Paul Halmos Bücher

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.

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.

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.

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.

Originally published: New York: Chelsea Publishing Company, 1962.

Originally published: Princeton, NJ: D. Van Nostrand Company, Inc., 1958.