Books : reviews

Ian Stewart, David O. Tall.
The Foundations of Mathematics.
OUP. 1977

This is a book for readers in transition from ‘school mathematics’ to the fully-fledged type of thinking used by professional mathematicians. It should prove useful for first-year students in universities, polytechnics, and colleges, to sixth-formers contemplating further study, and anyone else interested in the critical change in mathematical thinking from intuition to rigour. It develops the more formal approach as a natural outgrowth of the pattern of underlying ideas, building on a school mathematics background to develop the viewpoint of an advanced practising mathematician. The topics covered include: the nature of mathematical thinking; a review of the intuitive development of familiar number systems; sets, relations, functions; an introduction to logic as used by practising mathematicians, methods of proof (including how a mathematical proof is written); development of axiomatic number systems from natural numbers and proof by induction to the construction of the real and complex numbers; the real numbers as a complete ordered field; cardinal numbers; foundations in retrospect.

Ian Stewart, David O. Tall.
Complex Analysis: the hitch-hiker's guide to the plane.
CUP. 1983