Are human misery, poverty and despair a result of personal inadequacy or social injustice? Therefore is the solution to these problems psychotherapy or political action? In one of the most important books on social work for a decade, Paul Halmos tries to resolve a dilemma which many social workers experience acutely – the conflict between a desire to help those in need and a fear that, by doing so, they merely support a political system which should, itself, be changed. Such a dilemma was highlighted during the sixties when 'casework' and personal counselling became discredited by the 'rediscovery' of widespread poverty and inequality in western society. To many the only solution seemed to be urgent and radical political action. For Professor Halmos the realities are more complex – an exclusive preoccupation with either personal or political solutions is unlikely to prove fruitful – what is needed is a dual sensitivity and balance. Yet for the author it is the political solution which carries within it the greater risk and he warns of the dangers inherent in the total politicization of social concerns. He argues that social action can become political action and ultimately political control.

The personal and the political: Social work and political action

Politics & Social Sciences

Paul R. Halmos

Social Sciences

Hutchinson

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."

A Hilbert Space Problem Book (Graduate Texts in Mathematics,)

Science & Math

Mathematics

Springer

IN 1959 I lectured on Boolean algebras at the University of Chicago. A mimeographed version of the notes on which the lectures were based circulated for about two years; this volume contains those notes, corrected and revised. Most of the corrections were suggested by Peter Crawley. To judge by his detailed and precise suggestions, he must have read every word, checked every reference, and weighed every argument, and I am lIery grateful to hirn for his help. This is not to say that he is to be held responsible for the imperfec tions that remain, and, in particular, I alone am responsible for all expressions of personal opinion and irreverent view point. P. R. H. Ann Arbor, Michigan ] anuary, 1963 Contents Section Page 1 1 Boolean rings ............................ . 2 Boolean algebras ......................... . 3 9 3 Fields of sets ............................ . 4 Regular open sets . . . . . . . . . . . . . . . . . . . 12 . . . . . . 5 Elementary relations. . . . . . . . . . . . . . . . . . 17 . . . . . 6 Order. . . . . . . . . . . . . . . . . . . . . . . . . . . 21 . . . . . . . . . 7 Infinite operations. . .. . . . . . . . . . . . . . . . . 25 . . . . . 8 Subalgebras . . . . . . . . . . . . . . . . . . . . .. . . . 31 . . . . . . 9 Homomorphisms . . . . . . . . . . . . . . . . . . . . 35 . . . . . . . 10 Free algebras . . . . . . . . . . . . . . . . . . . . . . 40 . . . . . . . 11 Ideals and filters. . . . . . . . . . . . . . . . . . . . 47 . . . . . . 12 The homomorphism theorem. . . . . . . . . . . . .. . . 52 . . 13 Boolean a-algebras . . . . . . . . . . . . . . . . . . 55 . . . . . . 14 The countable chain condition . . . . . . . . . . . . 61 . . . 15 Measure algebras . . . . . . . . . . . . . . . . . . . 64 . . . . . . . 16 Atoms.. . . . .. . . . . .. .. . . . ... . . . . .. . . ... . . .. 69 17 Boolean spaces . . . . . . . . . . . . . . . . . . . . 72 . . . . . . . 18 The representation theorem. . . . . . . . . . . . . . 77 . . . 19 Duali ty for ideals . . . . . . . . . . . . . . . . . .. . . 81 . . . . . 20 Duality for homomorphisms . . . . . . . . . . . . . . 84 . . . . 21 Completion . . . . . . . . . . . . . . . . . . . . . . . 90 . . . . . . . . 22 Boolean a-spaces . . . . . . . . . . . . . . . . . .. . . 97 . . . . . 23 The representation of a-algebras . . . . . . . . .. . . 100 . 24 Boolean measure spaces . . . . . . . . . . . . . .. . . 104 . . . 25 Incomplete algebras . . . . . . . . . . . . . . . .. . . 109 . . . . . 26 Products of algebras . . . . . . . . . . . . . . . .. . . 115 . . . . 27 Sums of algebras . . . . . . . . . . . . . . . . . .. . . 119 . . . . . 28 Isomorphisms of factors . . . . . . . . . . . . . .. . . 122 . . .

