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".

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.

Hilbert Space Problem Book 1ST Edition by Paul Halmos (Author) (9.25x6.3x1.3in 365pgs Hardcover NO DJ) D VAN NOSTRAND COMPANY INC (1967)

This is a book of aspirations fulfilled, those of the author and his colleagues. It tells us what it is to be a mathematician and to do mathematics. It will be read with interest and enjoyment by those in mathematics and by those who might want to know what mathematicians and mathematical careers are like. Halmos, mathematician and expositor, has contributed much to ergodic theory, algebraic logic, operator theory, and the mathematical literature in general.

Book by Paul R. Halmos

This is a book of aspirations fulfilled, those of the author and his colleagues. It tells us what it is to be a mathematician and to do mathematics. It will be read with interest and enjoyment by those in mathematics and by those who might want to know what mathematicians and mathematical careers are like. Halmos, mathematician and expositor, has contributed much to ergodic theory, algebraic logic, operator theory, and the mathematical literature in general.