Universität Wien
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250067 VO Integration and Stochastics (2024W)

6.00 ECTS (4.00 SWS), SPL 25 - Mathematik
Moodle
Mo 07.10. 11:30-13:00 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock

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Details

Language: English

Lecturers

Classes (iCal) - next class is marked with N

  • Wednesday 02.10. 11:30 - 13:00 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 09.10. 11:30 - 13:00 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 14.10. 11:30 - 13:00 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 16.10. 11:30 - 13:00 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 21.10. 11:30 - 13:00 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 23.10. 11:30 - 13:00 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 28.10. 11:30 - 13:00 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 30.10. 11:30 - 13:00 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 04.11. 11:30 - 13:00 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 06.11. 11:30 - 13:00 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 11.11. 11:30 - 13:00 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 13.11. 11:30 - 13:00 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 18.11. 11:30 - 13:00 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 20.11. 11:30 - 13:00 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 25.11. 11:30 - 13:00 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 27.11. 11:30 - 13:00 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 02.12. 11:30 - 13:00 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 04.12. 11:30 - 13:00 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 09.12. 11:30 - 13:00 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 11.12. 11:30 - 13:00 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 16.12. 11:30 - 13:00 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 08.01. 11:30 - 13:00 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 13.01. 11:30 - 13:00 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 15.01. 11:30 - 13:00 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 20.01. 11:30 - 13:00 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 22.01. 11:30 - 13:00 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 27.01. 11:30 - 13:00 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 29.01. 11:30 - 13:00 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock

Information

Aims, contents and method of the course

We will cover the basics of measure theory: construction of measures, the construction of Lebesgue measure. We will then move to the associated integration theory: monotone convergence theorem, Fatou's lemma, dominated convergence theorem, an introduction to the theory of L^p spaces, Fubini's theorem.
Finally we will see how these ideas can be used to develop a rigorous approach to probability theory. We will discuss random variables, expectation and moments, independence, variance, Markov's and Chebyshev's inequailities, culminating in a proof of the law of large numbers.

I plan to stay close to teh manuscript of Roland Zweimüller, see reading list below.

Assessment and permitted materials

Minimum requirements and assessment criteria

Examination topics

Reading list

Lecture notes by Roland Zweimüller (in German). Downloadable at:
https://www.dropbox.com/scl/fi/8j2v1pwiy7x6hjkyj06sw/IST_Roland.pdf?rlkey=r67iy0jlz07go5mjg15ajhbb9&dl=0

The book "Real and Complex Analysis" by Walter Rudin is a classic.

Association in the course directory

IST

Last modified: Fr 27.09.2024 13:46