Lectures on Boolean Algebras

Springer, Verlag

2012 Reprint of 1942 Edition.  Exact facsimile of the original edition, not reproduced with Optical Recognition Software.  As a newly minted Ph.D., Paul Halmos came to the Institute for Advanced Study in 1938--even though he did not have a fellowship--to study among the many giants of mathematics who had recently joined the faculty. He eventually became John von Neumann's research assistant, and it was one of von Neumann's inspiring lectures that spurred Halmos to write "Finite Dimensional Vector Spaces." The book brought him instant fame as an expositor of mathematics.  Finite Dimensional Vector Spaces combines algebra and geometry to discuss the three-dimensional area where vectors can be plotted. The book broke ground as the first formal introduction to linear algebra, a branch of modern mathematics that studies vectors and vector spaces. The book continues to exert its influence sixty years after publication, as linear algebra is now widely used, not only in mathematics but also in the natural and social sciences, for studying such subjects as weather problems, traffic flow, electronic circuits, and population genetics. In 1983 Halmos received the coveted Steele Prize for exposition from the American Mathematical Society for "his many graduate texts in mathematics dealing with finite dimensional vector spaces, measure theory, ergodic theory, and Hilbert space."

Finite-Dimensional Vector Spaces. (Undergraduate Texts in Mathematics)

This volume and its companion present a selection of the mathematical writings of P. R. Halmos. The present volume consists of research publications plus two papers which, although of a more expository nature, were deemed primarily of interest to the specialist ("Ten Problems in Hilbert Space" (1970d), and" Ten Years in Hilbert Space" (1979b)). The remaining expository and all the popular writings are in the second volume. The papers in the present volume are arranged chronologically. As it happens, that arrangement also groups the papers according to subject matter: those published before 1950 deal with probability and measure theory, those after 1950 with operator theory. A series of papers from the mid 1950's on algebraic logic is excluded; the papers were republished by Chelsea (New York) in 1962 under the title" Algebraic Logic." This volume contains two introductory essays, one by Nathaniel Friedman on Halmos's work in ergodic theory, one by Donald Sarason on Halmos's work in operator theory. There is an essay by Leonard Gillman on Halmos's expository and popular writings in the second volume. The editors wish to express their thanks to the staff of Springer-Verlag. They are grateful also for the help of the following people: C. Apostol, W. B. Arveson, R. G. Douglas, C. Pearcy, S. Popa, P. Rosenthal, A. L. Shields, D. Voiculescu, S. Walsh. Berkeley, CA Donald E. Sarason vii WORK IN OPERATOR THEORY P. R. Halmos's first papers on Hilbert space operators appeared in 1950.

