What is mathematics? : an elementary approach to ideas and methods
Courant Richard
- 2ND ED
- New York : Oxford University Press, 1996.
- 566 pages : illustrations ; . 23 cm
Chapter I. The natural numbers -- Supplement to Chapter I. The theory of numbers -- Chapter II. The number system of mathematics -- Supplement to Chapter II. The algebra of sets -- Chapter III. Geometrical construction. The algebra of number fields -- Chapter IV. Projective geometry. axiomatics. non-euclidean geometries -- Chapter V. Topology -- Chapter VI. Functions and limits -- Supplement to Chapter VI. More examples on limits and continuity -- Chapter VII. Maxima and minima -- Chapter VIII. The calculus -- Supplement to Chapter VIII -- Chapter IX. Recent developments -
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 the 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