# Module MAT-10-11P-M-2

## Fundamentals of Mathematics I (for Students of Physics) (M, 15.0 LP)

## Module Identification

Module Number | Module Name | CP (Effort) |
---|---|---|

MAT-10-11P-M-2 | Fundamentals of Mathematics I (for Students of Physics) | 15.0 CP (450 h) |

## Basedata

CP, Effort | 15.0 CP = 450 h |
---|---|

Position of the semester | 1 Sem. in WiSe/SuSe |

Level | [2] Bachelor (Fundamentals) |

Language | [DE] German |

Module Manager | |

Lecturers | |

Area of study | [MAT-Service] Mathematics for other Departments |

Reference course of study | [PHY-82.128-SG] B.Sc. Physics |

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. | |
---|---|---|---|---|---|---|---|---|---|---|

2V+2U | MAT-10-11B-K-2 | Fundamentals of Mathematics I: Linear Algebra
| P | 56 h | 124 h |
SL1
| ja | PL1 | 6.0 | WiSe/SuSe |

4V+2U+2T | MAT-10-11A-K-2 | Fundamentals of Mathematics I: Analysis
| P | 112 h | 158 h |
SL1
| ja | PL1 | 9.0 | WiSe/SuSe |

- About [MAT-10-11B-K-2]: Title: "Fundamentals of Mathematics I: Linear Algebra"; Presence-Time: 56 h; Self-Study: 124 h
- About [MAT-10-11B-K-2]:
The study achievement
**SL1**must be obtained.- It is a
__prerequisite for the examination__for PL1.

- It is a
- About [MAT-10-11A-K-2]: Title: "Fundamentals of Mathematics I: Analysis"; Presence-Time: 112 h; Self-Study: 158 h
- About [MAT-10-11A-K-2]:
The study achievement
**SL1**must be obtained.- It is a
__prerequisite for the examination__for PL1.

- It is a

## Study achievement SL1

- Verification of study performance: proof of successful participation in the exercise classes (incl. written examination)
- Study achievement is a prerequisite for the examination.
- Examination number (Study achievement): 82015
("Exercise Class Fundamentals of Mathematics I")
The proof of successful participation in the exercise classes (incl. written examination) for "Fundamentals of Mathematics I" can be obtained in two parts (proof of successful participation in the exercise classes of [MAT-10-11B-K-2] "Fundamentals of Mathematics I: Linear Algebra" and proof of successful participation in the exercise classes of [MAT-10-11A-K-2] "Fundamentals of Mathematics I: Analysis").

## Examination achievement PL1

- Form of examination: oral examination (30-45 Min.)
- Examination Frequency: each semester

## Evaluation of grades

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

## Contents

a) Fundamentals of Mathematics I: Linear Algebra:

- vector spaces,
- linear mappings,
- linear systems of equations,
- matrices,
- determinants.

b) Fundamentals of Mathematics I: Analysis:

- real and complex numbers,
- sequences, limit values and series; power series,
- elementary functions; continuity,
- differentiation (in the one-dimensional case),
- integration (in the one-dimensional case).

## Competencies / intended learning achievements

Upon successful completion of this module, the students

- have mastered the basic concepts of Linear Algebra and one-dimensional Analysis as a foundation for further scientific studies; through the exercises and the tutorials they have acquired a confident, precise and independent handling of the terms, statements and methods dealt with in the lectures;
- are trained in analytical thinking; they are able to recognise abstract structures and to work on mathematical problems imaginatively;
- are able to convey elementary mathematical facts; their teamwork and communication skills have been trained through exercises and tutorials.

## Literature

- G. Fischer: Lineare Algebra,
- K. Jänich: Lineare Algebra,
- H.-J. Kowalsky, G.O. Michler: Lineare Algebra,
- S. Bosch: Lineare Algebra,
- O. Forster: Analysis 1,
- H. Heuser: Lehrbuch der Analysis, Teil 1,
- M. Barner, F. Flohr: Analysis I,
- K. Königsberger: Analysis 1.

## Materials

Further literature will be announced in the lecture(s); exercise material is provided.

## Registration

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

## Requirements for attendance of the module (informal)

**None**

## Requirements for attendance of the module (formal)

**None**

## References to Module / Module Number [MAT-10-11P-M-2]

Course of Study | Section | Choice/Obligation |
---|---|---|

[PHY-82.128-SG] B.Sc. Physics | [Fundamentals] Mathematikmodule | [P] Compulsory |

## Notice

The courses are also offered in distance learning as part of the programme „Früheinstieg in das Mathematikstudium“ (FiMS), see https://fims.mathematik.uni-kl.de