Selecta I - Research Contributions

I. Student.- 1 Reading and writing and' rithmetic.- Words.- Books.- Writing.- Languages.- Numbers.- Study or worry.- Learning English.- High school.- 2 A college education.- Move to Chambana.- How not to be a freshman.- Trig and analyt.- Calculus, and is there a doctor on the faculty?.- Elementary mathematics and culture.- Mathematical daydreams and BARBARA.- All Gaul.- A Bachelor of Science.- 3 Graduate school.- Statistics.- The end of the affair.- Matrices.- The Dean.- First class.- Hazlett and Netzorg.- Good morning, analysis.- Why geometry?.- 4 Learning to study.- Doob arrives.- All work and politics.- Born again.- Other forces, other tongues.- Prelims.- For example.- Statistics, no.- Readings and ratings.- Reprints: Doob's and others'.- Study.- 5 Learning to think.- Optional skipping.- Roller coaster.- Jobs, no.- On my own.- The end of an era.- 6 The Institute.- The common room.- The center of the world.- Insignificant people.- Work.- Work and between work.- A weak paper and a pretty good book.- Collaboration.- Measures and Harvard.- Classical mechanics.- Birthdays.- 7 Winning the war.- Back home in Illinois.- Meetings.- Teaching at Syracuse.- Research at Syracuse.- Radiation Laboratory.- Referee and review.- From Syracuse to Chicago.- II. Scholar.- 8 A great university.- Eckhart Hall.- Days of glory.- What makes a great university?.- Teaching.- Students and visitors.- 9 The early years.- Guggenheim.- Measure Theory.- Master's exams.- Judgments.- Jimmie Savage.- Students and courses.- The beginning of Hilbert space.- Ph.D. students.- The Cambridge Congress.- Follow the sun.- 10 Montevideo.- Where to go?.- Saturation in Spanish.- Room and board.- Weather and climate.- How to get a chair.- Humanities and sciences.- Faculty of engineering.- Instituto de Matemca.- Institute people.- Teaching in Montevideo.- Research in Uruguay.- Spy, junior grade.- Small memories.- 11 The fabulous fifties.- Back home.- Is formal logic mathematics?.- Boolean logic.- The road to polyadic algebras.- All logic and all mathematics.- Logic students and logicians.- The passport saga.- Service.- Editing.- How to be a big shot.- How to be an editor.- Recent progress in ergodic theory.- Writing for a living.- The Institute again.- Boolean algebras and sets.- Farewell.- III. Senior.- 12 How to teach.- Shifting gears.- The Moore method.- Moore and covering material.- How to be a pro.- Musings on teaching.- How to supervise.- More Ph.D. students.- 13 To Sydney, to Moscow, and back.- Sydney 1964.- Budapest 1964.- Scotland 1965.- Tourist in Moscow and Leningrad.- Life with Anosov.- Fomin and Gelfand.- Mathematicians in Moscow.- As others see us.- 14 How to do almost everything.- Rejections.- How to do research.- The invariant subspace problem.- Friends can help.- How to recommend.- How to advise.- Honolulu, here I come!.- 15 Service, one way or another.- Democracy ad absurdum.- How to be a chairman.- How not to be a chairman.- Life in Bloomington.- Indiana students.- Committees of one: Wabash.- Committees of one: Bulletin.- The Monthly.- Here and there.- How to write mathematics.- How to write about von Neumann.- How to write history?.- Coda How to be a mathematician.- Index of Photographs.

I Want to Be A Mathematician: An Automathography

Some tanning/foxing to first few and last few pages and page edges. No dustcover. Portions of dustcover pasted on inside of front board. Owner name, date and price on inside cover. Text is clean. Binding is tight. Solid Book.

Finite-Dimensional Vector Spaces

D.Van Nostrand Company Inc.

Contains four essays on expository writing of books and papers at the research level and at the level of graduate texts.

How to Write Mathematics

Norman E. Steenrod

Menahem M. Schiffer

Jean A. Dieudonne

Amer Mathematical Society

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. It is now available in a paperback edition.

I Have a Photographic Memory

American Mathematical Society

This classic book is based on lectures given by the author at the University of Chicago in 1956. The topics covered include, in particular, recurrence, the ergodic theorems, and a general discussion of ergodicity and mixing properties. There is also a general discussion of the relation between conjugacy and equivalence. With minimal prerequisites of some analysis and measure theory, this work can be used for a one-semester course in ergodic theory or for self-study. Readership Graduate students and research mathematicians interested in number theory. Table of Contents Introduction Examples Recurrence Mean convergence Pointwise convergence Comments on the ergodic theorem Ergodicity Consequences of ergodicity Mixing Measure algebras Discrete spectrum Automorphisms of compact groups Generalized proper values Weak topology Weak approximation Uniform topology Uniform approximation Category Invariant measures Invariant measures: the solution Invariant measures: the problem Generalized ergodic theorems Unsolved problems References

Lectures on Ergodic Theory

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Books by Paul R. Halmos