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
.
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
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
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 selfcontained. 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
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 selfcontained. 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
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
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
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
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 uptodate 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
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 uptodate 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
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
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
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 padic numbers and proved the socalled "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 selfcontained and uptodate, and proofs are given in full detail. Thus, it will be an invaluable resource for graduate students and research mathematicians."Jacket
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 padic numbers and proved the socalled "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 selfcontained and uptodate, 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
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
11 editions published in 1972 in French and held by 230 WorldCat member libraries worldwide
The RiemannRoch theorem for algebraic curves
by
Paulo Ribenboim(
Book
)
6 editions published in 1965 in English and held by 219 WorldCat member libraries worldwide
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
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
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
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
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
5 editions published in 2009 in German and held by 137 WorldCat member libraries worldwide
more
fewer
Audience Level
0 

1  
Kids  General  Special 
Related Identities
 Ciliberto, C. (Ciro) 1950 Editor
 Sernesi, E. (Edoardo) Editor
 Queen's University (Kingston, Ont.) Publisher
 Geramita, A. V. Author Editor
 Samuel, Pierre 1921 Author
 Aubert, Karl Egil Author
 Metsänkylä, Tauno Editor
 Inkeri, Kustaa 1908 Author
 Suzuki, Satoshi 19301991 Author
 Nagell, Trygve 18951988 Author
Useful Links
Associated Subjects
Abelian groups Algebra, Abstract Algebraic fields Algebraic functions Algebraic number theory Consecutive powers (Algebra) Differential algebra Diophantine analysis Fermat's last theorem Fermat's theorem Finite groups Galois theory Group theory Ideals (Algebra) Mathematical analysis Mathematics Modules (Algebra) Numbers, Prime Number theory Representations of groups RiemannRoch theorems Rings (Algebra) Valuation theory