- propositions, sets, methods of proof, mappings, semi-orderings and equivalence relations,
- integers, division with remainder, greatest common divisor and Euclidean algorithm, Chinese remainder theorem over ℤ,
- vector spaces, Gaussian algorithm, bases and dimension, vector space homomorphisms, solving linear systems of equations, representing matrix of a homomorphism
- determinants, eigenvectors.

# Module MAT-02-90-M-1

## Mathematics for Socioinformatics: Linear Algebra and Analysis (M, 9.0 LP)

## Module Identification

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

MAT-02-90-M-1 | Mathematics for Socioinformatics: Linear Algebra and Analysis | 9.0 CP (270 h) |

## Basedata

CP, Effort | 9.0 CP = 270 h |
---|---|

Position of the semester | 2 Sem. from WiSe |

Level | [1] Bachelor (General) |

Language | [DE] German |

Module Manager | |

Lecturers | |

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

Reference course of study | [INF-82.B16-SG] B.Sc. Socioinformatics |

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-02-11a-K-1 | Mathematics for Socioinformatics: Linear Algebra
| P | 56 h | 64 h |
U-Schein
| - | no | 4.0 | WiSe |

2V+2U | MAT-02-13a-K-1 | Mathematics für Socioinformatics: Analysis
| P | 56 h | 94 h |
UK-Schein
| - | no | 5.0 | SuSe |

- About [MAT-02-11a-K-1]: Title: "Mathematics for Socioinformatics: Linear Algebra"; Presence-Time: 56 h; Self-Study: 64 h
- About [MAT-02-11a-K-1]:
The study achievement
**"[U-Schein] proof of successful participation in the exercise classes (ungraded)"**must be obtained. - About [MAT-02-13a-K-1]: Title: "Mathematics für Socioinformatics: Analysis"; Presence-Time: 56 h; Self-Study: 94 h
- About [MAT-02-13a-K-1]:
The study achievement
**"[UK-Schein] proof of successful participation in the exercise classes (incl. written examination, ungraded)"**must be obtained.

## Evaluation of grades

The module is not graded (only study achievements)..

## Contents

- integer and rational numbers, countability,
- sequences, convergence, Cauchy sequences, convergence criteria, application: existence and calculation of square roots, real numbers,
- series, geometric series, convergence and divergence criteria, Cauchy product of series, functions, continuity,
- intermediate value theorem, power series, exponential function and functional equation, sine and cosine,
- differentiability, rules of derivation, derivation of power series, Taylor series, extreme values, mean value theorem, rule of l'Hospital,
- Riemann integral, antiderivative and fundamental theorem of calculus, integration rules,

inverse function, logarithm, general powers, derivative of the inverse function,

- outlook on ideas and concepts of multivariate analysis: limit values and continuity in several variables, partial derivatives, gradient and Hesse matrix, Taylor formula and local extrema.

## Competencies / intended learning achievements

Upon successful completion of this module, the students have achieved the following learning outcomes:

- The students know the fundamental formation of mathematical concepts and basic proof methods in mathematics (in particular, proof by contraposition and proof by induction).
- On the basis of a structure-oriented approach, they are trained in analytical thinking and their ability to think abstractly has been promoted.
- They have learned to comprehend mathematical proofs and are able to prove or disprove mathematical statements independently in simple examples.
- They know and understand the basic concepts of linear algebra. Through an algorithmic approach they have learned the fundamental statements and methods of linear algebra and are able to apply them to practical problems.
- They know and understand the basic concepts, statements and methods of one-dimensional analysis and know applications of those in computer science.
- Based on an outlook they have developed an elementary understanding of the generalisation of these concepts to multi-dimensional analysis.
- In the exercise classes they have acquired a confident, precise and independent handling of the terms, statements and methods from the lecture.
- In addition, their presentation skills and ability to work in a team have been promoted.

## Literature

- G. Fischer: Lineare Algebra,
- S. Bosch: Lineare Algebra,
- K. Jänich: Linear Algebra,
- B. Kreußler, G. Pfister: Mathematik für Informatiker: Algebra, Analysis, Diskrete Strukturen.

- O. Forster: Analysis 1, Analysis 2,
- H. Heuser: Lehrbuch der Analysis, Teil 1 und Teil 2,
- M. Barner, F. Flohr: Analysis I, Analysis II,
- K. Königsberger: Analysis 1, Analysis 2,
- B. Kreußler, G. Pfister: Mathematik für Informatiker: Algebra, Analysis, Diskrete Strukturen.

## Registration

Registration for the exercise classes 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-02-90-M-1]

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

[INF-82.B16-SG] B.Sc. Socioinformatics | [Compulsory Modules] Computer Science | [P] Compulsory |