Mathematical analysis during the 20th century
著者
書誌事項
Mathematical analysis during the 20th century
Oxford University Press, 2001
- : hbk
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注記
Includes bibliographical references (p. [350]-409) and index
内容説明・目次
内容説明
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.
目次
- 1. INTRODUCTION
- 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
- 10.DIFFERENTIAL TOPOLOGY
- 11.PROBABILITY
- 12.ALGEBRAIC GEOMETRY
- REFERENCES
- INDEX OF NAMES
- INDEX OF TERMS
- APPENDIX: LIST OF SYMBOLS
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