Module Handbook

  • Dynamischer Default-Fachbereich geändert auf MAT

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

Notice

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.

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)