# Search result: Catalogue data in Autumn Semester 2021

Mathematics Bachelor | ||||||

Electives | ||||||

Selection: Geometry | ||||||

Number | Title | Type | ECTS | Hours | Lecturers | |
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401-3057-00L | Finite Geometries IIDoes not take place this semester. | W | 4 credits | 2G | N. Hungerbühler | |

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. | |||||

401-4207-71L | Coxeter Groups from a Geometric Viewpoint | W | 4 credits | 2V | M. Cordes | |

Abstract | Introduction to Coxeter groups and the spaces on which they act. | |||||

Learning objective | Understand the basic properties of Coxeter groups. | |||||

Literature | Brown, Kenneth S. "Buildings" Davis, Michael "The geometry and topology of Coxeter groups" | |||||

Prerequisites / Notice | Students must have taken a first course in algebraic topology or be familiar with fundamental groups and covering spaces. They should also be familiar with groups and group actions. |

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