Warning! The directory is not yet complete and will be amended until the beginning of the term.

250091 VO Number theoretic methods in numerical analysis (2024S)

3.00 ECTS (2.00 SWS), SPL 25 - Mathematik

MAMV

Moodle

Registration/Deregistration

Note: The time of your registration within the registration period has no effect on the allocation of places (no first come, first served).

Details

Language: English

Examination dates

Tuesday 27.08.2024

Lecturers

Nicki Holighaus

Classes (iCal) - next class is marked with N

The lecture on 12.06. Is cancelled. Please see the course Moodle for details/homework.

Wednesday 06.03. 09:45 - 11:15 Hörsaal 17 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 13.03. 09:45 - 11:15 Hörsaal 17 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 20.03. 09:45 - 11:15 Hörsaal 17 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 10.04. 09:45 - 11:15 Hörsaal 17 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 17.04. 09:45 - 11:15 Hörsaal 17 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 24.04. 09:45 - 11:15 Hörsaal 17 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 08.05. 09:45 - 11:15 Hörsaal 17 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 15.05. 09:45 - 11:15 Hörsaal 17 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 22.05. 09:45 - 11:15 Hörsaal 17 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 29.05. 09:45 - 11:15 Hörsaal 17 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 05.06. 09:45 - 11:15 Hörsaal 17 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 12.06. 09:45 - 11:15 Hörsaal 17 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 19.06. 09:45 - 11:15 Hörsaal 17 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 26.06. 09:45 - 11:15 Hörsaal 17 Oskar-Morgenstern-Platz 1 2.Stock

Information

Aims, contents and method of the course

In this lecture, we will develop the fundamental theoretical results underlying the quasi-Monte Carlo method for numerical integration, including the concepts of uniform distribution modulo 1 and discrepancy. In particular, for a chosen, finite point set in the domain of integration, we can bounded the integration error of the quasi-Monte Carlo (QMC) method by a quantity depending solely on the smoothness of the function to be integrated and the discrepancy of the point set (the Koksma-Hlawka inequality). As a consequence, point sets (and sequences) that have low discrepancy are crucial for successful application of QMC. Hence, we will also study some of the most important construction rules for low discrepancy sets.

Note: The lecture will be held in English language.

Assessment and permitted materials

Unless the number of attendees is unexpectedly high, participants that require the ECTS credits can arrange an oral exam with the lecturer. In the oral exam, the candidate should be able to convincingly demonstrate their understanding of the course materials.

Minimum requirements and assessment criteria

A positive result on the oral exam is required to pass.

Examination topics

The exam will cover material selected from all contents of the lecture.

Reading list

This lecture is based on Prof. Friedrich Pillichhammer's (JKU Linz) lecture notes "Zahlentheoretische Methoden in der Numerik" (in German) and the book "Leobacher, G. and Pillichshammer, F., Introduction to Quasi-Monte Carlo Integration and Applications, Birkhäuser/Springer, 2014". The (German) lecture notes will be made available, piece by piece, during the lecture. Unfortunately, at the moment, it is not expect that typeset English lecture notes can be offered.

Extended literature suggestions for students interested in delving deeper will be provided when appropriate and/or on request.

Association in the course directory