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).
Requirements for attendance (informal)
Modules:
- [MAT-10-11-M-2] Fundamentals of Mathematics A: Linear Algebra I and Analysis I (M, 15.0 LP)
- [MAT-10-12L-M-2] Fundamentals of Mathematics B: Linear Algebra II and Analysis II (M, 9.0 LP)
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 |