# 401-3056-00L Finite Geometries I

Semester | Spring Semester 2022 |

Lecturers | N. Hungerbühler |

Periodicity | two-yearly recurring course |

Language of instruction | German |

### Courses

Number | Title | Hours | Lecturers | ||||
---|---|---|---|---|---|---|---|

401-3056-00 G | Endliche Geometrien I | 2 hrs |
| N. Hungerbühler |

### Catalogue data

Abstract | Finite geometries I, II: Finite geometries combine aspects of geometry, discrete mathematics and the algebra of finite fields. In particular, we will construct models of axioms of incidence and investigate closing theorems. Applications include test design in statistics, block design, and the construction of orthogonal Latin squares. |

Learning objective | Finite geometries I, II: Students will be able to construct and analyse models of finite geometries. They are familiar with closing theorems of the axioms of incidence and are able to design statistical tests by using the theory of finite geometries. They are able to construct orthogonal Latin squares and know the basic elements of the theory of block design. |

Content | Finite geometries I, II: finite fields, rings of polynomials, finite affine planes, axioms of incidence, Euler's thirty-six officers problem, design of statistical tests, orthogonal Latin squares, transformation of finite planes, closing theorems of Desargues and Pappus-Pascal, hierarchy of closing theorems, finite coordinate planes, division rings, finite projective planes, duality principle, finite Moebius planes, error correcting codes, block design |

Literature | - Max Jeger, Endliche Geometrien, ETH Skript 1988 - Albrecht Beutelspacher: Einführung in die endliche Geometrie I,II. Bibliographisches Institut 1983 - Margaret Lynn Batten: Combinatorics of Finite Geometries. Cambridge University Press - Dembowski: Finite Geometries. |

### Performance assessment

Performance assessment information (valid until the course unit is held again) | |

Performance assessment as a semester course | |

ECTS credits | 4 credits |

Examiners | N. Hungerbühler |

Type | session examination |

Language of examination | German |

Repetition | The performance assessment is offered every session. Repetition possible without re-enrolling for the course unit. |

Mode of examination | oral 20 minutes |

This information can be updated until the beginning of the semester; information on the examination timetable is binding. |

### Learning materials

Main link | Skript in der Polybox |

Recording | Aufzeichung der Vorlesung im ETH Videoarchiv |

Livestream der Vorlesung | |

Only public learning materials are listed. |

### Groups

No information on groups available. |

### Restrictions

There are no additional restrictions for the registration. |