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...

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...

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...

"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.)