This book is designed for readers with prior knowledge of Hilbert space theory. It offers a collection of problems accompanied by definitions, historical insights, and hints. The extensive solutions section provides proofs and constructions, making it a valuable resource for active learners rather than an introductory text.
As a groundbreaking work, this book serves as the first formal introduction to linear algebra, combining algebra and geometry to explore three-dimensional vector spaces. Written by Paul Halmos, inspired by John von Neumann, it gained immediate acclaim for its clarity and exposition of complex mathematical concepts. Since its publication, it has significantly influenced various fields, including mathematics, natural and social sciences, aiding in the analysis of diverse topics like weather patterns and population genetics. Halmos's contributions to mathematics earned him the prestigious Steele Prize in 1983.
Ann Arbor, Michigan ] anuary, 1963 Contents Section Page 1 1 Boolean rings ............................ 4 Regular open sets . 10 Free algebras . 13 Boolean a-algebras . 15 Measure algebras . 69 17 Boolean spaces . 22 Boolean a-spaces . 24 Boolean measure spaces . 25 Incomplete algebras . 26 Products of algebras . 27 Sums of algebras .
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.
The collection showcases the mathematical contributions of Paul R. Halmos, featuring two volumes that highlight his research and expository works. Volume I includes research papers and two significant expository pieces on Hilbert Space, while Volume II contains 27 articles and a transcript of an interview, spanning from 1949 to 1981. This selection reflects Halmos's influential role in mathematics and his ability to communicate complex ideas effectively.
Focusing on measure theory's applications in modern analysis, this book serves as both a textbook for students and a reference for advanced mathematicians. It provides a comprehensive approach that caters to beginning graduate students and advanced undergraduates alike, ensuring accessibility and depth in understanding key concepts.
Classic by prominent mathematician offers a concise introduction to set theory using language and notation of informal mathematics. Topics include the basic concepts of set theory, cardinal numbers, transfinite methods, more. 1960 edition.
Renowned for its mastery of linear algebra, this book has been updated with a new title and improved typesetting, making it more accessible to readers. Originally published as "Finite-Dimensional Vector Spaces," it addresses the complexities of the subject while correcting previous oversights. The revised edition aims to attract both math majors and a broader audience who may have previously overlooked its value.
This collection showcases the mathematical writings of P. R. Halmos, featuring research publications primarily focused on probability, measure theory, and operator theory, organized chronologically. Key expository papers, including "Ten Problems in Hilbert Space," are included, alongside introductory essays discussing Halmos's contributions to ergodic theory and operator theory. Notably, papers from the mid-1950s on algebraic logic are excluded, having been published separately. The volume highlights Halmos's impact on mathematics through both specialized and popular writings.