Dynamischer Default-Fachbereich geändert auf MAT

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	Lossen, Christoph, Dr. habil. (WMA \| DEPT: MAT)
Lecturers	Korn, Ralf, Prof. Dr. (PROF \| DEPT: MAT) Redenbach, Claudia, Prof. Dr. (PROF \| DEPT: MAT) Ritter, Klaus, Prof. Dr. (PROF \| DEPT: MAT) Sass, Jörn, Prof. Dr. (PROF \| DEPT: MAT)
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.

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).

Requirements for attendance (informal)

Modules:

Requirements for attendance (formal)

None

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

Module Handbook