Ribenboim, Paulo
Overview
Works:  146 works in 682 publications in 6 languages and 12,813 library holdings 

Genres:  Conference papers and proceedings 
Roles:  Author, Editor, Other 
Publication Timeline
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Most widely held works by
Paulo Ribenboim
The book of prime number records by
Paulo Ribenboim(
Book
)
30 editions published between 1988 and 2012 in English and held by 995 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
30 editions published between 1988 and 2012 in English and held by 995 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
)
29 editions published between 1979 and 1996 in 3 languages and held by 744 WorldCat member libraries worldwide
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
29 editions published between 1979 and 1996 in 3 languages and held by 744 WorldCat member libraries worldwide
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 by
Paulo Ribenboim(
Book
)
30 editions published between 2000 and 2009 in 3 languages and held by 731 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
30 editions published between 2000 and 2009 in 3 languages and held by 731 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(
Book
)
29 editions published between 1899 and 2005 in English and Polish and held by 628 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." "The Epilogue is a serious attempt to render accessible the strategy of the recent proof of Fermat's last theorem, a great mathematical feat."Jacket
29 editions published between 1899 and 2005 in English and Polish and held by 628 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." "The Epilogue is a serious attempt to render accessible the strategy of the recent proof of Fermat's last theorem, a great mathematical feat."Jacket
Algebraic numbers by
Paulo Ribenboim(
Book
)
17 editions published in 1972 in English and held by 558 WorldCat member libraries worldwide
17 editions published in 1972 in English and held by 558 WorldCat member libraries worldwide
The little book of big primes by
Paulo Ribenboim(
Book
)
20 editions published between 1991 and 2001 in English and Japanese and held by 532 WorldCat member libraries worldwide
This book could have been called "Selections from the Book of Prime Number Records." However, I prefered the title which propelled you on the first place to open it, and perhaps (so I hope) to buy it! Richard K. Guy, with his winning ways, suggested the title to me, and I am grateful. But the book isn't very different from its parent. Like a bonsai, which has all the main characteristics of the fullsized tree, this little paperback should exert the same fatal attraction. I wish it to be as dangerous as the other one, in the saying of John Brillhart. I wish that you, young student, teacher or retired mathematician, engineer, computer buff, all of you who are friends of numbers, to be driven into thinking about the beautiful theory of prime numbers, with its inherent mystery. I wish you to exercise your brain and fingersnot viceversa. But I do not wish you, specialist in number theory to look at this little bookmost likely you have been eliminated from this shorter versionwhat a terrible feeling. But do not cry, you had your book already. This one is for those who will be taking over and should put their steps forward, mostly little, occasionally giant, to develop the science of numbers. Paulo Ribenboim Contents Preface vii Guiding the Reader xii Index of Notations xiii Introduction 1 1 How Many Prime Numbers Are There? 3 I. Euclid's Proof . 3 11. Kummer's Proof 4 II. P6lya's Proof
20 editions published between 1991 and 2001 in English and Japanese and held by 532 WorldCat member libraries worldwide
This book could have been called "Selections from the Book of Prime Number Records." However, I prefered the title which propelled you on the first place to open it, and perhaps (so I hope) to buy it! Richard K. Guy, with his winning ways, suggested the title to me, and I am grateful. But the book isn't very different from its parent. Like a bonsai, which has all the main characteristics of the fullsized tree, this little paperback should exert the same fatal attraction. I wish it to be as dangerous as the other one, in the saying of John Brillhart. I wish that you, young student, teacher or retired mathematician, engineer, computer buff, all of you who are friends of numbers, to be driven into thinking about the beautiful theory of prime numbers, with its inherent mystery. I wish you to exercise your brain and fingersnot viceversa. But I do not wish you, specialist in number theory to look at this little bookmost likely you have been eliminated from this shorter versionwhat a terrible feeling. But do not cry, you had your book already. This one is for those who will be taking over and should put their steps forward, mostly little, occasionally giant, to develop the science of numbers. Paulo Ribenboim Contents Preface vii Guiding the Reader xii Index of Notations xiii Introduction 1 1 How Many Prime Numbers Are There? 3 I. Euclid's Proof . 3 11. Kummer's Proof 4 II. P6lya's Proof
