Courant R., Robbins H., Siewart I. What is Mathematics?

2nd ed. — Oxford University Press, 1996. — xxii, 566 p. — ISBN 0-19-510519-2, 978-0195105193.Written for beginners and scholars, for students and teachers, for philosophers and engineers, What is Mathematics? is a sparkling collection of mathematical gems that offers an entertaining and accessible portrait of (he mathematical world. Brought up to date with a new chapter by Ian Stewart, this second edition offers new insights into recent mathematical developments and describes proofs of the Four-Color Theorem and Fermat's Last Theorem, problems that were still open when Courant and Robbins wrote this masterpiece, but ones that have since been solved.
A marvelously literate story, What is Mathematics? opens a window onto the world of mathematics.The Natural Numbers.
The Number System of Mathematics.
Geometrical Constructions. The Algebra of Number Fields.
Projective Geometry. Axiomatics. Non-Euclidean Geometries.
Topology.
Functions and Limits.
MAXIMA and Minima.
The Calculus.
Recent Developments.