# 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 | |

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 |

## 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.

- It is a
- 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.

## Contents

- 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 of the module (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 of the module (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 | [Section (non-specific)] Compulsory Modules | [P] Compulsory |

## Notice