Search result: Catalogue data in Spring Semester 2020

Mathematics Bachelor Information
Electives
Selection: Geometry
NumberTitleTypeECTSHoursLecturers
401-3056-00LFinite Geometries IW4 credits2GN. Hungerbühler
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.
401-3556-20LTopics in Symplectic TopologyW6 credits3VP. Biran
AbstractThis will be an introductory course in symplectic geometry and topology.
We will cover the simplest instances of symplectic rigidity phenomena, and techniques to detect and study them. The last part of the course will be devoted to more advanced techniques such as Floer theory.
ObjectiveGet acquainted with the basics of symplectic topology and phenomena
of symplectic rigidity.
Literature1) Book: "Introduction to Symplectic Topology", 3'rd edition, by McDuff and Salamon.
Oxford Graduate Texts in Mathematics

2) Some published articles that will be announced during the semester.
401-3574-61LIntroduction to Knot Theory Information
Does not take place this semester.
W6 credits3G
AbstractIntroduction to the mathematical theory of knots. We will discuss some elementary topics in knot theory and we will repeatedly centre on how this knowledge can be used in secondary school.
ObjectiveThe aim of this lecture course is to give an introduction to knot theory. In the course we will discuss the definition of a knot and what is meant by equivalence. The focus of the course will be on knot invariants. We will consider various knot invariants amongst which we will also find the so called knot polynomials. In doing so we will again and again show how this knowledge can be transferred down to secondary school.
ContentDefinition of a knot and of equivalent knots.
Definition of a knot invariant and some elementary examples.
Various operations on knots.
Knot polynomials (Jones, ev. Alexander.....)
LiteratureAn extensive bibliography will be handed out in the course.
Prerequisites / NoticePrerequisites are some elementary knowledge of algebra and topology.
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