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Search result: Catalogue data in Autumn Semester 2016

Mathematics Master Information
Electives
For the Master's degree in Applied Mathematics the following additional condition (not manifest in myStudies) must be obeyed: At least 15 of the required 28 credits from core courses and electives must be acquired in areas of applied mathematics and further application-oriented fields.
Electives: Pure Mathematics
Selection: Algebra, Topology, Discrete Mathematics, Logic
NumberTitleTypeECTSHoursLecturers
401-3117-66LIntroduction to the Circle MethodW6 credits2V + 1UE. Kowalski
AbstractThe circle method, invented by Hardy and Ramanujan and developped by Hardy and Littlewood and Kloosterman, is one of the most versatile methods currently available to determine the asymptotic behavior of the number of integral solutions to polynomial equations, when the number of solutions is sufficiently large.
Objective
ContentThe circle method, invented by Hardy and Ramanujan and developped by Hardy and
Littlewood and Kloosterman, is one of the most versatile methods currently available
to determine the asymptotic behavior of the number of integral solutions to
polynomial equations, when the number of solutions is sufficiently large.

The lecture will present an introduction to this method. In particular, it will
present the solution of Waring's Problem concerning the representability of integers
as sums of a bounded numbers of (fixed) powers of integers.
LiteratureH. Davenport, "Analytic methods for Diophantine equations and Diophatine
inequalities", Cambridge

H. Iwaniec and E. Kowalski, "Analytic number theory", chapter 20; AMS

R. Vaughan, "The Hardy-Littlewood method", Cambridge
401-4209-66LGroup and Representation Theory: Beyond an IntroductionW8 credits3V + 1UT. H. Willwacher
AbstractThe goal of the course is to study several classical and important (and beautiful!) topics in group and representation theory, that are otherwise often overlooked in a standard curriculum.
In particular, we plan to study reflection and Coxeter groups, classical invariant theory, and the theory of real semi simple Lie algebras and their representations.
ObjectiveDespite the title, the course will begin by a recollection of basic concepts of group and representation theory, in particular that of finite groups and Lie groups.
Hence the course should be accessible also for students who only had a brief exposure to representation theory, as for example in the MMP course.
401-3059-00LCombinatorics II
Does not take place this semester.
W4 credits2GN. Hungerbühler
AbstractThe course Combinatorics I and II is an introduction into the field of enumerative combinatorics.
ObjectiveUpon completion of the course, students are able to classify combinatorial problems and to apply adequate techniques to solve them.
ContentContents of the lectures Combinatorics I and II: congruence transformation of the plane, symmetry groups of geometric figures, Euler's function, Cayley graphs, formal power series, permutation groups, cycles, Bunside's lemma, cycle index, Polya's theorems, applications to graph theory and isomers.
401-4145-66LReading Course: Abelian Varieties over Finite FieldsW2 credits4AJ. Fresán, P. S. Jossen
Abstract
Objective
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