This book is a collection of inter-connected topics in areas of mathematics which particularly interest the author, ranging over the two millennia from the work of Archimedes, who died in the year 212 BC, to the "Werke" of Gauss, who was born in 1777. The book is intended for those who love mathematics, including undergraduate students of mathematics, more experienced students and the vast unseen host of amateur mathematicians. It will also be a useful source of material for those who teach mathematics.

Autorentext

George Phillips has lectured and researched in mathematics at the University of St. Andrews, Scotland. His most recent book, Two Millenia of Mathematics: From Archimedes to Gauss (Springer 2000), received enthusiastic reviews in the USA, Britain and Canada. He is well known for his clarity of writing and his many contributions as a researcher in approximation theory.

Inhalt
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.