Halmos begins, 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 ... with the minimum of philosophical discourse and logical formalism. The mathematician, scientist, or engineer who needs to know the facts of set theory will find this crisp, clear, concise book, by a master expositor, ideal.

This book Naive Set Theory uses the language and notation of ordinary informal mathematics to state the basic set-theoretic facts which a beginning student of advanced mathematics needs to know... Because of the informal method of presentation, the book is eminently suited for use as a textbook or for self-study. The reader should derive from this volume a maximum of understanding of the theorems of set theory and of their basic importance in the study of mathematics.

Written by a prominent analyst Paul R. Halmos, this is the most famous, popular, and widely used textbook in the subject. The book is readable for its conciseness and clear explanation.

This emended edition is newly typeset and corrected.

Asymmetry of the book cover is due to a formal display problem. Actual books are printed symmetrically. Please look at the paperback edition for the correct image.

The free PDF file available on the publisher's website www.bwpest2018.org

Written by a prominent analyst Paul R. Halmos, this is the most famous, popular, and widely used textbook in the subject. The book is readable for its conciseness and clear explanation.

This emended edition is newly typeset and corrected.

The free PDF file available on the publisher's website www.bwpest2018.org

Paul Halmos's writing affected the professional lives of nearly every mathematician in the latter half of the twentieth century, and it will continue to influence the profession for years to come. -- J. Ewing, Notices of teh Amer. Math. Spc.

An exposition which is always fresh, proofs which are sophisticated, and a choice of subject matter which is certainly timely. - Bulletin of the American Mathematical Society.

In one hundred and nine well-packed pages one finds an exposition which is always fresh, proofs which are sophisticated, and a choice of subject matter which is certainly timely. ... Most pages exhibit a zest for play as well as work which is refreshing. - E. R. Lorch (Bull. Amer. Math. Soc.)

This classic by one of the twentieth century's most prominent mathematicians offers a concise introduction to set theory. Suitable for advanced undergraduates and graduate students in mathematics, it employs the language and notation of informal mathematics. There are very few displayed theorems; most of the facts are stated in simple terms, followed by a sketch of the proof. Only a few exercises are designated as such since the book itself is an ongoing series of exercises with hints. The treatment covers the basic concepts of set theory, cardinal numbers, transfinite methods, and a good deal more in 25 brief chapters.
This book is a very specialized but broadly useful introduction to set theory. It is aimed at 'the beginning student of advanced mathematics' ... who wants to understand the set-theoretic underpinnings of the mathematics he already knows or will learn soon. It is also useful to the professional mathematician who knew these underpinnings at one time but has now forgotten exactly how they go. ... A good reference for how set theory is used in other parts of mathematics. -- Allen Stenger, The Mathematical Association of America, September 2011.

Halmos begins, 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 ... with the minimum of philosophical discourse and logical formalism. The mathematician, scientist, or engineer who needs to know the facts of set theory will find this crisp, clear, concise book, by a master expositor, ideal.

Halmos begins, 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 ... with the minimum of philosophical discourse and logical formalism. The mathematician, scientist, or engineer who needs to know the facts of set theory will find this crisp, clear, concise book, by a master expositor, ideal.

Master expositor Paul Halmos presents Linear Algebra in the pure axiomatic spirit. He writes My purpose in this book is to treat linear transformations on finite dimensional vector spaces by the methods of more general theories. The idea is to emphasize the simple geometric notions common to many parts of mathematics and its applications, and to do so in a language that gives away the trade secrets .... This text is an ideal supplement to modern treatments of Linear Algebra. 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 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. --Zentralblatt für Mathematik.

2011 Reprint of 1960 Edition. Full facsimile of the original edition, not reproduced with Optical Recognition Software. Paul Richard Halmos (1916-2006) was a Hungarian-born American mathematician who made fundamental advances in the areas of probability theory, statistics, operator theory, ergodic theory, and functional analysis (in particular, Hilbert spaces). He was also recognized as a great mathematical expositor. ...He (the author) uses the language and notation of ordinary informal mathematics to state the basic set-theoretic facts which a beginning student of advanced mathematics needs to know...Because of the informal method of presentation, the book is eminently suited for use as a textbook or for self-study. The reader should derive from this volume a maximum of understanding of the theorems of set theory and of their basic importance in the study of mathematics. - Philosophy and Phenomenological Research.

2013 Reprint of 1956 Edition. Full facsimile of the original edition, not reproduced with Optical Recognition Software. Ergodic theory is a branch of mathematics that studies dynamical systems with an invariant measure and related problems. Its initial development was motivated by problems of statistical physics. A central concern of ergodic theory is the behavior of a dynamical system when it is allowed to run for a long time. Paul Richard Halmos (1916 - 2006) was a Hungarian-born American mathematician who made fundamental advances in the areas of probability theory, statistics, operator theory, ergodic theory, and functional analysis (in particular, Hilbert spaces). He was also recognized as a great mathematical expositor.

