Two Millennia of Mathematics From Archimedes to Gauss
This book is intended for those who love mathematics, including under graduate students of mathematics, more experienced students, and the vast number of amateurs, in the literal sense of those who do something for the love of it. I hope it will also be a useful source of material for those who tea...
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| Format: | eBook |
| Language: | English |
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New York, NY
Springer New York
2000, 2000
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| Edition: | 1st ed. 2000 |
| Series: | CMS Books in Mathematics, Ouvrages de mathématiques de la SMC
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| Subjects: | |
| Online Access: | |
| Collection: | Springer Book Archives -2004 - Collection details see MPG.ReNa |
Table of Contents:
- 1 From Archimedes to Gauss
- 1.1 Archimedes and Pi
- 1.2 Variations on a Theme
- 1.3 Playing a Mean Game
- 1.4 Gauss and the AGM
- 2 Logarithms
- 2.1 Exponential Functions
- 2.2 Logarithmic Functions
- 2.3 Napier and Briggs
- 2.4 The Logarithm as an Area
- 2.5 Further Historical Notes
- 3 Interpolation
- 3.1 The Interpolating Polynomial
- 3.2 Newton’s Divided Differences
- 3.3 Finite Differences
- 3.4 Other Differences
- 3.5 Multivariate Interpolation
- 3.6 The Neville-Aitken Algorithm
- 3.7 Historical Notes
- 4 Continued Fractions
- 4.1 The Euclidean Algorithm
- 4.2 Linear Recurrence Relations
- 4.3 Fibonacci Numbers
- 4.4 Continued Fractions
- 4.5 Historical Notes
- 5 More Number Theory
- 5.1 The Prime Numbers
- 5.2 Congruences
- 5.3 Quadratic Residues
- 5.4 Diophantine Equations
- 5.5 Algebraic Integers
- 5.6 The equation x3 + y3 = z3
- 5.7 Euler and Sums of Cubes
- References