Probability theory [MA2409]
Lecture
- Lecturer: Prof. Dr. Noam Berger Steiger
- Time and location of the lecture:
Tuesday 8:15 – 9:45 BC2 0.01.17, Hörsaal (8102.EG.117), Parkring 35-39, Garching-Hochbrück Friday 8:30 – 10:00 Interims Hörsaal 1, Garching-Forschungszentrum - First lecture: Tuesday, April 10, 2018
- Prerequisites: Maß- und Integrationstheorie (MA 2003) and Einführung in die Wahrscheinlichkeitstheorie (MA 1401)
- Content: Based on measure and integration theory, in this course the fundamental concepts of probability theory are presented. Of central importance are the different types of convergence, the concept of stochastic independence, and conditional expectations. In addition, the course will deal with the Radon-Nikodym theorem, product spaces and the construction of stochastic processes. For sequences of independent random variables, laws of large numbers and the central limit theorem will be proved. As an important generalization of partial sums of independent random variables, martingales will be introduced and on this basis we will investigate stopping times and prove the martingale convergence theorem.
- Literature:
- R. Durrett: Probability: theory and examples, fourth edition, Cambridge University press, 2010. Link to the ebook
- A. Gut: Probability: A graduate course, second edition, Springer, 2013. Link to the ebook
- A. Klenke: Wahrscheinlichkeitstheorie, 3. Auflage, Springer, 2013. Link to the ebook
- A. Klenke: Probability theory, Springer, second Edition, 2014. Link to the ebook
Final exams
- Time and place: see TUM-Online
- Remark on the exam: calculators, lecture notes, etc. are not allowed
Exercise sessions
- Organisation of the exercise sessions: Dr. Diana Conache
- Please sign up for one of the exercise groups in TUM-Online. This is necessary in order to obtain access to moodle.
- The exercise sessions start in the week of April 16, 2018.
- Time and location of the exercise sessions:
Group time location tutor language 2 Wed, 08:30-10:00 MI 03.10.011, Garching-Forschungszentrum Diana Conache German 3 Wed, 10:15-11:45 MI 03.10.011, Garching-Forschungszentrum Diana Conache German 8 Fri, 10:00-12:00 MI 03.10.011, Garching-Forschungszentrum Katharina Eichinger English 7 Fri, 10:00-12:00 MI 03.06.011, Garching-Forschungszentrum Johannes Bäumler German 4 Thu, 10:00-12:00 MI 02.08.020, Garching-Forschungszentrum Nannan Hao and Dominik Schmidt English 6 Thu, 16:00-18:00 MI 02.08.020, Garching-Forschungszentrum Stefan Junk English 1 Tue, 10:00-11:30 BC2 3.1.08, Parkring 37-35, Garching-Hochbrück Julian Sieber English 5 Thu, 12:00-14:00 BC2 0.01.05, Parkring 37-35, Garching-Hochbrück Stefan Junk German
Homework
- Every week you will be assigned a problem sheet (homework). You will have access to it via moodle. You should try to solve all homework problems. Your solutions can be written in German or in English. Groups of up to 2 students can hand in their solutions together. Please use the provided cover, and put your solutions in the mailbox "probability theory" in the basement of the mathematics building. Your homework is due on Tuesday at 18:00 one week after it was assigned. Please note that only hand-written homework is accepted. No submission per email is allowed.
- Graded homework will be returned during the exercise sessions two weeks after it was handed in. Homework which is not picked up during the exercise sessions can be found in the shelf located on the right-hand side after the first glass door in building part 03.12. of the MI building.
- Grades on homework: Each exercise is graded from 0 to 4 points, where 4 stands for a perfect solution, 3 for few minor mistakes or missing arguments, 2 for major lacks and 1 for reasonably worked out. If an exercise consists of several parts, each of them has to be worked out reasonably for the whole exercise to count as reasonably worked out. Please check your grade on the homework in moodle. If you disagree with the number of points you obtained, please contact Dr. Diana Conache as soon as possible and at the latest one week after the homework assignment was returned.
- Final grade: The final grade is the grade obtained in the final exam plus a possible bonus. If 70% of all homework problems (not exercise sheets!) are reasonably worked out, then you get a bonus: If you pass one of the final exams (i.e. your grade is 4.0 or better), then your grade is improved by 0.3 (for example 4.0 becomes 3.7, 3.7 becomes 3.3, 3.3 becomes 3.0 etc.). A grade of 1.0 is not changed.