WorldCat Identities

Halmos, Paul R. (Paul Richard) 1916-2006

Works: 321 works in 1,428 publications in 8 languages and 23,569 library holdings
Genres: Biography  Autobiographies  Pictorial works  History  Portraits  Illustrated works  Documentary films  Interviews  Filmed interviews  Biographical films 
Roles: Author, Editor, Honoree, Other, Author of introduction, Dedicatee
Classifications: QA248, 515.42
Publication Timeline
Most widely held works about Paul R Halmos
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Most widely held works by Paul R Halmos
Finite-dimensional vector spaces by Paul R Halmos( Book )

137 editions published between 1942 and 2017 in 6 languages and held by 2,480 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 and colorful 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, or equally high value for both student and teacher"--(Zentralblatt Für Mathematik) Back cover
Naive set theory by Paul R Halmos( Book )

111 editions published between 1960 and 2018 in 5 languages and held by 2,037 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 set-theoretic wisdom is still Hausdorff's Set theory. A recent and highly readable addition to the literature, with an extensive and up-to-date bibliography, is Axiomatic set theory by Suppes
Measure theory by Paul R Halmos( Book )

102 editions published between 1950 and 2014 in English and Undetermined and held by 1,849 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
Introduction to Hilbert space and the theory of spectral multiplicity by Paul R Halmos( Book )

60 editions published between 1951 and 2018 in English and Undetermined and held by 1,278 WorldCat member libraries worldwide

Concise introductory treatment consists of three chapters: The Geometry of Hilbert Space, The Algebra of Operators, and The Analysis of Spectral Measures. A background in measure theory is the sole prerequisite. 1957 edition
Linear algebra problem book by Paul R Halmos( Book )

18 editions published between 1994 and 2011 in 3 languages and held by 1,115 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 self-study. 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
Problems for mathematicians, young and old by Paul R Halmos( Book )

13 editions published in 1991 in English and Undetermined and held by 944 WorldCat member libraries worldwide

A collection of math problems for people of varying skills from high school through professional level, organized into fourteen categories such as matrices, space, probability, and puzzles, and including hints and solutions
A Hilbert space problem book by Paul R Halmos( Book )

37 editions published between 1967 and 2012 in English and Undetermined and held by 900 WorldCat member libraries worldwide

The purpose of this book is to use problems and their solutions to communicate to the reader many of the central techniques and ideas of Hilbert spaces. The first part consists of problems, frequently preceded by definitions and motivation, and sometimes followed by corollaries and historical remarks. Most of the problems are statements to be proved, but some are questions, and some are challenges. The second part, a very short one, consists of hints. The third part consists of solutions: proofs, answers, or constructions, depending on the nature of the problem. The solution may also introduce standard nomenclature, discuss the history of the subject, and mention pertinent references.--
Lectures on Boolean algebras by Paul R Halmos( Book )

34 editions published between 1963 and 2018 in English and Undetermined and held by 865 WorldCat member libraries worldwide

This presentation on the basics of Boolean algebra has ranked among the fundamental books on this important subject in mathematics and computing science since its initial publication in 1963. Concise and informal as well as systematic, the text draws upon lectures delivered by Professor Halmos at the University of Chicago to cover many topics in brief individual chapters. The approach is suitable for advanced undergraduates and graduate students in mathematics. Starting with Boolean rings and algebras, the treatment examines fields of sets, regular open sets, elementary relations, infinite operations, subalgebras, homomorphisms, free algebras, ideals and filters, and the homomorphism theorem. Additional topics include measure algebras, Boolean spaces, the representation theorem, duality for ideals and for homomorphisms, Boolean measure spaces, isomorphisms of factors, projective and injective algebras, and many other subjects. Several chapters conclude with stimulating exercises; the solutions are not included
Algebraic logic by Paul R Halmos( Book )

23 editions published between 1962 and 2016 in English and Undetermined and held by 828 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 )

29 editions published between 1956 and 2018 in English and Undetermined and held by 762 WorldCat member libraries worldwide

"This concise classic by a well-known master of mathematical exposition has served as a basic introduction to aspects of ergodic theory since its first publication in 1956. Topics include recurrence, ergodic theorems, ergodicity and mixing properties, and the relation between conjugacy and equivalence. "The material is organized very well and painlessly presented." -- Bulletin of the American Mathematical Society"--
Introduction to boolean algebras by Steven R Givant( )

18 editions published between 2008 and 2010 in English and held by 702 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 college-level mathematics. With carefully crafted prose, lucid explanations, and illuminating insights, it guides students to some of the deeper results of Boolean algebra-and in particular to the important interconnections with topology-without 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 Stone-Cech 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
A Hilbert space problem book by Paul R Halmos( Book )

