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An Enlarged View of the Mathematical Universe
by
Robert Goldblatt
Victoria University of Wellington
Nonstandard analysis was originally conceived by Abraham Robinson as a way of using methods from mathematical logic to develop the differential and integral calculus on the basis of infinitely small and infinitely large numbers.
This talk will begin by discussing some of the historical background to these ideas, particularly in relation to the work of Archimedes, Leibniz, and Euler. That will be followed by a general description of the hyperreal number system and some of the axioms used to develop its concepts and properties, along with examples of proofs from the nonstandard point of view.
The underlying theme is that nonstandard analysis continues to evolve as a powerful methodology for providing new approaches to old ideas and theorems, new objects of mathematical interest, and new principles for reasoning about them.
Robert Goldblatt, Lectures on the Hyperreals, Graduate Texts in Mathematics, Springer-Verlag, 1998.
Date received: June 9, 1998
Copyright © 1998 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cabd-43.