A brief history of numbers
著者
書誌事項
A brief history of numbers
Oxford University Press, 2015
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注記
Includes bibliographical references (p. 295-301) and index
内容説明・目次
内容説明
The world around us is saturated with numbers. They are a fundamental pillar of our modern society, and accepted and used with hardly a second thought. But how did this state of affairs come to be?
In this book, Leo Corry tells the story behind the idea of number from the early days of the Pythagoreans, up until the turn of the twentieth century. He presents an overview of how numbers were handled and conceived in classical Greek mathematics, in the mathematics of Islam, in European mathematics of the middle ages and the Renaissance, during the scientific revolution, all the way through to the mathematics of the 18th to the early 20th century.
Focusing on both foundational debates and practical use numbers, and showing how the story of numbers is intimately linked to that of the idea of equation, this book provides a valuable insight to numbers for undergraduate students, teachers, engineers, professional mathematicians, and anyone with an interest in the history of mathematics.
目次
- 1. The System of Numbers: An Overview
- 2. Writing Numbers: Now and Back Then
- 3. Numbers and Magnitudes in the Greek Mathematical Tradition
- 4. Construction Problems and Numerical Problems in the Greek Mathematical Tradition
- 5. Numbers in the Tradition of Medieval Islam
- 6. Numbers in Europe from the 12th to the 16th Centuries
- 7. Number and Equations at the Beginning of the Scientific Revolution
- 8. Number and Equations in theWorks of Descartes, Newton, and their Contemporaries
- 9. New Definitions of Complex Numbers in the Early 19th Century
- 10. "What are numbers and what should they be?" Understanding Numbers in the Late 19th Century
- 11. Exact Definitions for the Natural Numbers: Dedekind, Peano and Frege
- 12. Numbers, Sets and Infinity. A Conceptual Breakthrough at the Turn of the Twentieth Century
- 13. Epilogue: Numbers in Historical Perspective
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