Mathematical Analysis During The 20th Century Hardcover

Jean-Paul Pier

For several centuries, analysis has been one of the most prestigious and important subjects in mathematics. The present book sets off by tracing the evolution of mathematical analysis, and then endeavours to understand the developments of main trends, problems, and conjectures. It features chapters on general topology, 'classical' integration and measure theory, functional analysis, harmonic analysis and Lie groups, theory of functions and analytic geometry, differential and partial differential equations, topological and differential geometry. The ubiquitous presence of analysis also requires the consideration of related topics such as probability theory or algebraic geometry. Each chapter features a comprehensive first part on developments during the period 1900-1950, and then provides outlooks on representative achievements during the later part of the century. The book provides many original quotations from outstanding mathematicians as well as an extensive bibliography of the seminal publications. It will be an interesting and useful reference work for graduate students, lecturers, and all professional mathematicians and other scientists with an interest in the history of mathematics.

0198503946

9780198503941

English

Oxford University Press

6 September 2001

440

Professor Jean-Paul Pier, Department of Mathematics, Luxembourg University Centre.

This is a superb history of 20th century mathematical analysis. One is taken on a tour of all the major areas with a lot of clear detail and many quotes from those who took part in the developments ... a book from which most mathematicians would find a lot to interest them. * Zentralblatt Mathematik * Will be a valuable source book for analysts interested in the history of the main ideas of analysis, as well as for others wanting to know about developments in other fields. * EMS * Pier marshals hundreds of quotations from the writings of twentieth-century analysts, weaving them into his text to form a coherent picture ... The impressive 60-page list of references is a major resource for historians of mathematics ... It is a major achievement, providing a superb reference for mathematicians who wish to understand how ideas have developed in analysis. * The Mathematical Gazette *