Scenes from the History of Real Functions

1. Front Matter

   Pages 1-10

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2. The place of the theory of functions of a real variable among the mathematical disciplines

   • Fyodor A. Medvedev

   Pages 11-24

3. The history of the concept of a function

   • Fyodor A. Medvedev

   Pages 25-81

4. Sequences of functions. Various kinds of convergence

   • Fyodor A. Medvedev

   Pages 82-167

5. The derivative and the integral in their historical connection

   • Fyodor A. Medvedev

   Pages 168-211

6. Nondifferentiable continuous functions

   • Fyodor A. Medvedev

   Pages 212-234

7. Back Matter

   Pages 235-265

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To attempt to compile a relatively complete bibliography of the theory of functions of a real variable with the requisite bibliographical data, to enumer­ ate the names of the mathematicians who have studied this subject, exhibit their fundamental results, and also include the most essential biographical data about them, to conduct an inventory of the concepts and methods that have been and continue to be applied in the theory of functions of a real variable ... in short, to carry out anyone of these projects with appropriate completeness would require a separate book involving a corresponding amount of work. For that reason the word essays occurs in the title of the present work, allowing some freedom in the selection of material. In justification of this selection, it is reasonable to try to characterize to some degree the subject to whose history these essays are devoted. The truth of the matter is that this is a hopeless enterprise if one requires such a characterization to be exhaustively complete and concise. No living subject can be given a final definition without provoking some objections, usually serious ones. But if we make no such claims, a characterization is possible; and if the first essay of the present book appears unconvincing to anyone, the reason is the personal fault of the author, and not the objective necessity of the attempt.

• Isaac Newton
• classification
• history of mathematics
• liberty
• project

• Institute for History of Science and Technology, Moskva, USSR

  Fyodor A. Medvedev

Policies and ethics