Dynamischer Default-Fachbereich geändert auf MAT

Module MAT-14-00L-M-3

Mathematics as a Potential for Solving Problems A: Modelling and Applied Mathematics (M, 10.0 LP)

Module Identification

Module Number	Module Name	CP (Effort)
MAT-14-00L-M-3	Mathematics as a Potential for Solving Problems A: Modelling and Applied Mathematics	10.0 CP (300 h)

Basedata

CP, Effort	10.0 CP = 300 h
Position of the semester	2 Sem. from WiSe/SuSe
Level	[3] Bachelor (Core)
Language	[DE] German
Module Manager	Lossen, Christoph, Dr. habil. (WMA \| DEPT: MAT)
Lecturers	Lecturers of the department Mathematics
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

Notice

For students who complete their Bachelor's examination according to the examination regulations from 24.10.2007, the version of this module from the summer semester 2019 (7 CP, without the part "Introduction to Scientific Programming") applies.

Module Part #A "Introduction to Scientific Programming" (Obligatory, 3.0 LP)

Type/SWS	Course Number	Title	Choice in Module-Part	Presence-Time / Self-Study		SL	SL is required for exa.	PL	Sem.
1V+1U	MAT-14-00L-K-2	Introduction to Scientific Programming (for Students of Teacher Training Programmes)	P	28 h	62 h	U-Schein	-	no	WiSe/SuSe

About [MAT-14-00L-K-2]: Title: "Introduction to Scientific Programming (for Students of Teacher Training Programmes)"; Presence-Time: 28 h; Self-Study: 62 h
About [MAT-14-00L-K-2]: The study achievement [U-Schein] proof of successful participation in the exercise classes (ungraded) must be obtained.

Module Part #B "Practical Mathematics" (Obligatory, 4.0 LP)

Type/SWS	Course Number	Title	Choice in Module-Part	Choice in Course-Pool	Presence-Time / Self-Study		SL	SL is required for exa.	PL	Sem.
KPOOL	MAT-14L-KPOOL-3	Practical Mathematics (B.Ed. Mathematics)	P	WP-1			U-Schein	-	PL1	*

About [MAT-14L-KPOOL-3]: Title: "Practical Mathematics (B.Ed. Mathematics)";
About [MAT-14L-KPOOL-3]: A course from the course pool must be selected.
About [MAT-14L-KPOOL-3]: The study achievement [U-Schein] proof of successful participation in the exercise classes (ungraded) must be obtained.

Module Part #C "Modelling/Practical Mathematics" (Obligatory, 3.0 LP)

In this part of the module either one of the courses on mathematical modelling (3 LP each) or a practical course from the catalogue on Practical Mathematics (2 LP) has to be successfully attended. If the practical course from the catalogue of Practical Mathematics (2 LPs) is chosen, an additional course from the catalogue of Practical Mathematics (without proof of successful participation in the exercise classes) must be selected.

Type/SWS	Course Number	Title	Choice in Module-Part	Choice in Course-Pool	Presence-Time / Self-Study		SL	SL is required for exa.	PL	Sem.
2S	MAT-16-14-K-3	Proseminar Mathematical Modelling	WP		28 h	62 h	PS-Schein	ja	PL2	WiSe
2V	MAT-14-01-K-3	Mathematical Modelling	WP		28 h	62 h	PROJ-Schein	-	PL1	SuSe
KPOOL	MAT-14LP-KPOOL-3	Practical Courses on Practical Mathematics (B.Ed. Mathematics)	WP	WP-1			L-Schein	-	no	*
KPOOL	MAT-14L-KPOOL-3	Practical Mathematics (B.Ed. Mathematics)	WP	WP-1			-	-	PL1	*

About [MAT-16-14-K-3]: Title: "Proseminar Mathematical Modelling"; Presence-Time: 28 h; Self-Study: 62 h
About [MAT-16-14-K-3]: The study achievement [PS-Schein] proof of successful participation in the proseminar must be obtained. It is a prerequisite for the examination for PL2.
About [MAT-14-01-K-3]: Title: "Mathematical Modelling"; Presence-Time: 28 h; Self-Study: 62 h
About [MAT-14-01-K-3]: The study achievement [PROJ-Schein] proof of successful completion of the project(s) must be obtained.
About [MAT-14LP-KPOOL-3]: Title: "Practical Courses on Practical Mathematics (B.Ed. Mathematics)";
About [MAT-14LP-KPOOL-3]: When choosing the course pool, a course must be selected from it.
About [MAT-14LP-KPOOL-3]: The study achievement [L-Schein] proof of successful participation in the practical course / lab must be obtained.
About [MAT-14L-KPOOL-3]: Title: "Practical Mathematics (B.Ed. Mathematics)";
About [MAT-14L-KPOOL-3]: When choosing the course pool, a course must be selected from it.

Examination achievement PL1

Form of examination: oral examination (20-30 Min.)
Examination Frequency: each semester

Examination achievement PL2

Form of examination: combination of talk and written elaboration
Examination Frequency: Examination only within the course

If one of the chosen courses is the proseminar "Mathematical Modelling", the examination consists of two parts: an individual oral examination (PL1) covering the topics of the selected lecture on Practical Mathematics and a written and/or oral examination for the proseminar (usually a combination of an oral presentation and a written paper); the type and duration of the examination will be announced by the lecturer (no later than) at the beginning of the proseminar.

Evaluation of grades

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

Selection from the following topics of Practical Mathematics: numerical solving of linear systems of equations; perturbation theory; linear curve fitting problems; linear optimisation (simplex method, interior-point methods, duality theory); numerical computation of eigenvalues; numerical solving of non-linear systems of equations; approximation and interpolation; numerical integration; numerical solving of differential equations; graph theory; shortest graph problems; network flows;
Modelling: fundamentals of model construction/modelling; modelling of small and medium application problems; independent processing of small problems (starting with the choice of the model, the application of mathematical algorithms up to the interpretation of the solution); discussion of the possible implementations;
Introduction to scientific programming / practical course on programming: fundemental ideas of programming and basic programming structures, introduction to a current programming language, introduction to current mathematical software.

Competencies / intended learning achievements

The students

know the basic principles of mathematical modelling and are able to work on real problems from different fields of application with (previously known or also newly introduced) mathematical methods;
recognise the sensitive dependence of the solutions found on the chosen model and method and they develop an understanding of the relevance of the mathematical theorems on which they are based and their prerequisites when applying numerical methods;
use (depending on the choice of the course) methods for solving linear and non-linear systems of equations or for solving linear optimisation problems, are able to practically implement solution methods on the computer and to use standard software;
are able to recognise and take into account problems that arise during the realisation of numerical methods on the computer;
understand the idea of the approximate solution of mathematical problems and know typical application examples for the occurrence of optimisation and approximation problems;
master a programming language and the use of current mathematical software; they learn to implement mathematical solution algorithms on the computer; they know about the limits of the applicability of computers and mathematical software.

Literature

see the respective course descriptions in the course catalogue [MAT-14L-KPOOL-3].

Materials

Further literature will be announced in the courses; exercise material will be provided.

Registration

Registration for proseminars, exercise classes and practical courses via online procedures (to be announced in advance or in the lecture).

Requirements for attendance (informal)

Modules:

Requirements for attendance (formal)

None

References to Module / Module Number [MAT-14-00L-M-3]

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

Module Handbook