Course MAT-14-14-K-3
Stochastic Methods (4V+2U, 9.0 LP)
Course Type
| SWS | Type | Course Form | CP (Effort) | Presence-Time / Self-Study | |
|---|---|---|---|---|---|
| - | K | Lecture with exercise classes (V/U) | 186 h | ||
| 4 | V | Lecture | 6.0 CP | 56 h | |
| 2 | U | Exercise class (in small groups) | 3.0 CP | 28 h | |
| (4V+2U) | 9.0 CP | 84 h | 186 h | ||
Basedata
| SWS | 4V+2U |
|---|---|
| CP, Effort | 9.0 CP = 270 h |
| Position of the semester | 1 Sem. in WiSe |
| Level | [3] Bachelor (Core) |
| Language | [DE] German |
| Lecturers |
+ further Lecturers of the department Mathematics
|
| Area of study | [MAT-GRU] Mathematics (B.Sc. year 1 and 2) |
| Livecycle-State | [NORM] Active |
Possible Study achievement
- Verification of study performance: proof of successful participation in the exercise classes (ungraded)
- Examination number (Study achievement): 83220 ("Exercise Class Stochastic Methods")
- Details of the examination (type, duration, criteria) will be announced at the beginning of the course.
Contents
Fundamentals of probability theory:
- basic concepts of probability theory (probability space, random variable, distribution),
- distribution of real-valued random variables (binomial, Poisson, exponential and normal distribution, etc.),
- expected value, variance, covariance,
- distribution of random vectors, multivariate normal distribution as an example,
- conditional probability, independence,
- law of large numbers,
- central limit theorem.
Fundamentals of statistics:
- parameter estimator,
- interval estimator,
- tests.
Outlook on the following areas:
- Monte Carlo simulation,
- linear regression,
- big data and machine learning,
- Markov chains.
Competencies / intended learning achievements
The students know and understand stochastic concepts, the fundamental concepts of probability theory and statistics. They are able to apply stochastic methods to simple practical problems.
Literature
- D. Williams: Weighing the Odds - A Course in Probability and Statistics,
- H.O. Georgii: Stochastik - Einführung in die Wahrscheinlichkeitstheorie und Statistik,
- U. Krengel: Einführung in die Wahrscheinlichkeitstheorie und Statistik,
- K.L. Chung: Elementare Wahrscheinlichkeitsrechnung und stochastische Prozesse.
Materials
Further literature will be announced in the lecture(s); exercise material is provided.
Registration
Registration for the exercise classes via the online administration system URM (https://urm.mathematik.uni-kl.de).
Requirements for attendance (informal)
Modules:
Requirements for attendance (formal)
None
References to Course [MAT-14-14-K-3]
| Module | Name | Context | |
|---|---|---|---|
| [MAT-14-14LBBS-M-3] | Mathematics as Solution Potential B: Introduction to Stochastics (BBS) | P: Obligatory | 4V, 6.0 LP |
| [MAT-14-14-M-3] | Stochastic Methods | P: Obligatory | 4V+2U, 9.0 LP |
| Course-Pool | Name | ||
| [MAT-14-KPOOL-3] | Practical Mathematics (B.Sc. Mathematics) |
Notice