Paul Halmos

Q: What Schools Are Affiliated With Paul Halmos

Paul Halmos is affiliated with the following schools: Santa Clara University, Reed College, Indiana University Bloomington, University of California, Santa Barbara, Indiana University, University of Michigan, University of Wales, Syracuse University, University of Chicago, University of Illinois Urbana-Champaign

Paul Halmos's AcademicInfluence.com Rankings

Paul Halmos

Mathematics

#11

World Rank

#58

Historical Rank

Functional Analysis

World Rank

Historical Rank

Probability Theory

World Rank

#13

Historical Rank

Measure Theory

World Rank

#15

Historical Rank

mathematics Degrees

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Mathematics

Why Is Paul Halmos Influential?

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According to Wikipedia, Paul Richard Halmos was a Hungarian-born American mathematician and statistician who made fundamental advances in the areas of mathematical logic, probability theory, statistics, operator theory, ergodic theory, and functional analysis . He was also recognized as a great mathematical expositor. He has been described as one of The Martians.

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Paul Halmos's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

A Hilbert Space Problem Book (1967) (1686)
Finite-Dimensional Vector Spaces (1960) (997)
Lectures on ergodic theory (1956) (624)
Algebraic Properties of Toeplitz operators. (1964) (537)
Lectures on Boolean Algebras (1963) (486)
Naive Set Theory (1961) (440)
Ten problems in Hilbert space (1970) (379)
Shifts on Hilbert spaces. (1961) (353)
Introduction to Hilbert Space: And the Theory of Spectral Multiplicity (1998) (345)
Application of the Radon-Nikodym Theorem to the Theory of Sufficient Statistics (1949) (295)
Bounded integral operators on L²spaces (1978) (288)
The Theory of Unbiased Estimation (1946) (246)
The Marriage Problem (1950) (212)
Introduction to Boolean Algebras (2008) (211)
Operator Methods in Classical Mechanics, II (1942) (207)
The Heart of Mathematics. (1980) (191)
Normal Dilations and Extensions of Operators (1983) (191)
TWO SUBSPACES (2010) (174)
Algebraic logic, I. Monadic boolean algebras (1956) (173)
On automorphisms of compact groups (1943) (154)
What Does the Spectral Theorem Say (1963) (124)
I Want to be a Mathematician (1985) (122)
How to Write Mathematics (1973) (116)
The personal and the political (1978) (115)
In General a Measure Preserving Transformation is Mixing (1944) (110)
The Sociology of sociology (1970) (110)
The range of a vector measure (1948) (100)
What Is Teaching (1994) (98)
Asymptotic Toeplitz operators (1982) (94)
Reflexive Lattices of Subspaces (1971) (91)
The Faith of the Counsellors (1966) (87)
Products of involutions (1976) (86)
The personal service society (1967) (74)
Invariant subspaces of polynomially compact operators. (1966) (70)
Introduction to Boolean algebras. Undergraduate Texts in Mathematics (2010) (69)
I Want to Be A Mathematician: An Automathography (1986) (68)
Some unsolved problems of unknown depth about operators on Hilbert space (1976) (68)
How to teach (1985) (64)
Approximation theories for measure preserving transformations (1944) (62)
Positive Approximants of Operators (1983) (61)
Logic As Algebra (1998) (60)
Mathematics as a Creative Art (1983) (59)
Commutators of operators (1952) (58)
COMMUTATORS OF OPERATORS, II.* (1954) (55)
