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Classical Theory of Algebraic Numbers (Hardcover, 2nd ed. 2001): Paulo Ribenboim Classical Theory of Algebraic Numbers (Hardcover, 2nd ed. 2001)
Paulo Ribenboim
R3,448 Discovery Miles 34 480 Ships in 10 - 15 working days

This book has a clear and thorough exposition of the classical theory of algebraic numbers, and contains a large number of exercises as well as worked out numerical examples. The introduction is a recapitulation of results about principal ideal domains, unique factorization domains and commutative fields. Part one is devoted to residue classes and quadratic residues. In part two one finds the study of algebraic integers, ideals, units, class numbers, the theory of decomposition, inertia and ramification of ideals. part three is devoted to Kummerżs theory of cyclotomic fields, and includes Bernoulli numbers and the proof of Fermatżs Last Theorem for regular prime exponents. Finally, in part four, the emphasis is on analytical methods and it includes Dirichletżs Theorem on primes in arithmetic progressions, the theorem of Chebotarev and class number formulas. A careful study of this book will provide a solid background to the learning of more recent topics, as suggested at the end of the book.

The New Book of Prime Number Records (Hardcover, 3rd ed. 1996): Paulo Ribenboim The New Book of Prime Number Records (Hardcover, 3rd ed. 1996)
Paulo Ribenboim
R3,122 Discovery Miles 31 220 Ships in 10 - 15 working days

The Guinness Book made records immensely popular. This book is devoted, at first glance, to present records concerning prime numbers. But it is much more. It explores the interface between computations and the theory of prime numbers. The book contains an up-to-date historical presentation of the main problems about prime numbers, as well as many fascinating topics, including primality testing. It is written in a language without secrets, and thoroughly accessible to everyone. The new edition has been significantly improved due to a smoother presentation, many new topics and updated records.

The Theory of Classical Valuations (Hardcover, 1999 ed.): Paulo Ribenboim The Theory of Classical Valuations (Hardcover, 1999 ed.)
Paulo Ribenboim
R3,032 Discovery Miles 30 320 Ships in 10 - 15 working days

In his studies of cyclotomic fields, in view of establishing his monumental theorem about Fermat's last theorem, Kummer introduced "local" methods. They are concerned with divisibility of "ideal numbers" of cyclotomic fields by lambda = 1 - psi where psi is a primitive "p"-th root of 1 (p any odd prime). Henssel developed Kummer's ideas, constructed the field of "p"-adic numbers and proved the fundamental theorem known today. Kurschak formally introduced the concept of a valuation of a field, as being real valued functions on the set of non-zero elements of the field satisfying certain properties, like the "p"-adic valuations. Ostrowski, Hasse, Schmidt and others developed this theory and collectively, these topics form the primary focus of this book.

13 Lectures on Fermat's Last Theorem (Hardcover, 1979 ed.): Paulo Ribenboim 13 Lectures on Fermat's Last Theorem (Hardcover, 1979 ed.)
Paulo Ribenboim
R2,644 R1,646 Discovery Miles 16 460 Save R998 (38%) Ships in 12 - 17 working days

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.

Fermat's Last Theorem for Amateurs (Hardcover, 1st ed. 1999. Corr. 2nd printing 2000): Paulo Ribenboim Fermat's Last Theorem for Amateurs (Hardcover, 1st ed. 1999. Corr. 2nd printing 2000)
Paulo Ribenboim
R2,489 Discovery Miles 24 890 Ships in 12 - 17 working days

This book is intended for amateurs, students and teachers. The author presents partial results which could be obtained with exclusively elementary methods. The proofs are given in detail, with minimal prerequisites. An original feature are the ten interludes, devoted to important topics of elementary number theory, thus making the reading of this book self-contained. Their interest goes beyond Fermat's theorem. The Epilogue is a serious attempt to render accessible the strategy of the recent proof of Fermat's last theorem, a great mathematical feat.

Prime Numbers, Friends Who Give Problems: A Trialogue With Papa Paulo (Paperback): Paulo Ribenboim Prime Numbers, Friends Who Give Problems: A Trialogue With Papa Paulo (Paperback)
Paulo Ribenboim
R1,017 Discovery Miles 10 170 Ships in 12 - 17 working days

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.

Prime Numbers, Friends Who Give Problems: A Trialogue With Papa Paulo (Hardcover): Paulo Ribenboim Prime Numbers, Friends Who Give Problems: A Trialogue With Papa Paulo (Hardcover)
Paulo Ribenboim
R1,888 Discovery Miles 18 880 Ships in 12 - 17 working days

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.