42 editions published between 1967 and 2009 in 3 languages and held by 642 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."
Logic as algebra by Paul R Halmos( Book )

13 editions published between 1998 and 2008 in English and held by 607 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 606 WorldCat member libraries worldwide

Bounded integral operators on L²spaces by Paul R Halmos( Book )

14 editions published between 1978 and 1985 in 3 languages and held by 561 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 so-called integral operators of the second kind), or, more generally, a multiplication operator may be added (as in the theory of the so-called 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 Lebesgue-Stieltjes integrals on classical non-pathological 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
Selecta : expository writing by Paul R Halmos( Book )

14 editions published between 1982 and 1983 in English and Undetermined and held by 520 WorldCat member libraries worldwide

I have a photographic memory by Paul R Halmos( Book )

15 editions published between 1987 and 1988 in English and Undetermined and held by 474 WorldCat member libraries worldwide

Paul R. Halmos, eminent mathematician and brilliant expositor, is also a snapshot addict. Between 1943 and 1988, Halmos photographed mathematicians, their spouses, their brothers and sisters and other relatives, their offices, their dogs, and their carillon towers. From the 6000 or so photographs in his collection, Halmos has chosen about 600 for this book. The pictures are candid shots showing mathematicians just being themselves. The accompanying captions, in addition to identifying the subjects, contain anecdotes and bits of history that reveal Halmos's inimitable wit, charm, and insight. This delightful collection of mathematical memorabilia has become a favorite browsing book as well as a valuable historical record
Selecta : research contributions by Paul R Halmos( Book )

16 editions published between 1983 and 2014 in English and Undetermined and held by 367 WorldCat member libraries worldwide

Linear algebra problem book by Paul R Halmos( )

4 editions published between 1995 and 2013 in English and held by 362 WorldCat member libraries worldwide

Paul Halmos celebrating 50 years of mathematics by John H Ewing( Book )

10 editions published in 1991 in English and held by 333 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 Springer-Verlag. For over 35 years, Paul has contributed to mathematics publishing as founder and editor of many outstanding series
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Audience Level
Audience Level
  Kids General Special  
Audience level: 0.45 (from 0.20 for Linear alg ... to 0.99 for Halmos, Pa ...)

Measure theory
Naive set theoryMeasure theoryLinear algebra problem bookProblems for mathematicians, young and oldA Hilbert space problem bookLectures on ergodic theoryIntroduction to boolean algebrasA Hilbert space problem book
Alternative Names
Chalmoš, P. 1916-2006

Chalmoš, P. R. 1916-2006


Halmoš, P.

Halmos, P. R.

Halmos P. R. 1916-2006

Halmos, P. R. 1916- (Paul Richard)

Halmos, P. R. (Paul Richard), 1916-2006

Halmos, Pál 1916-2006

Halmos Pál Amerikai magyar matematikus

Halmos, Paul.

Halmos, Paul 1916-2006

Halmos, Paul (Paul Richard), 1916-2006

Halmos, Paul R.

Halmos Paul R. 1916-2006

Halmos, Paul R. (Paul Richard)

Halmos, Paul R. (Paul Richard), 1916-

Halmos, Paul R. (Paul Richard), 1916-2006

Halmos, Paul Richard

Halmos, Paul Richard 1916-

Halmos, Paul Richard 1916-2006

Halmos-Sunder, .. 1916-2006

Halmosi Paul

Khalmos P. 1916-2006

Khalmosh, P.

Khalmosh, P. 1916-2006

Khalmosh, P. 1916- (Paul)

Khalmosh, P. (Paul)

Khalmosh, P. (Paul), 1916-2006

Pál Halmos

Pál Halmos usona matematikisto

Paul Halmos Hongaars wiskundige (1916-2006)

Paul Halmos matemàtic estatunidenc

Paul Halmos matematico e statistico ungherese

Paul Halmos matemático estadounidense

Paul Halmos mathématicien américain

Paul Halmos US-amerikanischer Mathematiker ungarischer Herkunft

Пол Річард Халмош

Пол Річард Халмош американський математик угорського походження

Халмош, П..

Халмош, П 1916-2006

Халмош, П. Р..

Халмош, Пауль.

Халмош Пауль Р.

Халмош, Пол Ричард

פול הלמוש

פול הלמוש מתמטיקאי אמריקאי

پل ریچارد هالموس

पॉल हॅलमॉस

헐모시 팔

ハルモス, P. R.