Module Handbook

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Module MAT-14-14L-M-3

Mathematics as Solution Potential B: Introduction to Stochastics (Gym, RS) (M, 8.0 LP)

Module Identification

Module Number Module Name CP (Effort)
MAT-14-14L-M-3 Mathematics as Solution Potential B: Introduction to Stochastics (Gym, RS) 8.0 CP (240 h)
MAT-14-14L_ERW-M-3 Mathematics as Solution Potential B: Introduction to Stochastics 12.0 CP (360 h)
Hint concerning Module MAT-14-14L_ERW-M-3:
Due to previous knowledge from the modules [MAT-20-00-M-2] and [MAT-10-12L-M-2] (or [MAT-10-11-M-2]) that has to be acquired in self-study, students who study mathematics in the "Zertifikatsstudiengang Erweiterungsprüfung" receive 12 LP for this module.

Basedata

CP, Effort 8.0 CP = 240 h
Position of the semester 1 Sem. in WiSe
Level [3] Bachelor (Core)
Language [DE] German
Module Manager
Lecturers
Area of study [MAT-EDU] Mathematics (B.Ed./M.Ed.)
Reference course of study [MAT-31.105-SG] B.Ed. LaGR 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-14-14L-K-3
Stochastic Methods (für Students of Teacher Training Programmes)
P 84 h 156 h
U-Schein
- PL1 8.0 WiSe
  • About [MAT-14-14L-K-3]: Title: "Stochastic Methods (für Students of Teacher Training Programmes)"; Presence-Time: 84 h; Self-Study: 156 h
  • About [MAT-14-14L-K-3]: The study achievement [U-Schein] proof of successful participation in the exercise classes (ungraded) must be obtained.

Examination achievement PL1

  • Form of examination: oral examination (20-30 Min.)
  • Examination Frequency: each semester
  • Examination number: 80510 ("Stochastic Methods")

Evaluation of grades

The grade of the module examination is also the module grade.


Contents

Introduction to Stochastics.

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;
  • Monte Carlo simulation;
  • central limit value theorem.

Fundamental of statistics:

  • parameter estimator;
  • interval estimator;
  • tests.

Competencies / intended learning achievements

The students
  • are familiar with stochastic concepts, the fundamental concepts of probability theory and statistics;
  • can apply stochastic methods to simple practical problems
  • can recognise and take into account problems that arise when numerical methods are realised on the computer.

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.

Registration

Registration for the exercise classes via the online administration system URM (https://urm.mathematik.uni-kl.de).

References to Module / Module Number [MAT-14-14L_ERW-M-3]

Course of Study Section Choice/Obligation
[MAT-B4.105-SG] ZEP LaG Mathematics Compulsory Modules [P] Compulsory
[MAT-B2.105-SG] ZEP LaRSP Mathematics Compulsory Elective Modules [WP] Compulsory Elective
[MAT-B5.105-SG] ZEP LaBBS Mathematics Compulsory Elective Modules [WP] Compulsory Elective

References to Module / Module Number [MAT-14-14L-M-3]

Course of Study Section Choice/Obligation
[MAT-31.105-SG] B.Ed. LaGR Mathematics Compulsory Modules [P] Compulsory