Halmos, Paul R. (Paul Richard) 19162006
Overview
Works:  192 works in 1,025 publications in 11 languages and 20,831 library holdings 

Genres:  Biography Pictorial works History Portraits Interviews Filmed interviews Biographical films Nonfiction films Documentary films Biographies 
Roles:  Author, Editor, Honoree, Author of introduction, Dedicatee, Other 
Classifications:  QA248, 512.86 
Publication Timeline
.
Most widely held works about
Paul R Halmos
 I want to be a mathematician : an automathography by Paul R Halmos( Book )
 I want to be a mathematician : an automathography in three parts by Paul R Halmos( Book )
 A glimpse at Hilbert space operators : Paul R. Halmos in memoriam by Sheldon Jay Axler( Book )
 Selecta by Paul R Halmos( Book )
 John Von Neumann and Klara Dan Von Neumann papers by John Von Neumann( )
 Mathematical writing (CS 209) : by Donald Ervin Knuth( )
 Halmos, Paul Richard : pure mathematics( )
 Halmos, Paul R., Documentary Film Source Materials collection by Paul R Halmos( )
 Halmos, Paul R. photograph collection by Paul R Halmos( )
 Mathematical Association of America records by Mathematical Association of America( )
 Halmos, Paul Richard, papers by Paul R Halmos( )
 Many thanks by William McGowen Priestley( Book )
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fewer
Most widely held works by
Paul R Halmos
Naive set theory by
Paul R Halmos(
Book
)
123 editions published between 1960 and 2013 in 9 languages and held by 2,155 WorldCat member libraries worldwide
Every mathematician agrees that every mathematician must know some set theory; the disagreement begins in trying to decide how much is some. This book contains my answer to that question. The purpose of the book is to tell the beginning student of advanced mathematics the basic set theoretic facts of life, and to do so with the minimum of philosophical discourse and logical formalism. The point of view throughout is that of a prospective mathematician anxious to study groups, or integrals, or manifolds. From this point of view the concepts and methods of this book are merely some of the standard mathematical tools; the expert specialist will find nothing new here. Scholarly bibliographical credits and references are out of place in a purely expository book such as this one. The student who gets interested in set theory for its own sake should know, however, that there is much more to the subject than there is in this book. One of the most beautiful sources of settheoretic wisdom is still Hausdorff's Set theory. A recent and highly readable addition to the literature, with an extensive and uptodate bibliography, is Axiomatic set theory by Suppes
123 editions published between 1960 and 2013 in 9 languages and held by 2,155 WorldCat member libraries worldwide
Every mathematician agrees that every mathematician must know some set theory; the disagreement begins in trying to decide how much is some. This book contains my answer to that question. The purpose of the book is to tell the beginning student of advanced mathematics the basic set theoretic facts of life, and to do so with the minimum of philosophical discourse and logical formalism. The point of view throughout is that of a prospective mathematician anxious to study groups, or integrals, or manifolds. From this point of view the concepts and methods of this book are merely some of the standard mathematical tools; the expert specialist will find nothing new here. Scholarly bibliographical credits and references are out of place in a purely expository book such as this one. The student who gets interested in set theory for its own sake should know, however, that there is much more to the subject than there is in this book. One of the most beautiful sources of settheoretic wisdom is still Hausdorff's Set theory. A recent and highly readable addition to the literature, with an extensive and uptodate bibliography, is Axiomatic set theory by Suppes
Finitedimensional vector spaces by
Paul R Halmos(
Book
)
113 editions published between 1942 and 2012 in 6 languages and held by 2,152 WorldCat member libraries worldwide
"The theory is systematically developed by the axiomatic method that has, since von Neumann, dominated the general approach to linear functional analysis and that achieves here a high degree of lucidity and clarity. The presentation is never awkward or dry, as it sometimes is in other "modern" textbooks; it is as unconventional as one has come to expect from the author. The book contains about 350 well placed and instructive problems, which cover a considerable part of the subject. All in all this is an excellent work, of equally high value for both student and teacher." <EM>Zentralblatt f.r Mathematik</EM>
113 editions published between 1942 and 2012 in 6 languages and held by 2,152 WorldCat member libraries worldwide
"The theory is systematically developed by the axiomatic method that has, since von Neumann, dominated the general approach to linear functional analysis and that achieves here a high degree of lucidity and clarity. The presentation is never awkward or dry, as it sometimes is in other "modern" textbooks; it is as unconventional as one has come to expect from the author. The book contains about 350 well placed and instructive problems, which cover a considerable part of the subject. All in all this is an excellent work, of equally high value for both student and teacher." <EM>Zentralblatt f.r Mathematik</EM>
