FOM: Geometrical and Numerical Continuum.

[Colin McLarty]

Luigi Borzacchini <gibi at pascal.dm.uniba.it> wrote:

>I am looking for recent references about a classic topic: the relationship
between geometrical and numerical continuum.

        There will be many more recent references in John Bell's

A Primer of Infinitesimal Analysis. Cambridge University Press, 1998.

It uses "synthetic differential geometry" in a number of ways, rather than
arithmetized analysis. Here is the Table of Contents: 

1. Basic features of smooth worlds
2. Basic differential calculus
3. First applications of the differential calculus
4. Applications to physics
5. Multivariable calculus and applications
6. The definite integral. Higher order infinitesimals
7. Synthetic geometry
8. Smooth infinitesimal analysis as an axiomatic system

Appendix. Models for smooth infinitesimal analysis.

You can find a description at http://www.cup.org/Titles/62/0521624010.html