Products of symmetries (1958) (55)
Linear algebra problem book (1997) (53)
On Foguel’s answer to Nagy’s question (1964) (47)
Problems for mathematicians, young and old (1991) (46)
The Legend of John Von Neumann (1973) (45)
The Foundations of Probability (1944) (44)
The Basic Concepts of Algebraic Logic (1956) (42)
Sets and Classes (1974) (41)
II. The Problem of Learning to Teach (1975) (40)
THE COMPUTATION OF AGGREGATE LOSS DISTRIBUTIONS (1999) (38)
On Monothetic Groups. (1942) (36)
Review: W. H. Gottschalk and G. A. Hedlund, Topological dynamics (1955) (35)
On A Theorem of Dieudonné. (1949) (35)
The decomposition of measures (1941) (35)
Comment on the real line (1944) (34)
Numerical ranges and normal dilations (1983) (34)
The Sociological review monograph (1958) (32)
Square roots of operators (1953) (31)
Capacity in Banach Algebras (1983) (30)
THE TEACHING OF PROBLEM SOLVING (1975) (29)
Recent progress in ergodic theory (1961) (26)
Vector bases for two commuting matrices (1990) (26)
Algebraic logic. IV. Equality in polyadic algebras (1957) (25)
Commutators of Operators on Hilbert Space (1965) (25)
The William Lowell Putnam Mathematical Competition, Problems and Solutions: 1938-1964. (1981) (24)
Ten years in Hilbert space (1979) (24)
Applied Mathematics is Bad Mathematics (1981) (23)
Solitude and privacy;: A study of social isolation, its causes and therapy (1969) (23)
Spectral approximants of normal operators (1974) (23)
Professionalisation and social change (1973) (23)
The representation of σ-algebras (1974) (22)
On the set of values of a finite measure (1947) (22)
Continuous functions of Hermitian operators (1972) (21)
Does mathematics have elements? (1981) (21)
Review: Nelson Dunford and Jacob T. Schwartz, Linear operators. Part I: General theory (1959) (20)
Finite Dimensional Vector Spaces. (AM-7) (1947) (19)
Subnormal Suboperators and the Subdiscrete Topology (1984) (19)
Paul Halmos Celebrating 50 Years Of Mathematics (1991) (19)
Eigenvectors and adjoints (1971) (18)
Spectra and spectral manifolds (1952) (17)
Note on almost-universal forms (1938) (17)
The decomposition of measures, II (1942) (17)
The faith of the counsellors : a study in the theory and practice of social case work and psychotherapy (1966) (16)
Von Neumann on measure and ergodic theory (1958) (16)
Solitude and Privacy (1953) (16)
Has progress in mathematics slowed down (1990) (16)
A Non Homogeneous Ergodic Theorem (1949) (16)
Selecta : expository writing (1985) (15)
Square Roots of Measure Preserving Transformations (1942) (15)
Bad products of good matrices (1991) (15)
Finite-dimensional points of continuity of Lat (1980) (15)
The sociology of mass-media communicators (1969) (15)
Limits of Shifts (1983) (14)
Finite-Dimensional Hilbert Spaces (1970) (14)
The personal and the political: Social work and political action (1978) (14)
A nonhomogeneous ergodic theorem (1949) (14)
MEASURABLE TRANSFORMATIONS (2007) (12)
Innovation in Mathematics (1958) (12)
Algebraic logic. III. Predicates, terms, and operations in polyadic algebras (1956) (12)
Permutations of sequences and the Schröder-Bernstein theorem (1968) (12)
Square roots of operators. II (1954) (12)
MEASURABLE TRANSFORMATIONS (2007) (12)
Commutativity and spectral properties of normal operators (1983) (12)
Limsups of Lats (1983) (11)
A Glimpse into Hilbert Space (1983) (11)
Weakly transitive matrices (1984) (11)
Free monadic algebras (1959) (11)
