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.
`What this book is full of, on almost every page, are quotations. They are well chosen, trenchant, and presented in their original language and an English translation. The effect is to eavesdrop on a long, continuing conversation, the conversation that is the life of mathematics as discussed by leading mathematicians. Here they are caught saying interesting, insightful, provocative things. They are by no means confined to definitions and statements of
theorems, they are allowed to tell you why they think something is important, charming, useful, how it was found, who is responsible.'
2. General topology
3. Integration and measure
4. Functional analysis
5. Harmonic analysis
6. Lie groups
7. Theory of functions and analytic geometry
8. Ordinary and partial differential equations
9. Algebraic topology
Index of names
Index of terms
Appendix: List of symbols