Measure theory by
Paul R Halmos(
Book
)
109 editions published between 1950 and 2014 in 3 languages and held by 1,786 WorldCat member libraries worldwide
Useful both as a text for students and as a source of reference for the more advanced mathematician, this book presents a unified treatment of that part of measure theory which is most useful for its application in modern analysis. Topics studied include sets and classes, measures and outer measures, measurable functions, integration, general set functions, product spaces, transformations, probability, locally compact spaces, Haar measure and measure and topology in groups. The text is suitable for the beginning graduate student as well as the advanced undergraduate
109 editions published between 1950 and 2014 in 3 languages and held by 1,786 WorldCat member libraries worldwide
Useful both as a text for students and as a source of reference for the more advanced mathematician, this book presents a unified treatment of that part of measure theory which is most useful for its application in modern analysis. Topics studied include sets and classes, measures and outer measures, measurable functions, integration, general set functions, product spaces, transformations, probability, locally compact spaces, Haar measure and measure and topology in groups. The text is suitable for the beginning graduate student as well as the advanced undergraduate
A Hilbert space problem book by
Paul R Halmos(
Book
)
66 editions published between 1967 and 2012 in 3 languages and held by 1,437 WorldCat member libraries worldwide
From the Preface: "This book was written for the active reader. The first part consists of problems, frequently preceded by definitions and motivation, and sometimes followed by corollaries and historical remarks ... The second part, a very short one, consists of hints ... The third part, the longest, consists of solutions: proofs, answers, or contructions, depending on the nature of the problem ... This is not an introduction to Hilbert space theory. Some knowledge of that subject is a prerequisite: at the very least, a study of the elements of Hilbert space theory should proceed concurrently with the reading of this book."
66 editions published between 1967 and 2012 in 3 languages and held by 1,437 WorldCat member libraries worldwide
From the Preface: "This book was written for the active reader. The first part consists of problems, frequently preceded by definitions and motivation, and sometimes followed by corollaries and historical remarks ... The second part, a very short one, consists of hints ... The third part, the longest, consists of solutions: proofs, answers, or contructions, depending on the nature of the problem ... This is not an introduction to Hilbert space theory. Some knowledge of that subject is a prerequisite: at the very least, a study of the elements of Hilbert space theory should proceed concurrently with the reading of this book."
Introduction to Hilbert space and the theory of spectral multiplicity by
Paul R Halmos(
Book
)
45 editions published between 1951 and 2013 in English and Undetermined and held by 1,186 WorldCat member libraries worldwide
45 editions published between 1951 and 2013 in English and Undetermined and held by 1,186 WorldCat member libraries worldwide
Problems for mathematicians, young and old by
Paul R Halmos(
Book
)
15 editions published between 1991 and 2000 in English and French and held by 1,061 WorldCat member libraries worldwide
15 editions published between 1991 and 2000 in English and French and held by 1,061 WorldCat member libraries worldwide
Linear algebra problem book by
Paul R Halmos(
Book
)
24 editions published between 1994 and 2013 in 3 languages and held by 1,058 WorldCat member libraries worldwide
Can one learn linear algebra solely by solving problems? Paul Halmos thinks so, and you will too once you read this book. The Linear Algebra Problem Book is an ideal text for a course in linear algebra. It takes the student step by step from the basic axioms of a field through the notion of vector spaces, on to advanced concepts such as inner product spaces and normality. All of this occurs by way of a series of 164 problems, each with hints and, at the back of the book, full solutions. This book is a marvelous example of how to teach and learn mathematics by 'doing' mathematics. It will work well for classes taught in small groups and can also be used for selfstudy. After working their way through the book, students will understand not only the theorems of linear algebra, but also some of the questions which were asked which enabled the theorems to be discovered in the first place. They will gain confidence in their problem solving abilities and be better prepared to understand more advanced courses. As the author explains, 'I don't think I understand a subject until I know the questions ... I wrote this book to organize those questions, problems, in my own mind.' Try this book with your students and they too will be able to organize and understand the questions of linear algebra.  Publisher
24 editions published between 1994 and 2013 in 3 languages and held by 1,058 WorldCat member libraries worldwide
