Die Welt Der Primzahlen: Geheimnisse Und Rekorde (springer-lehrbuch) (german Edition)

Die Welt der Primzahlen - in faszinierender Weise werden die wesentlichen Ergebnisse über die elementaren Bausteine der natürlichen Zahlen vorgestellt. Grundlegende Sätze und die wichtigsten offenen Fragen und ungelösten Probleme werden von einer wohl einmaligen Sammlung von Rekorden über Primzahlen begleitet. Ein umfangreiches Literaturverzeichnis ergänzt das Buch zu einer wichtigen Quelle für jeden Leser, der sich für die Zahlentheorie und insbesondere für Primzahlen interessiert. In der englischen Originalfassung fast schon ein Klassiker, erscheint das Buch jetzt aktualisiert in deutscher Sprache. Paulo Ribenboim ist emeritierter Professor der kanadischen Queen's University, Fellow der Royal Society of Canada und Träger des George Pólya-Preises der Mathematical Association of America. Er ist Autor von 13 Büchern und über 150 Forschungsartikeln. A Deep Understanding Of Prime Numbers Is One Of The Great Challenges In Mathematics. In This Book, Fundamental Theorems, Challenging Open Problems, And The Most Recent Computational Records Are Presented In A Language Without Secrets. The Impressive Wealth Of Material And References Will Make This Book A Favorite Companion And A Source Of Inspiration To All Readers. Paulo Ribenboim Is Professor Emeritus At Queen's University In Canada, Fellow Of The Royal Society Of Canada, And Recipient Of The George Pólya Award Of The Mathematical Association Of America. He Is The Author Of 13 Books And More Than 150 Research Articles. From The Reviews Of The First Edition: Number Theory And Mathematics As A Whole Will Benefit From Having Such An Accessible Book Exposing Advanced Material. There Is No Question That This Book Will Succeed In Exciting Many New People To The Beauty And Fascination Of Prime Numbers, And Will Probably Bring More Young People To Research In These Areas. - Andrew Granville, Zentralblatt Ribenboim Is A Rare Creature - An Academic Who Writes In An Unstuffy Way - And His Book Gives An Overview Of What Is Currently Known About Primes. - Robert Matthews, The Sunday Telegraph ...this Genially Reader-friendly Tour De Force, By A Scientist With An Encyclopedic And Up-to-the-minute Knowledge Of The Subject, Is A Wholly Admirable Addition To Anyone’s Bookshelf. - John H. Halton, American Scientist Epigraph -- Preface -- Acknowledgements -- Guiding The Reader -- Table Of Notations -- Introduction -- How Many Prime Numbers Are There?- How To Recognize Whether A Natural Number Is A Prime -- Are There Functions Defining Prime Numbers?- How Are The Prime Numbers Distributed?- Which Special Kinds Of Primes Have Been Considered?- Heuristic And Probabilistic Results About Prime Numbers -- Appendix 1 -- Appendix 2 -- Conclusion -- Bibliography -- Primes Up To 10,000 -- Index Of Tables -- Index Of Records -- Index Of Names -- Gallimawfries -- Subject Index. Paulo Ribenboim. Includes Bibliographical References (p. [281]-324) And Index. The immensely popular Guinness Book of World Records lacked a chapter on prime numbers. The also popular Book of Prime Number Records, however, fills this need. This abridged version, written by the same author, is devoted to presenting records concerning prime numbers, but it also explores the interface between computations and the theory of prime numbers. The book contains an up-to-date historical presentation of the main problems pertaining to prime numbers, as well as many fascinating topics, including primality testing. It is written in a light and humours language without secrets and is thoroughly accessible to everyone. TOC:* Preface * Guiding the Reader * Index of Notations * Introduction * How Many Prime Numbers Are There? * How to Recognize Whether a Natural Number is a Prime * Are There Functions Defining Prime Numbers? * How Are the Prime Numbers Distributed? * Which Special Kinds of Primes Have Been Considered? * Heuristic and Probabilistic Results about Prime Numbers * Conclusion * Bibliography * Primes up to 10,000 * Index of Tables * Index of Records * Index of Names * Gallimawfries * Subject Index A deep understanding of prime numbers is one of the great challenges in mathematics. In this new edition, fundamental theorems, challenging open problems, and the most recent computational records are presented in a language without secrets. The impressive wealth of material and references will make this book a favorite companion and a source of inspiration to all readers. Paulo Ribenboim is Professor Emeritus at Queen's University in Canada, Fellow of the Royal Society of Canada, and recipient of the George Plya Award of the Mathematical Association of America. He is the author of 13 books and more than 150 research articles. From the reviews of the First Edition: Number Theory and mathematics as a whole will benefit from having such an accessible book exposing advanced material. There is no question that this book will succeed in exciting many new people to the beauty and fascination of prime numbers, and will probably bring more young people to research in these areas. ( Andrew Granville, Zentralblatt ) Die Welt der Primzahlen - in faszinierender Weise stellt Paulo Ribenboim die wesentlichen Ergebnisse zu den Bausteinen der natürlichen Zahlen vor. Fundamentale Sätze, offene Fragen und ungelöste Probleme bereichert er durch eine wohl einmalige Sammlung von Rekorden über Primzahlen. Eine umfangreiche Liste mit Literaturhinweisen ergänzt das Buch und macht es zu einer wichtigen Quelle für alle Leser, die sich für die Zahlentheorie interessieren. Einleitung....Pages 1-2 Wieviele Primzahlen gibt es?....Pages 3-13 Wie kann man Primzahlen erkennen?....Pages 15-134 Gibt es primzahldefinierende Funktionen?....Pages 135-160 Wie sind die Primzahlen verteilt?....Pages 161-228 Welche besonderen Arten von Primzahlen wurden untersucht?....Pages 229-255 Heuristische und probabilistische Betrachtungen....Pages 257-275