A fine example of a great mathematician's intellect and mathematical style, this classic on linear algebra is widely cited in the literature. The treatment is an ideal supplement to many traditional linear algebra texts and is accessible to undergraduates with some background in algebra.
This is a classic but still useful introduction to modern linear algebra. It is primarily about linear transformations ... It's also extremely well-written and logical, with short and elegant proofs. ... The exercises are very good, and are a mixture of proof questions and concrete examples. The book ends with a few applications to analysis ... and a brief summary of what is needed to extend this theory to Hilbert spaces. -- Allen Stenger, MAA Reviews, maa.org, May, 2016.
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. -- Zentralblatt für Mathematik.

This book, originally published as Finite-Dimensional Vector Spaces has been regarded as a masterpiece of linear algebra. Due to its non-standard title, the book was often overlooked even by math majors. Now the book appears with the new title, new typesetting, and corrections.

Asymmetry of the book cover is due to a formal display problem. Actual books are printed symmetrically. Please look at the paperback edition for the correct image.

The free PDF file available on the publisher's website www.bwpest2018.org

This book, originally published as Finite-Dimensional Vector Spaces has been regarded as a masterpiece of linear algebra. Due to its non-standard title, the book was often overlooked even by math majors. Now the book appears with the new title, new typesetting, and corrections.

The free PDF file available on the publisher's website www.bwpest2018.org

This concise introductory treatment consists of three chapters: The Geometry of Hilbert Space, The Algebra of Operators, and The Analysis of Spectral Measures. Author Paul R. Halmos notes in the Preface that his motivation in writing this text was to make available to a wider audience the results of the third chapter, the so-called multiplicity theory. The theory as he presents it deals with arbitrary spectral measures, including the multiplicity theory of normal operators on a not necessarily separable Hilbert space. His explication covers, as another useful special case, the multiplicity theory of unitary representations of locally compact abelian groups.
Suitable for advanced undergraduates and graduate students in mathematics, this volume's sole prerequisite is a background in measure theory. The distinguished mathematician E. R. Lorch praised the book in the Bulletin of the American Mathematical Society as an exposition which is always fresh, proofs which are sophisticated, and a choice of subject matter which is certainly timely.

This concise classic by Paul R. Halmos, a well-known master of mathematical exposition, has served as a basic introduction to aspects of ergodic theory since its first publication in 1956. The book is written in the pleasant, relaxed, and clear style usually associated with the author, noted the Bulletin of the American Mathematical Society, adding, The material is organized very well and painlessly presented.
Suitable for advanced undergraduates and graduate students in mathematics, the treatment covers recurrence, mean and pointwise convergence, ergodic theorem, measure algebras, and automorphisms of compact groups. Additional topics include weak topology and approximation, uniform topology and approximation, invariant measures, unsolved problems, and other subjects.

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.

Master expositor Paul Halmos presents Linear Algebra in the pure axiomatic spirit. He writes My purpose in this book is to treat linear transformations on finite dimensional vector spaces by the methods of more general theories. The idea is to emphasize the simple geometric notions common to many parts of mathematics and its applications, and to do so in a language that gives away the trade secrets .... This text is an ideal supplement to modern treatments of Linear Algebra. 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 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. --Zentralblatt f r Mathematik.

2013 Reprint of 1951 Edition. Full facsimile of the original edition, not reproduced with Optical Recognition Software. The subject matter of the book is funneled into three chapters: 1] The geometry of Hubert space; 2] the structure of self-adjoint and normal operators; 3] and multiplicity theory for a normal operator. For the last, an expert knowledge of measure theory is indispensable. Indeed, multiplicity theory is a magnificent measure-theoretic tour de force. The subject matter of the first two chapters might be said to constitute an introduction to Hilbert space, and for these, an a priori knowledge of classic measure theory is not essential. Paul Richard Halmos (1916-2006) was a Hungarian-born American mathematician who made fundamental advances in the areas of probability theory, statistics, operator theory, ergodic theory, and functional analysis (in particular, Hilbert spaces). He was also recognized as a great mathematical expositor.

2013 Reprint of 1963 Edition. Full facsimile of the original edition, not reproduced with Optical Recognition Software. The theory of Boolean algebras is one of the most attractive parts of mathematics. On the one hand, Boolean algebras arise naturally in such diverse fields as logic, measure theory, topology, and ring theory, so that the study of these objects is motivated by important applications. At the same time, the theory which has been developed constitutes one of the most elegant parts of modern algebra. Finally, the subject still poses many challenging questions, some of which have considerable importance. A graduate student who wishes to study Boolean algebras will find several excellent books to smooth his way: for an introduction, the book by Halmos is probably the best of these monographs. It offers a quick route to the most attractive parts of the theory.