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› Find signed collectible books: '13 Lectures on Fermat's Last Theorem'
Fermat's problem, also ealled Fermat's last theorem, has attraeted the attention of mathematieians far more than three eenturies. Many clever methods have been devised to attaek the problem, and many beautiful theories have been ereated with the aim of proving the theorem. Yet, despite all the attempts, the question remains unanswered. The topie is presented in the form of leetures, where I survey the main lines of work on the problem. In the first two leetures, there is a very brief deseription of the early history , as well as a seleetion of a few of the more representative reeent results. In the leetures whieh follow, I examine in sue- eession the main theories eonneeted with the problem. The last two lee tu res are about analogues to Fermat's theorem. Some of these leetures were aetually given, in a shorter version, at the Institut Henri Poineare, in Paris, as well as at Queen's University, in 1977. I endeavoured to produee a text, readable by mathematieians in general, and not only by speeialists in number theory. However, due to a limitation in size, I am aware that eertain points will appear sketehy. Another book on Fermat's theorem, now in preparation, will eontain a eonsiderable amount of the teehnieal developments omitted here. It will serve those who wish to learn these matters in depth and, I hope, it will clarify and eomplement the present volume.
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› Find signed collectible books: 'The Book of Prime Number Records'
This text originated as a lecture delivered November 20, 1984, at Queen's University, in the undergraduate colloquium series established to honour Professors A. J. Coleman and H. W. Ellis and to acknowledge their long-lasting interest in the quality of teaching undergraduate students. In another colloquium lecture, my colleague Morris Orzech, who had consulted the latest edition of the Guinness Book oj Records, reminded me very gently that the most "innumerate" people of the world are of a certain tribe in Mato Grosso, Brazil. They do not even have a word to express the number "two" or the concept of plurality. "Yes Morris, I'm from Brazil, but my book will contain numbers different from 'one.' " He added that the most boring 800-page book is by two Japanese mathematicians (whom I'll not name), and consists of about 16 million digits of the number 11. "I assure you Morris, that in spite of the beauty of the apparent randomness of the decimal digits of 11, I'll be sure that my text will also include some words." Acknowledgment. The manuscript of this book was prepared on the word processor by Linda Nuttall. I wish to express my appreciation for the great care, speed, and competence of her work. Paulo Ribenboim CONTENTS Preface vii Guiding the Reader xiii Index of Notations xv Introduction Chapter 1. How Many Prime Numbers Are There? 3 I. Euclid's Proof 3 II.
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› Find signed collectible books: 'Catalans Conjecture: Are 8 and 9 the Only Consecutive Powers?'
In 1844, Catalan conjectured that 8 and 9 were the only consecutive integral powers. The problem of consecutive powers is more easily grasped than Fermats last theorem, so recently vanquished. In this book, Paulo Ribenboim brings together for the first time the diverse approaches to proving Catalans conjecture. These range from the elementary methods that apply in special cases (Part A) to powerful and general results in diophantine approximation (Part C) which yieldthe strongest results to date.
In 1976, Tijdeman found a computable bound above which there are no consecutive powers. Langerin reduced this to an exponential: exp (exp (exp (exp (730)))). The enormous gap between such bonds-and the only known consecutive powers, 8 and 9-has been narrowed, but its immensity suggests the difficulty of such problems, as well as the interesting and fruitful methods developed for attacking them.
Ribenboims book will appeal to anyone interested in how number theorists attack difficult problems. Its concrete focus on an easy to state problem is a relief from such generalities as the related A, B, C conjecture, and will prove to be a good point ofdeparture for seminars in number theory. The text includes many beautiful results of classical number theory not found in any other book. The treatment is fully accessible and self-contained, making this book as attractive as the authors 13 Lectures on Fermats Last Theorem, and his book, Book of Prime Records.
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› Find signed collectible books: 'Classical Theory of Algebraic Numbers (Universitext)'
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.
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› Find signed collectible books: 'Collected papers of Paulo Ribenboim (Queen's papers in pure and applied mathematics)'
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› Find signed collectible books: 'Fermat's Last Theorem for Amateurs'
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.
