This book is published by Springer-Verlag, in the Springer Undergraduate Mathematics Series, in February 1999. |

Another book in the series is Geoff Smith's Introductory Mathematics: Algebra and Analysis.

A PDF file of the preface and table of contents is available.

Solutions to the exercises (PDF files):

- Chapter 1: Naive set theory
- Chapter 2: Ordinal numbers
- Chapter 3: Logic
- Chapter 4: First-order logic

Here is a list of known misprints, together with comments and improvements from various readers.

From the review by A. M. Coyne in *Zentralblatt für Mathematik*:

The text is clearly written. It would make an excellent first course in foundational issues in mathematics at the undergraduate level.

- For topos theory: S. MacLane & I. Moerdijk,
*Sheaves in Geometry and Logic: A first introduction to topos theory*, Springer 1990. (Suggested by Steve Awodey.) - A computer scientist's view: Paul Taylor,
*Practical Foundations of Mathematics*, Cambridge University Press, 1999. - A book about how our brains are wired to do mathematics: Brian
Butterworth,
*The Mathematical Brain*, Macmillan, London, 1999. - "Journey into a Dark Heart", by Peter Høeg, from
*Tales of the Night*, Harville Press, London, 1990, features Gödel's Theorem as part of the plot.

- Venn diagrams by Frank Ruskey
- Beginnings of set theory (on MacTutor History of Mathematics site at St Andrews)
- British Logic Colloquium (with many further links!)
- Theory and Applications of Categories (electronic journal)
- Gödel on the Net
- Fast-growing functions and unprovable theorems by Andrew Burbanks
- Joshu's Mu: further information by Richard Leedham-Green

Peter J. Cameron

27 January 2003.