Can one learn linear algebra solely by solving problems? Paul Halmos thinks so, and you will too once you read this book. The Linear Algebra Problem Book is an ideal text for a course in linear algebra. It takes the student step by step from the basic axioms of a field through the notion of vector spaces, on to advanced concepts such as inner product spaces and normality. All of this occurs by way of a series of 164 problems, each with hints and, at the back of the book, full solutions. This book is a marvelous example of how to teach and learn mathematics by 'doing' mathematics. It will work well for classes taught in small groups and can also be used for selfstudy. After working their way through the book, students will understand not only the theorems of linear algebra, but also some of the questions which were asked which enabled the theorems to be discovered in the first place. They will gain confidence in their problem solving abilities and be better prepared to understand more advanced courses. As the author explains, 'I don't think I understand a subject until I know the questions ... I wrote this book to organize those questions, problems, in my own mind.' Try this book with your students and they too will be able to organize and understand the questions of linear algebra.  Publisher
Selecta : expository writing by
Paul R Halmos(
Book
)
33 editions published between 1982 and 1983 in English and Undetermined and held by 912 WorldCat member libraries worldwide
33 editions published between 1982 and 1983 in English and Undetermined and held by 912 WorldCat member libraries worldwide
Lectures on Boolean algebras by
Paul R Halmos(
Book
)
44 editions published between 1963 and 2013 in 3 languages and held by 892 WorldCat member libraries worldwide
44 editions published between 1963 and 2013 in 3 languages and held by 892 WorldCat member libraries worldwide
Algebraic logic by
Paul R Halmos(
Book
)
19 editions published between 1962 and 2016 in English and Undetermined and held by 775 WorldCat member libraries worldwide
This book addresses some of the problems of mathematical logic and the theory of polyadic Boolean algebras in particular. It is intended to be an efficient way of treating algebraic logic in a unified manner
19 editions published between 1962 and 2016 in English and Undetermined and held by 775 WorldCat member libraries worldwide
This book addresses some of the problems of mathematical logic and the theory of polyadic Boolean algebras in particular. It is intended to be an efficient way of treating algebraic logic in a unified manner
Lectures on ergodic theory by
Paul R Halmos(
Book
)
31 editions published between 1956 and 2013 in 4 languages and held by 745 WorldCat member libraries worldwide
31 editions published between 1956 and 2013 in 4 languages and held by 745 WorldCat member libraries worldwide
Logic as algebra by
Paul R Halmos(
Book
)
13 editions published between 1998 and 2008 in English and held by 612 WorldCat member libraries worldwide
Publisher Description (unedited publisher data) Here is an introduction to modern logic that differs from others by treating logic from an algebraic perspective. What this means is that notions and results from logic become much easier to understand when seen from a familiar standpoint of algebra. The presentation, written in the engaging and provocative style that is the hallmark of Paul Halmos, from whose course the book is taken, is aimed at a broad audience, students, teachers and amateurs in mathematics, philosophy, computer science, linguistics and engineering; they all have to get to grips with logic at some stage. All that is needed to understand the book is some basic acquaintance with algebra. Library of Congress subject headings for this publication: Logic, Symbolic and mathematical
13 editions published between 1998 and 2008 in English and held by 612 WorldCat member libraries worldwide
Publisher Description (unedited publisher data) Here is an introduction to modern logic that differs from others by treating logic from an algebraic perspective. What this means is that notions and results from logic become much easier to understand when seen from a familiar standpoint of algebra. The presentation, written in the engaging and provocative style that is the hallmark of Paul Halmos, from whose course the book is taken, is aimed at a broad audience, students, teachers and amateurs in mathematics, philosophy, computer science, linguistics and engineering; they all have to get to grips with logic at some stage. All that is needed to understand the book is some basic acquaintance with algebra. Library of Congress subject headings for this publication: Logic, Symbolic and mathematical
Problem book for first year calculus by
George W Bluman(
Book
)
4 editions published in 1984 in English and held by 571 WorldCat member libraries worldwide
4 editions published in 1984 in English and held by 571 WorldCat member libraries worldwide
Bounded integral operators on L²spaces by
Paul R Halmos(
Book
)
29 editions published between 1978 and 2012 in 4 languages and held by 543 WorldCat member libraries worldwide
