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250071 VO Nonstandard Analysis and Applications (2016S)

3.00 ECTS (2.00 SWS), SPL 25 - Mathematik

Details

Language: English

Examination dates

Lecturers

Classes (iCal) - next class is marked with N

Wednesday 02.03. 16:45 - 18:15 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 09.03. 16:45 - 18:15 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 16.03. 16:45 - 18:15 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 06.04. 16:45 - 18:15 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 13.04. 16:45 - 18:15 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 20.04. 16:45 - 18:15 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 27.04. 16:45 - 18:15 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 04.05. 16:45 - 18:15 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 11.05. 16:45 - 18:15 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 18.05. 16:45 - 18:15 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 25.05. 16:45 - 18:15 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 01.06. 16:45 - 18:15 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 08.06. 16:45 - 18:15 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 15.06. 16:45 - 18:15 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 22.06. 16:45 - 18:15 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 29.06. 16:45 - 18:15 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock

Information

Aims, contents and method of the course

The aim of the course is to present many ideas and methods of Nonstandard Analysis (NSA), focusing more on applications than on foundational aspects. The course will be divided in three parts. In the first part (two to three lessons) we will present the concept of non-Archimedean extension of the reals (in particular of infinite and infinitesimal element), and we will show how this notion can be used to simplify the definitions of many basic concepts of real analysis and topology, as well as the proofs of many important basic results.

In the second part (two to three lessons) we will present several ways to formalize the construction of nonstandard extensions, and we will present the important concepts of transfer, saturation, internal and external objects. In the third part (all the remaining lessons) we will present several applications of NSA in different mathematical settings, e.g. to analysis,
topology, probability and combinatorial number theory. Many of these applications will be based on the notions of "hyperfinite extension" and Loeb measure.

Assessment and permitted materials

oral exam

Minimum requirements and assessment criteria

reproducing the notions, results, and proofs presented at the blackboard during the lectures (at least in a mathematically equivalent way)

Examination topics

All the topics presented in the course.

Reading list

R.Goldblatt, Lectures on the Hyperreals (An Introduction to
Nonstandard Analysis), Springer, 1988.
S.Albeverio, J.E.Fenstad, R.Hoegh-Krohn, T.Lindstrom, Nonstandard Methods
in Stochastic Analysis and Mathematical Physics, Dover Books on
Mathematics, 2009.
P.A.Loeb, M.P.H.Wold (eds.), Nonstandard Analysis for the Working
Mathematician, Springer, 2nd edition, 2015.

Association in the course directory

MANV

Last modified: Mo 07.09.2020 15:40