Old and New Unsolved Problems in Plane Geometry and Number Theory. By Victor Klee and Stan Wagon (1992) (10)
The representation of monadic Boolean algebras (1959) (10)
Products of shifts (1972) (9)
Invariants of certain stochastic transformations: The mathematical theory of gambling systems (1939) (9)
TOEPLITZ AND WIENER-HOPF OPERATORS IN H«+C (2007) (9)
I have a photographic memory (1987) (9)
The Development of Industrial Societies (1964) (9)
How to talk Mathematics (2010) (9)
Learning to study (1985) (8)
The Serre Conjecture (1978) (8)
Sociology and the Personal Service Professions (1971) (7)
Finite monadic algebras (1959) (7)
An autobiography of Polyadic Algebras (2000) (7)
The foundation year in the University of Keele: A report (1968) (6)
Personal Involvement in Learning about Personality (1953) (6)
The thrills of abstraction (1982) (5)
Pure Thought is Better Yet (1985) (5)
Sociological Studies in British University Education (1963) (4)
Entropy in ergodic theory : [lectures at] University of Chicago, Sept., 1959 (1959) (4)
Large intersections of large sets (1992) (4)
PREDICATES, TERMS, OPERATIONS, AND EQUALITY IN POLYADIC BOOLEAN ALGEBRAS. (1956) (4)
Entropy in Ergodic Theory (2011) (4)
Logic from A to G (1977) (4)
Shorter Notes: Permutations of Sequences and the Schroder-Bernstein Theorem (1968) (4)
Inverses and Composites (1974) (3)
The representation theorem (1974) (3)
Hungarian sociological studies (1972) (3)
On a Necessary Condition for the Strong Law of Large Numbers (1939) (3)
The Thrills of Abstraction. (1982) (3)
Sociology and medicine : studies within the framework of the British National Health Service (1964) (3)
Book Review: Lectures on invariant subspaces (1965) (3)
The Peano Axioms (1974) (3)
Review: N. Bourbaki, Intégration (1953) (3)
The sociology of science (1972) (3)
The fabulous fifties (1985) (2)
The Schröder-Bernstein Theorem (1974) (2)
Use of Mathematical Literature. (1978) (2)
Review: G. Pólya, Mathematics and plausible reasoning (1955) (2)
Generalized Numerical Range (2015) (2)
Sociological studies in the British penal services (1965) (2)
The harmonic Cesàro and Copson operators on the spaces L p ( R ) , 1 ≤ p ≤ 2 by Ferenc Móricz (2)
About Books (1982) (2)
American Mathematics from 1940 to the Day Before Yesterday (1976) (2)
What to Publish (1983) (2)
Selecta : research contributions (1983) (2)
Why is a congress? (1987) (2)
Papers on the teaching of personality development (1965) (2)
Postcards from Max (1993) (2)
Stochastic processes in sociology (1973) (2)
Think It Gooder (1982) (2)
Review: F. J. Murray, An Introduction to Linear Transformations in Hilbert Space (1942) (1)
The teaching of sociology to students of education and social work (1961) (1)
Research on Loneliness (1953) (1)
Psychologies of Love (1966) (1)
Review: Howard Levi, Elements of algebra (1955) (1)
T. H. Marshall (1974) (1)
Invariant Subspaces 1969 (1983) (1)
Readings in general psychology (1959) (1)
Latin American Sociological Studies (1967) (1)
Ideals and filters (1974) (1)
ii. What to Publish (1975) (1)
The Canford families : a study in social casework and group work (1962) (1)
Introduction a la theorie des ensembles (1968) (1)
Unions and Intersections (1974) (1)
Review: A. C. Zaanen, Linear analysis (1954) (1)
Review: Alfred Tarski, Logic, semantics, metamathematics (1957) (1)
Isomorphisms of factors (1974) (1)
The Axiom of Extension (1974) (1)
Elementary Problems: E2920-E2925 (1982) (1)