The subject. The phrase "integral operator" (like some other mathematically informal phrases, such as "effective procedure" and "geometric construction") is sometimes defined and sometimes not. When it is defined, the definition is likely to vary from author to author. While the definition almost always involves an integral, most of its other features can vary quite considerably. Superimposed limiting operations may enter (such as L2 limits in the theory of Fourier transforms and principal values in the theory of singular integrals), IJ' spaces and abstract Banach spaces may intervene, a scalar may be added (as in the theory of the socalled integral operators of the second kind), or, more generally, a multiplication operator may be added (as in the theory of the socalled integral operators of the third kind). The definition used in this book is the most special of all. According to it an integral operator is the natural "continuous" generali zation of the operators induced by matrices, and the only integrals that appear are the familiar LebesgueStieltjes integrals on classical nonpathological mea sure spaces. The category. Some of the flavor of the theory can be perceived in finite dimensional linear algebra. Matrices are sometimes considered to be an un natural and notationally inelegant way of looking at linear transformations. From the point of view of this book that judgement misses something
29 editions published between 1978 and 2012 in 4 languages and held by 543 WorldCat member libraries worldwide
The subject. The phrase "integral operator" (like some other mathematically informal phrases, such as "effective procedure" and "geometric construction") is sometimes defined and sometimes not. When it is defined, the definition is likely to vary from author to author. While the definition almost always involves an integral, most of its other features can vary quite considerably. Superimposed limiting operations may enter (such as L2 limits in the theory of Fourier transforms and principal values in the theory of singular integrals), IJ' spaces and abstract Banach spaces may intervene, a scalar may be added (as in the theory of the socalled integral operators of the second kind), or, more generally, a multiplication operator may be added (as in the theory of the socalled integral operators of the third kind). The definition used in this book is the most special of all. According to it an integral operator is the natural "continuous" generali zation of the operators induced by matrices, and the only integrals that appear are the familiar LebesgueStieltjes integrals on classical nonpathological mea sure spaces. The category. Some of the flavor of the theory can be perceived in finite dimensional linear algebra. Matrices are sometimes considered to be an un natural and notationally inelegant way of looking at linear transformations. From the point of view of this book that judgement misses something
I have a photographic memory by
Paul R Halmos(
Book
)
14 editions published in 1987 in English and Undetermined and held by 481 WorldCat member libraries worldwide
14 editions published in 1987 in English and Undetermined and held by 481 WorldCat member libraries worldwide
Paul Halmos celebrating 50 years of mathematics by
John H Ewing(
Book
)
9 editions published in 1991 in English and Undetermined and held by 321 WorldCat member libraries worldwide
Paul Halmos will celebrate his 75th birthday on the 3rd of March 1991. This volume, from colleagues, is an expression of affection for the man and respect for his contributions as scholar, writer, and teacher. It contains articles about Paul, about the times in which he worked and the places he has been, and about mathematics. Paul has furthered his profession in many ways and this collection reflects that diversity. Articles about Paul are not biographical, but rather tell about his ideas, his philosophy, and his style. Articles about the times and places in which Paul has worked describe people, events, and ways in which Paul has influenced students and colleagues over the past 50 years. Articles about mathematics are about all kinds of mathematics, including operator theory and Paul's research in the subject. This volume represents a slice of mathematical life and it shows how many parts of mathematics Paul has touched. It is fitting that this volume has been produced with the support and cooperation of SpringerVerlag. For over 35 years, Paul has contributed to mathematics publishing as founder and editor of many outstanding series
9 editions published in 1991 in English and Undetermined and held by 321 WorldCat member libraries worldwide
Paul Halmos will celebrate his 75th birthday on the 3rd of March 1991. This volume, from colleagues, is an expression of affection for the man and respect for his contributions as scholar, writer, and teacher. It contains articles about Paul, about the times in which he worked and the places he has been, and about mathematics. Paul has furthered his profession in many ways and this collection reflects that diversity. Articles about Paul are not biographical, but rather tell about his ideas, his philosophy, and his style. Articles about the times and places in which Paul has worked describe people, events, and ways in which Paul has influenced students and colleagues over the past 50 years. Articles about mathematics are about all kinds of mathematics, including operator theory and Paul's research in the subject. This volume represents a slice of mathematical life and it shows how many parts of mathematics Paul has touched. It is fitting that this volume has been produced with the support and cooperation of SpringerVerlag. For over 35 years, Paul has contributed to mathematics publishing as founder and editor of many outstanding series
Introduction to boolean algebras by
Steven R Givant(
Book
)
15 editions published between 2008 and 2009 in English and held by 286 WorldCat member libraries worldwide
