Stochastic Methods (4V+2U, 9.0 LP)
|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|
|CP, Effort||9.0 CP = 270 h|
|Position of the semester||1 Sem. in WiSe|
|Level|| Bachelor (Core)|
+ further Lecturers of the department Mathematics
|Area of study||[MAT-GRU] Mathematics (B.Sc. year 1 and 2)|
The course is accompanied by a programming lab course: [MAT-14-14P-K-3].
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.
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,
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.
- 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.
Further literature will be announced in the lecture(s); exercise material is provided.
Registration for the exercise classes via the online administration system URM (https://urm.mathematik.uni-kl.de).
Requirements for attendance (informal)
Requirements for attendance (formal)