3000 years of analysis : mathematics in history and culture
著者
書誌事項
3000 years of analysis : mathematics in history and culture
Birkhäuser , Springer, c2021
- タイトル別名
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3000 Jahre Analysis
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注記
"Original published by Springer-Verlag GmbH Deutschland 2016, 3000 Jahre Analysis"--T.p. verso
Includes bibliographical references (p. 641-659) and indexes
内容説明・目次
内容説明
What exactly is analysis? What are infinitely small or infinitely large quantities? What are indivisibles and infinitesimals? What are real numbers, continuity, the continuum, differentials, and integrals?
You'll find the answers to these and other questions in this unique book! It explains in detail the origins and evolution of this important branch of mathematics, which Euler dubbed the "analysis of the infinite." A wealth of diagrams, tables, color images and figures serve to illustrate the fascinating history of analysis from Antiquity to the present. Further, the content is presented in connection with the historical and cultural events of the respective epochs, the lives of the scholars seeking knowledge, and insights into the subfields of analysis they created and shaped, as well as the applications in virtually every aspect of modern life that were made possible by analysis.
目次
Prologue: 3000 Years of Analysis.- The Continuum in Greek-Hellenistic Antiquity.- How Knowledge Migrates - From Orientto Occident.- Continuum and Atomismin Scholasticism.- Indivisibles and Infinitesimals in the Renaissance.- At the Turn from the 16th to the 17thCentury.- Newton and Leibniz-Giants and Opponents.- Absolutism ,Enlightenment, Departure to New Shores.- On the Way to Conceptual Rigourin the 19th Century.- At theTurn to the 20th Century: Set Theory and the Search for the True Continuum.- Coming to full circle: Infinitesimals in Nonstandard Analysis.
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