"In a bold and refreshingly informal style, this exciting text steers a middle course between elementary texts emphasizing connections with philosophy, logic, and electronic circuit design, and profound treatises aimed at advanced graduate students and professional mathematicians. It is written for readers who have studied at least two years of collegelevel mathematics. With carefully crafted prose, lucid explanations, and illuminating insights, it guides students to some of the deeper results of Boolean algebraand in particular to the important interconnections with topologywithout assuming a background in algebra, topology, and set theory. The parts of those subjects that are needed to understand the material are developed within the text itself." "Highlights of the book include the normal form theorem; the homomorphism extension theorem; the isomorphism theorem for countable atomless Boolean algebras; the maximal ideal theorem; the celebrated Stone representation theorem; the existence and uniqueness theorems for canonical extensions and completions; Tarski's isomorphism of factors theorem for (J'algebras, and Hanf's related counterexamples; and an extensive treatment of the algebraictopological duality, including the duality between ideals and open sets, homomorphisms and continuous functions, subalgebras and quotient spaces, and direct products and StoneCech compactifications." "A special feature of the book is the large number of exercises of varying levels of difficulty, from routine problems that help readers understand the basic definitions and theorems, to intermediate problems that extend or enrich material developed in the text, to harder problems that explore important ideas either not treated in the text, or that go substantially beyond its treatment. Hints for the solutions to the harder problems are given in an appendix. A detailed solutions manual for all exercises is available for instructors who adopt the text for a course."Jacket
15 editions published between 2008 and 2009 in English and held by 286 WorldCat member libraries worldwide
"In a bold and refreshingly informal style, this exciting text steers a middle course between elementary texts emphasizing connections with philosophy, logic, and electronic circuit design, and profound treatises aimed at advanced graduate students and professional mathematicians. It is written for readers who have studied at least two years of collegelevel mathematics. With carefully crafted prose, lucid explanations, and illuminating insights, it guides students to some of the deeper results of Boolean algebraand in particular to the important interconnections with topologywithout assuming a background in algebra, topology, and set theory. The parts of those subjects that are needed to understand the material are developed within the text itself." "Highlights of the book include the normal form theorem; the homomorphism extension theorem; the isomorphism theorem for countable atomless Boolean algebras; the maximal ideal theorem; the celebrated Stone representation theorem; the existence and uniqueness theorems for canonical extensions and completions; Tarski's isomorphism of factors theorem for (J'algebras, and Hanf's related counterexamples; and an extensive treatment of the algebraictopological duality, including the duality between ideals and open sets, homomorphisms and continuous functions, subalgebras and quotient spaces, and direct products and StoneCech compactifications." "A special feature of the book is the large number of exercises of varying levels of difficulty, from routine problems that help readers understand the basic definitions and theorems, to intermediate problems that extend or enrich material developed in the text, to harder problems that explore important ideas either not treated in the text, or that go substantially beyond its treatment. Hints for the solutions to the harder problems are given in an appendix. A detailed solutions manual for all exercises is available for instructors who adopt the text for a course."Jacket
Entropy in ergodic theory by
Paul R Halmos(
Book
)
8 editions published between 1955 and 1959 in English and Undetermined and held by 95 WorldCat member libraries worldwide
8 editions published between 1955 and 1959 in English and Undetermined and held by 95 WorldCat member libraries worldwide
Boolean algebras by
Paul R Halmos(
Book
)
16 editions published between 1959 and 1981 in English and Undetermined and held by 95 WorldCat member libraries worldwide
16 editions published between 1959 and 1981 in English and Undetermined and held by 95 WorldCat member libraries worldwide
I want to be a mathematician a conversation with Paul Halmos(
Visual
)
4 editions published in 2009 in English and held by 93 WorldCat member libraries worldwide
In this interview, Paul Halmos, talks about his thoughts on mathematics, how to teach mathematics and also how to write about it
4 editions published in 2009 in English and held by 93 WorldCat member libraries worldwide
In this interview, Paul Halmos, talks about his thoughts on mathematics, how to teach mathematics and also how to write about it
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Audience Level
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Related Identities
 Sarason, Donald Other Editor
 Givant, Steven R. Author
 Bluman, George W. 1943 Author
 Gillman, Leonard Editor
 Sunder, V. S.
