Nonstandard Methods and Applications in Mathematics
Nigel J. Cultand, Mauro Di Nasso, David A. Ross , editors
Year: 2006
ISBN:1-56881-291-4
262 pages. Hardcover.
A collection of research articles that arose from a conference on Nonstandard Analysis and Applications in Mathematics held in Pisa, Italy, June 2002. The papers are a mix of survey articles and research articles. They cover the foundations of nonstandard analysis, nonstandard analysis in pure mathematics and in applied mathematics, and even teaching calculus with nonstandard analysis.
Table of Contents
- Preface
Foundations
- Vieri Benci, Mauro Di Nasso, and Marco Forti
The eightfold path to nonstandard analysis - Sergio Fajardo and H. Jerome Keisler
Neoclosed forcing - Karel Hrbacek
Nonstandard objects in set theory
Pure Mathematics
- Peter A. Loeb
The microscopic behavior of measurable functions - David A. Ross
Nonstandard measure contructions—solutions and problems - Renling Jin
Inverse problem for upper asymptotic density II - Angus Macintyre
Nonstandard analysis and cohomology
Applied Mathematics
- Niegel J. Cutland
Loeb space methods for stochastic Navier-Stokes equations - Manfred P.H. Wolff
Discrete approximations of compact operators and approximations of their spectra - Richard O’Donovan and John Kimber
Nonstandard analysis at pre-university level: Naive magnitude analysis