How to Remember Walter Kaufmann-Bühler (1987) (1)
Four Panel Talks on Publishing (1975) (1)
Measures and Outer Measures (1974) (1)
Review: A. A. Fraenkel, Abstract set theory (1953) (1)
I want to be a mathematician (excerpts) (1986) (1)
Properties of Compactness (1982) (1)
Boolean σ-algebras (1974) (1)
How to do almost everything (1985) (1)
A reason for hope (1970) (1)
Towards a Measure of Man: The Frontiers of Normal Adjustment (2010) (1)
Fields of sets (1974) (1)
The concept of social action (1978) (1)
Properties of spectra (1982) (1)
Review: M. Picone and T. Viola, Lezioni sulla teoria moderna dell'integrazione (1953) (1)
Review: Jean Dieudonn, Panorama des mathmatiques pures. Le choix bourbachique (1979) (1)
Book Review: Les systèmes axiomatiques de la théorie des ensembles (1954) (1)
Decisions in Professional Education (1954) (0)
T E N PROBLEMS IN HILBERT SPACE BY P. R. HALMOS Dedicated to my teacher and friend Joseph Leo Doob with admiration and affection. TABLE OF CONTENTS (2007) (0)
APPENDIX III. HILBERT SPACE (1947) (0)
Japanese Sociological Studies (1967) (0)
About books (1983) (0)
APPENDIX I. THE CLASSICAL CANONICAL FORM (1947) (0)
Pacific Journal of Mathematics SOLUTION OF AN INVARIANT SUBSPACE PROBLEM OF (2012) (0)
THE NOVEMBER MEETING IN EVANSTON (2007) (0)
Examples of Spectra (1982) (0)
ON THE COHOMOLOGY OF TWO-STAGE POSTNIKOV SYSTEMS (2007) (0)
INDEX OF DEFINITIONS (1947) (0)
Problems for Solution: 4097-4100 (1943) (0)
Algebraic logic (reprint) (2006) (0)
Japanese Sociological Studies. (1970) (0)
To Sydney, to Moscow, and back (1985) (0)
TABLE OP CONTENTS (1947) (0)
Measure and Topology in Groups (1950) (0)
Higher Education in Britain: A Review Essay@@@Sociological Studies in British University Education. (1964) (0)
Introduction to welfare : concepts and history (1978) (0)
Transformations and Functions (1950) (0)
The Personal and the Political (RLE Social Theory) : Social Work and Political Action (2014) (0)
List of Officers and Members of the Association for Symbolic Logic (1958) (0)
The problems arising from the teaching of personality development (1958) (0)
CMPT-497, Course Information, Spring 2010 (2010) (0)
A. H. Copeland Sr. Note on cylindric algebras and polyadic algebras. Michigan mathematical journal , vol. 3 (1955–1956) pp. 155–157. (1958) (0)
Moral issues in the training of teachers and social workers (1963) (0)
Complements and Powers (1974) (0)
About books (1971) (0)
Chapter III. ORTHOGONALITY (1947) (0)
Community Integration and the Community Centres (1948) (0)
Social Science and Social Change (1959) (0)
Some books on linear algebra (2004) (0)
Service, one way or another (1985) (0)
NOTE ON ALMOST-UNIVERSAL FORMSJ (2007) (0)
BOOKS, 1920–1943 (2005) (0)
Vectors and spaces (1974) (0)
Reading and writing and ’rithmetic (1985) (0)
Isomorphisms of countable factors (1974) (0)
Sums of algebras (1974) (0)
[Giant cell bone tumors]. (1972) (0)
Problems for Solution: E636-E640 (1944) (0)
Introduction a la the'orie des ensembles (1997) (0)
Extension of Measures (1974) (0)
The Axiom of Specification (1974) (0)
The Development of Industrial Societies. Papers Read at the Nottingham Conference of the British Sociological Association. Avril 1964 (1965) (0)
[Fixation of a fractured mastoid process using adhesives]. (1982) (0)
The Harmony of the World: Logic from A to G (2007) (0)
Problems for Solution: 4658-4662 (1955) (0)
Advanced Problems: 5727-5733 (1970) (0)
Chapter I. SPACES (1947) (0)
