Paulo Ribenboim Boeken

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 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 )

Exploring the fascinating world of prime numbers, this book builds on a lecture given at Queen's University and reflects on the nature of numeracy, referencing unique cultural perspectives. It highlights the contrast between vast numerical concepts and the simplicity of language, illustrated by a tribe in Brazil lacking a term for "two." The text promises a blend of engaging words and numbers, featuring updated sections and records compared to its predecessor, aiming to captivate readers with the allure of prime numbers and mathematical curiosities.

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.

This selection of expository essays by Paulo Ribenboim should be of interest to mathematicians from all walks. Ribenboim, a highly praised author of several popular titles, writes each essay in a light and humorous language without secrets, making them thoroughly accessible to everyone with an interest in numbers. This new collection includes essays on Fibonacci numbers, prime numbers, Bernoulli numbers, and historical presentations of the main problems pertaining to elementary number theory, such as Kummers work on Fermat's last theorem.

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.