 Gehring, Frederick W. Author Editor
 Axler, Sheldon Jay Editor
 Rosenthal, Peter 1941 Editor
 Friedman, Nathaniel A. Other Editor
 Ewing, John H. Author Editor
Useful Links
Associated Subjects
Aldor, Eva Algebra Algebra, Abstract Algebra, Boolean Algebraic logic Algebras, Linear American Mathematical Society ArithmeticFoundations Axiomatic set theory Ballistics Calculus Canada Chandrasekhar, S.(Subrahmanyan), Dan family Education Entropy Ergodic theory Generalized spaces Halmos, Paul R.(Paul Richard), Hilbert space Hyperspace Information theory Institute for Advanced Study (Princeton, N.J.) Integral operators Kent, R. H.(Robert Harrington), Logic, Symbolic and mathematical Los Alamos Scientific Laboratory Lp spaces Mathematical analysis Mathematical Association of America Mathematical models Mathematicians Mathematics MathematicsStudy and teaching Measure theory Newsom, Carroll V.(Carroll Vincent), Operator theory Porter, Gerald J Probabilities Set theory Spectral theory (Mathematics) Statistical mechanics Topological dynamics Topology Transformations (Mathematics) United States Vector analysis Vector spaces Von Neumann, John, Wiener, Norbert,
Alternative Names
Chalmoš, P. 19162006
Chalmoš, P. R. 19162006
Halmos
Halmoš, P.
Halmos, P. R.
Halmos P. R. 19162006
Halmos, P. R. (Paul Richard), 19162006
Halmos, Pál 19162006
Halmos Pál Amerikai magyar matematikus
Halmos, Paul.
Halmos, Paul 19162006
Halmos, Paul R.
Halmos Paul R. 19162006
Halmos, Paul R. (Paul Richard), 19162006
Halmos, Paul Richard
Halmos, Paul Richard 1916
Halmos, Paul Richard 19162006
HalmosSunder, ... 19162006
Halmosi Paul
Khalmos P. 19162006
Khalmosh, P.
Khalmosh, P. 19162006
Khalmosh, P. (Paul), 19162006
Pál Halmos
Paul Halmos Hongaars wiskundige (19162006)
Paul Halmos matematico e statistico ungherese
Paul Halmos USamerikanischer Mathematiker ungarischer Herkunft
Пол Річард Халмош
Халмош, П..
Халмош, П 19162006
Халмош, П. Р..
Халмош, Пауль.
Халмош, Пол Ричард
פול הלמוש
پل ریچارد هالموس
पॉल हॅलमॉस
헐모시 팔
保羅·哈爾莫斯
Languages
English
(651)
French (22)
Spanish (22)
Russian (19)
German (13)
Italian (4)
Chinese (2)
Dutch (2)
Ndonga (1)
Hungarian (1)
Multiple languages (1)
French (22)
Spanish (22)
Russian (19)
German (13)
Italian (4)
Chinese (2)
Dutch (2)
Ndonga (1)
Hungarian (1)
Multiple languages (1)
Covers