De la tutelle à l'autonomie: un projet d'appartement relais thérapeutique (1987) (0)
Winning the war (1985) (0)
Naive Set Theory.@@@Axiomatic Set Theory. (1961) (0)
Duality for ideals (1974) (0)
FREE MONADIC ALGEBRAS1 (2010) (0)
A great university (1985) (0)
list of Chauvenet Prize winners (2013) (0)
FREE MONADIC ALGEBRAS1 (2010) (0)
Regular open sets (1974) (0)
Book Review: Lezioni sulla teoria moderna dell'integrazione (1953) (0)
Boolean σ-spaces (1974) (0)
Products of algebras (1974) (0)
Review: L. Henkin, La Structure Algebrique des Theories Mathematiques (1957) (0)
Matrices I have met (1986) (0)
Review: L. Henkin, The Representation Theorem for Cylindrical Algebras (1957) (0)
Henkin L.. The representation theorem for cylindrical algebras. Mathematical interpretation of formal systems, Studies in logic and the foundations of mathematics, North-Holland Publishing Company, Amsterdam 1955, pp. 85–97. (1957) (0)
Chapter II. TRANSFORMATIONS (1947) (0)
The countable chain condition (1974) (0)
General Set Functions (1950) (0)
[Bilateral facial paralysis following fracture of the petrous pyramid]. (1970) (0)
Strong Operator Topology (1982) (0)
NPTEL COURSE ON QUANTUM PHYSICS (2013) (0)
Robinson Abraham. Théorie métamathématique des idéaux . Collection de logique mathématique, série A. Dactyl-offset. Gauthier-Villars, Paris; E. Nauwelaerts, Louvain; 1955, 186 pp. (1955) (0)
Psychiatric Aid in the Grammar Schools (1947) (0)
Locally Compact Spaces (1950) (0)
The Beauty of Doing Mathematics. By Serge Lang (1987) (0)
Boundedness and Invertibility (1974) (0)
Some Moral Issues of Mental Health Training in Professional Education (1960) (0)
Finite joins and meets (1969) (0)
Co je to učit (1995) (0)
Duality for homomorphisms (1974) (0)
Mathematics from poland. (1982) (0)
Problems for Solution: 4176-4180 (1945) (0)
The Sociological Review Monograph No. 3: Moral Issues in the Training of Teachers and Social Workers (1961) (0)
Strong and weak topologies (1974) (0)
The Axiom of Choice (1974) (0)
PARTIAL ISOMETRIES (2012) (0)
Art and Social Change (1970) (0)
Review: Oscar Varsavsky, Quantifiers and Equivalence Relations (1959) (0)
LIST OF NOTATIONS (1947) (0)
Henkin L.. La structure algébrique des théories matérmatiques . Collection de logique mathématique, série A. Gauthier-Villars, Paris; E. Nauwelaerts, Louvain; 1956, 52 pp. (1957) (0)
Examples of Compactness (1982) (0)
Linear Algebra Problem Book: Inner Product Spaces (1995) (0)
Banach Spaces and Hilbert Spaces (1986) (0)
Advanced Problems: 6423-6426 (1983) (0)
APPROXIMATION THEORIES FOR MEASURE PRE- (2010) (0)
Book Review Department : HOMO SOCIOLOGICUS, by Ralf Dahrendorf, Routledge & Kegan Paul, 1973, V + 97pp. £1:60p (1974) (0)
Introduction a la théorie des ensembles : (Naive set theory) (1967) (0)
Allen L. Shields (1990) (0)
The Work of F. Riesz (1983) (0)
Halmos 75th birthday volume (1991) (0)
Review: A. H. Copeland, Note on Cylindric Algebras and Polyadic Algebras (1958) (0)
Learning to think (1985) (0)
Backlog and You (1984) (0)
Introduction (1972) (0)
Boolean measure spaces (1974) (0)
Cosets, clusters, spinsters, and the Schröder-Bernstein theorem (1992) (0)
Sets of Ordinal Numbers (1974) (0)
Sociological studies in economics & administration, (1969) (0)
APPENDIX II. DIRECT PRODUCTS (1947) (0)
List of officers and members of the association for symbolic logic (1957) (0)

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