An episodic history of mathematics : mathematical culture through problem solving / / Steven G. Krantz.
"An Episodic History of Mathematics delivers a series of snapshots of mathematics and mathematicians from ancient times to the twentieth century. Giving readers a sense of mathematical culture and history, the book also acquaints readers with the nature and techniques of mathematics via exercis...
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| Year of Publication: | 2010 |
| Language: | English |
| Series: | MAA textbooks
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| Physical Description: | xiii, 381 p. :; ill. |
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Table of Contents:
- The ancient Greeks and the foundations of mathematics
- Zeno's paradox and the concept of limit
- The mystical mathematics of Hypatia
- The Islamic world and the development of algebra
- Cardano, Abel, Galois, and the solving of equations
- Rene Descartes and the idea of coordinates
- Pierre de Fermat and the invention of differential calculus
- The great Isaac Newton
- The complex numbers and the fundamental theorem of algebra
- Carl Friedrich Gauss: the prince of mathematics
- Sophie Germain and the attack on Fermat's last problem
- Cauchy and the foundations of analysis
- The prime numbers
- Dirichlet and how to count
- Bernhard Riemann and the geometry of surfaces
- Georg Cantor and the orders of infinity
- The number systems
- Henri Poincare, child phenomenon
- Sonya Kovalevskaya and the mathematics of mechanics
- Emmy Noether and algebra
- Methods of proof
- Alan Turing and cryptography.