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› Find signed collectible books: 'The Little Book of Bigger Primes'
The immensely popular Guiness 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 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 humorous language without secrets and is thoroughly accessible to everyone.
› Find signed collectible books: 'My Numbers, My Friends: Popular Lectures on Number Theory'
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.
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› Find signed collectible books: 'The New Book of Prime Number Records'
This text originated as a lecture delivered November 20, 1984, at Queen's University, in the undergraduate colloquium senes. In another colloquium lecture, my colleague Morris Orzech, who had consulted the latest edition of the Guinness Book of Records, reminded me very gently that the most "innumerate" people of the world are of a certain trible in Mato Grosso, Brazil. They do not even have a word to express the number "two" or the concept of plurality. "Yes, Morris, I'm from Brazil, but my book will contain numbers different from ·one.''' He added that the most boring 800-page book is by two Japanese mathematicians (whom I'll not name) and consists of about 16 million decimal digits of the number Te. "I assure you, Morris, that in spite of the beauty of the appar ent randomness of the decimal digits of Te, I'll be sure that my text will include also some words." And then I proceeded putting together the magic combina tion of words and numbers, which became The Book of Prime Number Records. If you have seen it, only extreme curiosity could impel you to have this one in your hands. The New Book of Prime Number Records differs little from its predecessor in the general planning. But it contains new sections and updated records.
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› Find signed collectible books: 'Paulo Ribenboim; career up to 1995'
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› Find signed collectible books: 'Rings and Modules.'
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› Find signed collectible books: 'The Theory of Classical Valuations (Springer Monographs in Mathematics)'
Valuation theory is used constantly in algebraic number theory and field theory, and is currently gaining considerable research interest. Ribenboim fills a unique niche in the literature as he presents one of the first introductions to classical valuation theory in this up-to-date rendering of the authors long-standing experience with the applications of the theory. The presentation is fully up-to-date and will serve as a valuable resource for students and mathematicians.
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› Find signed collectible books: '13 Lectures on Fermat's Last Theorem'
Fermat's problem, also ealled Fermat's last theorem, has attraeted the attention of mathematieians far more than three eenturies. Many clever methods have been devised to attaek the problem, and many beautiful theories have been ereated with the aim of proving the theorem. Yet, despite all the attempts, the question remains unanswered. The topie is presented in the form of leetures, where I survey the main lines of work on the problem. In the first two leetures, there is a very brief deseription of the early history , as well as a seleetion of a few of the more representative reeent results. In the leetures whieh follow, I examine in sue- eession the main theories eonneeted with the problem. The last two lee tu res are about analogues to Fermat's theorem. Some of these leetures were aetually given, in a shorter version, at the Institut Henri Poineare, in Paris, as well as at Queen's University, in 1977. I endeavoured to produee a text, readable by mathematieians in general, and not only by speeialists in number theory. However, due to a limitation in size, I am aware that eertain points will appear sketehy. Another book on Fermat's theorem, now in preparation, will eontain a eonsiderable amount of the teehnieal developments omitted here. It will serve those who wish to learn these matters in depth and, I hope, it will clarify and eomplement the present volume.
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› Find signed collectible books: 'Fermat's Last Theorem for Amateurs'
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› Find signed collectible books: 'Nombres premiers: mystères et records (French Edition)'
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› Find signed collectible books: 'Meine Zahlen, meine Freunde: Glanzlichter der Zahlentheorie (Springer-Lehrbuch) (German Edition)'
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› Find signed collectible books: 'Die Welt der Primzahlen. Springer Lehrbuch'
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.
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› Find signed collectible books: 'Die Welt der Primzahlen: Geheimnisse und Rekorde (Springer-Lehrbuch) (German Edition)'
Der Autor prasentiert in dem Band die grundlegenden Satze und die wichtigsten ungelosten Probleme aus der Welt der Primzahlen. Begleitet wird diese umfassende Darstellung zu den elementaren Bausteinen der naturlichen Zahlen von einer einmaligen Sammlung zu den Primzahlrekorden. In der englischen Originalfassung fast schon ein Klassiker, erscheint das Buch jetzt in der 2., vollstandig uberarbeiteten und aktualisierten Auflage.
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