Rings and modules by
Paulo Ribenboim(
Book
)
14 editions published in 1969 in English and Undetermined and held by 527 WorldCat member libraries worldwide
14 editions published in 1969 in English and Undetermined and held by 527 WorldCat member libraries worldwide
The little book of bigger primes by
Paulo Ribenboim(
Book
)
32 editions published between 2003 and 2011 in 3 languages and held by 427 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."Jacket
32 editions published between 2003 and 2011 in 3 languages and held by 427 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."Jacket
The new book of prime number records by
Paulo Ribenboim(
Book
)
22 editions published between 1995 and 2012 in English and German and held by 420 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
22 editions published between 1995 and 2012 in English and German and held by 420 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
Catalan's conjecture : are 8 and 9 the only consecutive powers? by
Paulo Ribenboim(
Book
)
12 editions published in 1994 in English and French and held by 391 WorldCat member libraries worldwide
12 editions published in 1994 in English and French and held by 391 WorldCat member libraries worldwide
Functions, limits, and continuity by
Paulo Ribenboim(
Book
)
8 editions published in 1964 in English and held by 385 WorldCat member libraries worldwide
8 editions published in 1964 in English and held by 385 WorldCat member libraries worldwide
Classical theory of algebraic numbers by
Paulo Ribenboim(
Book
)
18 editions published between 2000 and 2010 in English and Undetermined and held by 347 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
18 editions published between 2000 and 2010 in English and Undetermined and held by 347 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
)
13 editions published between 1998 and 1999 in English and held by 293 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
13 editions published between 1998 and 1999 in English and held by 293 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
)
32 editions published between 1964 and 1972 in 3 languages and held by 281 WorldCat member libraries worldwide
32 editions published between 1964 and 1972 in 3 languages and held by 281 WorldCat member libraries worldwide
L'arithmétique des corps by
Paulo Ribenboim(
Book
)
14 editions published in 1972 in French and held by 238 WorldCat member libraries worldwide
14 editions published in 1972 in French and held by 238 WorldCat member libraries worldwide
The RiemannRoch theorem for algebraic curves by
Paulo Ribenboim(
Book
)
9 editions published in 1965 in English and Undetermined and held by 225 WorldCat member libraries worldwide
9 editions published in 1965 in English and Undetermined and held by 225 WorldCat member libraries worldwide
Linear representation of finite groups by
Paulo Ribenboim(
Book
)
9 editions published in 1966 in English and held by 221 WorldCat member libraries worldwide
9 editions published in 1966 in English and held by 221 WorldCat member libraries worldwide
Proceedings of the Queen's Number Theory Conference, 1979 by Queen's Number Theory Conference(
Book
)
7 editions published in 1980 in English and Undetermined and held by 171 WorldCat member libraries worldwide
7 editions published in 1980 in English and Undetermined and held by 171 WorldCat member libraries worldwide
La conjecture d'Artin aur les équations diophantiennes by
Paulo Ribenboim(
Book
)
3 editions published in 1968 in French and held by 148 WorldCat member libraries worldwide
3 editions published in 1968 in French and held by 148 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 139 WorldCat member libraries worldwide
9 editions published between 1990 and 1992 in English and held by 139 WorldCat member libraries worldwide
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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 Other Editor
 Inkeri, Kustaa 1908 Author
 Suzuki, Satoshi 19301991 Author
 Nagell, Trygve 18951988 Author
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Associated Subjects
Abelian groups Algebra 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) Ktheory Mathematical analysis Mathematics Modules (Algebra) Numbers, Prime Number theory Representations of groups RiemannRoch theorems Rings (Algebra) Valuation theory
Alternative Names
Paulo Ribenboim brasilianischer Mathematiker
Paulo Ribenboim brasiliansk matematikar
Paulo Ribenboim brasiliansk matematiker
Paulo Ribenboim Brazilian mathematician
Paulo Ribenboim matemático brasileño
Paulo Ribenboim wiskundige uit Brazilië
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
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