen. Patterson und Hennessy achten darauf, nicht nur auf das "Wie" der dargestellten Konzepte, sondern auch auf ihr "Warum" einzugehen und zeigen damit Gründe für Veränderungen und neue Entwicklungen auf. Jedes der Kapitel steht für einen deutlich umrissenen Teilbereich der Rechnerorganisation und ist jeweils gleich aufgebaut: Eine Einleitung, gefolgt von immer tiefgreifenderen Grundkonzepten mit steigernder Komplexität. Darauf eine aktuelle Fallstudie, "Fallstricke und Fehlschlüsse", Zusammenfassung und Schlussbetrachtung, historische Perspektiven und Literaturhinweise sowie Aufgaben. In der neuen Auflage sind die Inhalte in den Kapiteln 1-5 an vielen Stellen punktuell verbessert und aktualisiert, mit der Vorstellung neuerer Prozessoren worden, und der Kapitel 6... from Client to Cloud wurde stark überarbeitetUmfangreiches Zusatzmaterial (Werkzeuge mit Tutorien etc.) stehtOnline zur Verfügung.

Lineare Algebra

Einführung, Grundlagen, Übungen

Author: Howard Anton

Publisher: Springer Verlag

ISBN: 9783827403247

Category: Mathematics

Page: 680

View: 6373

In Ihrer Hand liegt ein Lehrbuch - in sieben englischsprachigen Ausgaben praktisch erprobt - das Sie mit groem didaktischen Geschick, zudem angereichert mit zahlreichen Ubungsaufgaben, in die Grundlagen der linearen Algebra einfuhrt. Kenntnisse der Analysis werden fur das Verstandnis nicht generell vorausgesetzt, sind jedoch fur einige besonders gekennzeichnete Beispiele notig. Padagogisch erfahren, behandelt der Autor grundlegende Beweise im laufenden Text; fur den interessierten Leser jedoch unverzichtbare Beweise finden sich am Ende der entsprechenden Kapitel. Ein weiterer Vorzug des Buches: Die Darstellung der Zusammenhange zwischen den einzelnen Stoffgebieten - linearen Gleichungssystemen, Matrizen, Determinanten, Vektoren, linearen Transformationen und Eigenwerten.

Moderne Physik

Author: Paul A. Tipler,Ralph A. Llewellyn

Publisher: N.A

ISBN: 9783110347951

Category:

Page: N.A

View: 547


Differentialgleichungen und ihre Anwendungen

Author: Martin Braun

Publisher: Springer-Verlag

ISBN: 3642973418

Category: Mathematics

Page: 596

View: 7776

Dieses richtungsweisende Lehrbuch für die Anwendung der Mathematik in anderen Wissenschaftszweigen gibt eine Einführung in die Theorie der gewöhnlichen Differentialgleichungen. Fortran und APL-Programme geben den Studenten die Möglichkeit, verschiedene numerische Näherungsverfahren an ihrem PC selbst durchzurechnen. Aus den Besprechungen: "Die Darstellung ist überall mathematisch streng und zudem ungemein anregend. Abgesehen von manchen historischen Bemerkungen ... tragen dazu die vielen mit ausführlichem Hintergrund sehr eingehend entwickelten praktischen Anwendungen bei. ... Besondere Aufmerksamkeit wird der physikalisch und technisch so wichtigen Frage nach Stabilität von Lösungen eines Systems von Differentialgleichungen gewidmet. Das Buch ist wegen seiner geringen Voraussetzungen und vorzüglichen Didaktik schon für alle Studenten des 3. Semesters geeignet; seine eminent praktische Haltung empfiehlt es aber auch für alle Physiker, die mit Differentialgleichungen und ihren Anwendungen umzugehen haben." #Physikalische Blätter#

