WorldCat Identities

Ribenboim, Paulo

Overview
Works: 134 works in 563 publications in 4 languages and 12,265 library holdings
Genres: Conference proceedings 
Roles: Author, Editor
Classifications: QA246, 512.74
Publication Timeline
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Most widely held works by Paulo Ribenboim
The little book of big primes by Paulo Ribenboim( )

48 editions published between 1991 and 2011 in 3 languages and held by 1,537 WorldCat member libraries worldwide

"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."--BOOK JACKET
My numbers, my friends : popular lectures on number theory by Paulo Ribenboim( Book )

19 editions published between 2000 and 2005 in English and held by 1,199 WorldCat member libraries worldwide

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
Fermat's last theorem for amateurs by Paulo Ribenboim( )

26 editions published between 1899 and 2013 in English and held by 1,180 WorldCat member libraries worldwide

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
The book of prime number records by Paulo Ribenboim( Book )

24 editions published between 1988 and 1989 in English and held by 1,025 WorldCat member libraries worldwide

This book aims to be the analogue for prime numbers of the Guinness Book of World Records. It collects a large number of results and techniques related to all aspects of the theory of prime numbers. The book begins with a chapter on the proofs that there are infinitely many primes, and proceeds through such topics as primality tests, factorization methods, the distribution of primes, special types of primes, and heuristic results. The Book of Prime Number Records should have great appeal to anyone with an interest in number theory
13 lectures on Fermat's last theorem by Paulo Ribenboim( Book )

23 editions published between 1979 and 1996 in English and Undetermined and held by 752 WorldCat member libraries worldwide

Algebraic numbers by Paulo Ribenboim( Book )

13 editions published in 1972 in English and held by 556 WorldCat member libraries worldwide

Rings and modules by Paulo Ribenboim( Book )

10 editions published in 1969 in English and Undetermined and held by 535 WorldCat member libraries worldwide

The new book of prime number records by Paulo Ribenboim( Book )

16 editions published between 1995 and 2012 in English and German and held by 421 WorldCat member libraries worldwide

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 is thoroughly accessible to everyone with some mathematical education. This new book has an improved and smoother presentation
Functions, limits, and continuity by Paulo Ribenboim( Book )

8 editions published in 1964 in English and Undetermined and held by 405 WorldCat member libraries worldwide

Catalan's conjecture : are 8 and 9 the only consecutive powers? by Paulo Ribenboim( Book )

10 editions published in 1994 in English and held by 394 WorldCat member libraries worldwide

Classical theory of algebraic numbers by Paulo Ribenboim( Book )

14 editions published between 2000 and 2010 in English and held by 342 WorldCat member libraries worldwide

Gauss created the theory of binary quadratic forms in "Disquisitiones Arithmeticae" and Kummer invented ideals and the theory of cyclotomic fields in his attempt to prove Fermat's Last Theorem. These were the starting points for the theory of algebraic numbers, developed in the classical papers of Dedekind, Dirichlet, Eisenstein, Hermite and many others. This theory, enriched with more recent contributions, is of basic importance in the study of diophantine equations and arithmetic algebraic geometry, including methods in cryptography. 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 Kummer's theory of cyclomatic fields, and includes Bernoulli numbers and the proof of Fermat's Last Theorem for regular prime exponents. Finally, in Part Four, the emphasis is on analytical methods and it includes Dinchlet's 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
The theory of classical valuations by Paulo Ribenboim( Book )

12 editions published between 1998 and 2012 in English and held by 299 WorldCat member libraries worldwide

"In the second half of the last century, Kummer introduced "local" methods in his study of Fermat's last theorem. Hensel constructed the p-adic numbers and proved the so-called "Hensel lemma." Kurschak formally introduced the concept of a valuation of a field, and Ostrowski, Hasse, Schmidt, Krull, and others developed the theory. These classical valuations play a central cental role in the study of number fields and algebraic functions of one variable." "The present book is one of the first texts in English devoted to the beautiful theory of classical valuations. The book is self-contained and up-to-date, and proofs are given in full detail. Thus, it will be an invaluable resource for graduate students and research mathematicians."--Jacket
Théorie des valuations by Paulo Ribenboim( Book )

24 editions published between 1964 and 1972 in 3 languages and held by 265 WorldCat member libraries worldwide

L'arithmétique des corps by Paulo Ribenboim( Book )

11 editions published in 1972 in French and held by 230 WorldCat member libraries worldwide

The Riemann-Roch theorem for algebraic curves by Paulo Ribenboim( Book )

6 editions published in 1965 in English and held by 219 WorldCat member libraries worldwide

Linear representation of finite groups by Paulo Ribenboim( Book )

7 editions published in 1966 in English and held by 218 WorldCat member libraries worldwide

La conjecture d'Artin aur les équations diophantiennes by Paulo Ribenboim( Book )

12 editions published in 1968 in French and English and held by 200 WorldCat member libraries worldwide

Proceedings of the Queen's Number Theory Conference, 1979 by Queen's Number Theory Conference( Book )

3 editions published in 1980 in English and held by 165 WorldCat member libraries worldwide

Collected papers of Karl Egil Aubert by Karl Egil Aubert( Book )

9 editions published between 1990 and 1992 in English and held by 140 WorldCat member libraries worldwide

Meine Zahlen, meine Freunde Glanzlichter der Zahlentheorie by Paulo Ribenboim( )

5 editions published in 2009 in German and held by 137 WorldCat member libraries worldwide

 
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Audience Level
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Audience Level
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  Kids General Special  
Audience level: 0.65 (from 0.50 for Fermat's l ... to 0.95 for Proceeding ...)

Alternative Names
Ribenboim, P.

Ribenboim, P. 1928-

Ribenboim, P. (Paulo)

Ribenboim, Paulo

Ribenboin, Paulo

Ribenboin Paulo 1928-....

リーベンボイム, パウロ

Languages
English (230)

French (42)

German (19)

Japanese (4)

Covers
My numbers, my friends : popular lectures on number theoryFermat's last theorem for amateurs13 lectures on Fermat's last theoremThe new book of prime number recordsCatalan's conjecture : are 8 and 9 the only consecutive powers?Classical theory of algebraic numbersThe theory of classical valuationsMeine Zahlen, meine Freunde Glanzlichter der Zahlentheorie