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401-3057-00L  Finite Geometries II

SemesterAutumn Semester 2016
LecturersN. Hungerbühler
Periodicitytwo-yearly recurring course
Language of instructionGerman

AbstractFinite 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.
ObjectiveFinite 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.
ContentFinite 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.