Algebra

Aus dem Englischen übersetzt von Annette A’Campo

Author: Michael Artin

Publisher: Birkhäuser

ISBN: 9783764359386

Category: Mathematics

Page: 705

View: 6491

Important though the general concepts and propositions may be with which the modem and industrious passion for axiomatizing and generalizing has presented us, in algebra perhaps more than anywhere else, nevertheless I am convinced that the special problems in all their complexity constitute the stock and core of mathematics, and that to master their difficulties requires on the whole the harder labor. HERMANN WEYL Die Arbeit an diesem Buch begann vor etwa zwanzig Jahren mit Aufzeichnungen zur Ergänzung meiner Algebravorlesungen. Ich wollte einige konkrete Themen, wie Symmetrie, lineare Gruppen und quadratische Zahlkörper, ausführlicher be­ handeln als dies im vorgesehenen Text der Fall war, und darüberhinaus wollte ich den Schwerpunkt in der Gruppentheorie von den Permutationsgruppen auf Matrixgruppen verlagern. Ein anderes ständig wiederkehrendes Thema, nämlich Gitter, sind spontan aufgetaucht. Ich hoffte, der konkrete Stoff könne das Interesse der Studenten wecken und gleichzeitig die Abstraktionen verständlicher machen, kurz gesagt, sie sollten weiter kommen, indem sie beides gleichzeitig lernten. Das bewährte sich gut. Es dauerte einige Zeit, bis ich entschieden hatte, welche Themen ich behandeln wollte, und allmählich verteilte ich mehr und mehr Aufzeichnungen und ging schließlich dazu über, die ganze Vorlesung mit diesem Skript zu bestrei­ ten. Auf diese Weise ist ein Buch entstanden, das, wie ich meine, etwas anders ist als die existierenden Bücher. Allerdings haben mir die Probleme, die ich damit hatte, die einzelnen Teile des Buches zu einem Ganzen zusammenzufügen, einige Kopfschmerzen bereitet; ich kann also nicht empfehlen, auf diese Art anzufangen, ein Buch zu schreiben.

Android-Programmierung

Author: Zigurd Mednieks,Laird Dornin,G. Blake Meike,Masumi Nakamura

Publisher: O'Reilly Germany

ISBN: 3955611418

Category:

Page: 624

View: 7209

Android hat hierzulande die einstige Vorreiterstellung von Apple langst geknackt. Bei den Smartphones liegt das Betriebssystem von Google weit vorn, und auch bei den Tablets holt Android zugig auf. Zeit also, sich mit der App-Entwicklung fur Android zu beschaftigen! Dieses Buch wendet sich an Leser, die die Programmierung von Android-Apps von Grund auf lernen und auf professionellem Niveau betreiben mochten. Es richtet sich an Java-Entwickler und Leser mit Kenntnissen in einer anderen objektorientierten Sprache.

Numerische Methoden

Näherungsverfahren und ihre praktische Anwendung

Author: John Douglas Faires,Richard L. Burden

Publisher: Springer Verlag

ISBN: 9783827405968

Category: Science

Page: 630

View: 6949

Numerische Methoden a " NAherungsverfahren also a " sind im allgemeinen Bestandteil von Vorlesungen zur numerischen Analysis. Der Vorteil: Wissenschaftliche GrA1/4ndlichkeit, AusfA1/4hrlichkeit der BeweisfA1/4hrung. Der Nachteil: Mangel an praktischem Nutzen a " u.a. fA1/4r den (angehenden) Natur- und Ingenieurwissenschaftler. Faires und Burden haben daher Ballast abgeworfen: Die Betonung ihres Werkes "Numerische Methoden" liegt in der Anwendung von NAherungsverfahren a " und zwar auf solche Probleme, die fA1/4r Natur- und Ingenieurwissenschaftler charakteristisch sind. Alle Verfahren werden unter dem Aspekt der Implementierung beschrieben und eine vollstAndige mathematische BegrA1/4ndung nur dann diskutiert, falls sie beitrAgt, das Verfahren zu verstehen. Mit der beigefA1/4gten Software a " in FORTRAN und Pascal a " lassen sich die meisten der gestellten Probleme lAsen. "Numerische Methoden" ist so mit Lehrbuch und Nachschlagewerk zugleich.