Foundations of mathematics

the long version

This book is concerned with those foundational questions in elementary algebra, calculus and geometry, that are almost always left unanswered in undergraduate courses in these subjects. Among the topics considered are non-standard analysis, the relationship between classical geometric theorems (such as those of Pascal and Desargues) and field axioms, questions of decidability, and combinatorial logic. An attractive feature is the case given to the historical context in which foundational questions have arisen, and to the early attempts made to resolve them. From the ZENTRALBLATT review of the German edition: "It isone of those rare books which give you freedom and fantasy to reconsider themost common concepts of mathematics...The book explains carefully, using motivating examples and sometimes quite original proofs, the developmentof crucial ideas in important branches of mathematics. It is a pleasure to read it."