Fermat's Last Theorem for Amateurs (Paperback, Softcover reprint of the original 1st ed. 1999): Paulo Ribenboim Fermat's Last Theorem for Amateurs (Paperback, Softcover reprint of the original 1st ed. 1999)
Paulo Ribenboim
R1,747 Discovery Miles 17 470 Ships in 10 - 15 working days

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.

The Theory of Classical Valuations (Paperback, Softcover reprint of the original 1st ed. 1999): Paulo Ribenboim The Theory of Classical Valuations (Paperback, Softcover reprint of the original 1st ed. 1999)
Paulo Ribenboim
R2,825 Discovery Miles 28 250 Ships in 10 - 15 working days

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.

The New Book of Prime Number Records (Paperback, 3rd ed. 1996. Softcover reprint of the original 3rd ed. 1996): Paulo Ribenboim The New Book of Prime Number Records (Paperback, 3rd ed. 1996. Softcover reprint of the original 3rd ed. 1996)
Paulo Ribenboim
R1,549 Discovery Miles 15 490 Ships in 10 - 15 working days

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.

The Book of Prime Number Records (Paperback, Softcover reprint of the original 2nd ed. 1989): Paulo Ribenboim The Book of Prime Number Records (Paperback, Softcover reprint of the original 2nd ed. 1989)
Paulo Ribenboim
R3,064 Discovery Miles 30 640 Ships in 10 - 15 working days

This text originated as a lecture delivered November 20, 1984, at Queen's University, in the undergraduate colloquim series established to honor Professors A. J. Coleman and H. W. Ellis and to acknow ledge their long lasting interest in the quality of teaching under graduate students. In another colloquim lecture, my colleague Morris Orzech, who had consulted the latest edition of the Guilllless Book oj Records, remainded 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 include also 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."

Classical Theory of Algebraic Numbers (Paperback, Softcover reprint of hardcover 2nd ed. 2001): Paulo Ribenboim Classical Theory of Algebraic Numbers (Paperback, Softcover reprint of hardcover 2nd ed. 2001)
Paulo Ribenboim
R2,642 Discovery Miles 26 420 Ships in 10 - 15 working days

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.

13 Lectures on Fermat's Last Theorem (Paperback, Softcover reprint of the original 1st ed. 1979): Paulo Ribenboim 13 Lectures on Fermat's Last Theorem (Paperback, Softcover reprint of the original 1st ed. 1979)
Paulo Ribenboim
R1,580 Discovery Miles 15 800 Ships in 10 - 15 working days

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.

My Numbers, My Friends - Popular Lectures on Number Theory (Paperback, 2000 ed.): Paulo Ribenboim My Numbers, My Friends - Popular Lectures on Number Theory (Paperback, 2000 ed.)
Paulo Ribenboim
R1,517 Discovery Miles 15 170 Ships in 10 - 15 working days

This is a selection of expository essays by Paulo Ribenboim, the author of such popular titles as "The New Book of Prime Number Records" and "The Little Book of Big Primes". The book contains essays on Fibonacci numbers, prime numbers, Bernoulli numbers, and historical presentations of the main problems pertaining to elementary number theory, such as for instance Kummer's work on Fermat's Last Theorem. The essays are written in a light and humorous language without secrets and are thoroughly accessible to everyone with an interest in numbers.

The Little Book of Bigger Primes (Paperback, 2nd ed. 2004): Paulo Ribenboim The Little Book of Bigger Primes (Paperback, 2nd ed. 2004)
Paulo Ribenboim
R1,614 Discovery Miles 16 140 Ships in 10 - 15 working days

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 Polya 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 - Geheimnisse und Rekorde (German, Paperback, 2. Aufl. 2011): Paulo Ribenboim Die Welt der Primzahlen - Geheimnisse und Rekorde (German, Paperback, 2. Aufl. 2011)
Paulo Ribenboim; As told to Wilfrid Keller; Translated by Joerg Richstein
R1,144 Discovery Miles 11 440 Ships in 10 - 15 working days

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.

Meine Zahlen, meine Freunde - Glanzlichter der Zahlentheorie (German, Paperback, 2009 ed.): Joerg Richstein Meine Zahlen, meine Freunde - Glanzlichter der Zahlentheorie (German, Paperback, 2009 ed.)
Joerg Richstein; Paulo Ribenboim
R1,141 Discovery Miles 11 410 Ships in 10 - 15 working days

Paulo Ribenboim behandelt Zahlen in dieser aussergewohnlichen Sammlung von Ubersichtsartikeln wie seine personlichen Freunde. In leichter und allgemein zuganglicher Sprache berichtet er uber Primzahlen, Fibonacci-Zahlen (und das Nordpolarmeer ), die klassischen Arbeiten von Gauss uber binare quadratische Formen, Eulers beruhmtes 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."

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