- Types of convergence (stochastic, almost sure, weak, L_p-convergence, convergence in distribution),
- Characteristic functions,
- Sums of independent random variables,
- Strong laws of large numbers, variants of the central limit theorem,
- Conditional expectation,
- Martingales in discrete time,
- Brownian motion.
Module MAT-60-11-M-4
Probability Theory (M, 9.0 LP)
Module Identification
Module Number | Module Name | CP (Effort) |
---|---|---|
MAT-60-11-M-4 | Probability Theory | 9.0 CP (270 h) |
Basedata
CP, Effort | 9.0 CP = 270 h |
---|---|
Position of the semester | 1 Sem. in WiSe |
Level | [4] Bachelor (Specialization) |
Language | [EN] English |
Module Manager | |
Lecturers | |
Area of study | [MAT-STO] Stochastics/Statistics/Financial Mathematics |
Reference course of study | [MAT-88.105-SG] M.Sc. Mathematics |
Livecycle-State | [NORM] Active |
Courses
Type/SWS | Course Number | Title | Choice in Module-Part | Presence-Time / Self-Study | SL | SL is required for exa. | PL | CP | Sem. | |
---|---|---|---|---|---|---|---|---|---|---|
4V+2U | MAT-60-11-K-4 | Probability Theory
| P | 84 h | 186 h |
UK-Schein
| - | PL1 | 9.0 | WiSe |
- About [MAT-60-11-K-4]: Title: "Probability Theory"; Presence-Time: 84 h; Self-Study: 186 h
- About [MAT-60-11-K-4]: The study achievement [UK-Schein] proof of successful participation in the exercise classes (incl. written examination, ungraded) must be obtained.
Examination achievement PL1
- Form of examination: oral examination (20-30 Min.)
- Examination Frequency: each semester
- Examination number: 84270 ("Probability Theory")
Evaluation of grades
The grade of the module examination is also the module grade.
Contents
Competencies / intended learning achievements
Upon completion of the module, the students have gained advanced knowledge in stochastics and the foundations required for further research in the field of stochastic processes. They understand the proofs presented in the lecture and are able to comprehend and explain them.
By completing exercises, the students will have developed a skilled, precise and independent handling of the terms, propositions and techniques taught in the lecture. In addition, they have learnt how to apply these techniques to new problems, analyze them and develop solution strategies independently or by team work.
Literature
- H. Bauer: Probability Theory,
- P. Billingsley: Probability and Measure,
- P. Gänssler, W. Stute: Wahrscheinlichkeitstheorie,
- A. Klenke: Wahrscheinlichkeitstheorie.
Registration
Registration for the exercise classes via the online administration system URM (https://urm.mathematik.uni-kl.de)
Requirements for attendance (informal)
Modules:
- [MAT-10-1-M-2] Fundamentals of Mathematics (M, 28.0 LP)
- [MAT-14-14-M-3] Stochastic Methods (M, 9.0 LP)
Courses
Requirements for attendance (formal)
None
References to Module / Module Number [MAT-60-11-M-4]
Course of Study | Section | Choice/Obligation |
---|---|---|
[MAT-88.105-SG] M.Sc. Mathematics | Pure Mathematics | [WP] Compulsory Elective |
[MAT-88.105-SG] M.Sc. Mathematics | Applied Mathematics | [WP] Compulsory Elective |
[MAT-88.706-SG] M.Sc. Mathematics International | Pure Mathematics | [WP] Compulsory Elective |
[MAT-88.706-SG] M.Sc. Mathematics International | Applied Mathematics | [WP] Compulsory Elective |
[MAT-88.118-SG] M.Sc. Industrial Mathematics | General Mathematics | [WP] Compulsory Elective |
[MAT-88.276-SG] M.Sc. Business Mathematics | General Mathematics | [WP] Compulsory Elective |
Notice