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.
Glanzlichter der Zahlentheorie
Paulo Ribenboim behandelt Zahlen in dieser außergewöhnlichen Sammlung von Übersichtsartikeln wie seine persönlichen Freunde. In leichter und allgemein zugänglicher Sprache berichtet er über Primzahlen, Fibonacci-Zahlen (und das Nordpolarmeer!), die klassischen Arbeiten von Gauß über binäre quadratische Formen, Eulers berühmtes primzahlerzeugendes Polynom, irrationale und transzendente Zahlen. Nach dem großen Erfolg von „Die Welt der Primzahlen" ist dies das zweite Buch von Paulo Ribenboim, das in deutscher Sprache erscheint.
In 1995, Andrew Wiles completed a proof of Fermat's Last Theorem. Although this was certainly a great mathematical feat, one shouldn't dismiss earlier attempts made by mathematicians and clever amateurs to solve the problem. In this book, aimed at amateurs curious about the history of the subject, the author restricts his attention exclusively to elementary methods that have produced rich results.
Rooted in a 1984 lecture at Queen's University, this work explores the nuances of teaching and learning, particularly in relation to numerical concepts across cultures. The author reflects on the unique linguistic traits of a tribe in Brazil that lacks a term for "two," highlighting the diversity of mathematical understanding. Additionally, a humorous anecdote about a tedious 800-page book illustrates the balance between numbers and language, emphasizing the intention to present a text rich in both numerical and verbal content. Acknowledgments are given to Linda Nuttall for her meticulous work on the manuscript.
The narrative unfolds as a dialogue between mathematician Papa Paulo and his grandsons, offering insights into prime numbers and the thought processes of mathematicians. Through engaging conversations, readers are invited to explore mathematical concepts while gaining a deeper understanding of how mathematicians approach problems and inquiry.
The collection showcases Paulo Ribenboim's significant contributions to ordered structures and mathematical logic, featuring two unpublished papers and his first book on abelian groups. With over 240 publications, Ribenboim's influential research spans number theory, algebraic structures, and model theory, including collaborations with notable mathematicians. The volumes delve into topics such as algebraic structures on directed graphs and real algebraic geometry, reflecting his profound impact on the field. Ribenboim is a professor emeritus at Queen's University, with a prestigious prize named in his honor.
Fermat's last theorem has captivated mathematicians for over three centuries, inspiring numerous theories and methods aimed at its proof. This collection of lectures offers a concise overview of the theorem's history, recent results, and key theories related to the problem. The content is accessible to a general mathematical audience, though some details may be abbreviated. The final lectures explore analogues to Fermat's theorem. A forthcoming companion book will delve deeper into the technical aspects for those seeking a more comprehensive understanding.
"This is a charming book, written as a conversation between mathematician Papa Paulo and his grandsons. A motivated reader can learn not only about prime numbers, but also something about how mathematicians think, work, and ask questions from reading this book." Mathematical Association of America Prime Numbers, Friends Who Give Problems is written as a trialogue, with two persons who are interested in prime numbers asking the author, Papa Paulo, intelligent questions. Starting at a very elementary level, the book advances steadily, covering all important topics of the theory of prime numbers, up to the most famous problems. The humorous conversations and the inclusion of a back-story add to the uniqueness of the book. Concepts and results are also explained with great care, making the book accessible to a wide audience.
The exposition of the classical theory of algebraic numbers is clear and thorough, and there is a large number of exercises as well as worked out numerical examples. A careful study of this book will provide a solid background to the learning of more recent topics.