## 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