# Search result: Catalogue data in Autumn Semester 2016

Mathematics Master | ||||||

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 | ||||||

Number | Title | Type | ECTS | Hours | Lecturers | |
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401-3117-66L | Introduction to the Circle Method | W | 6 credits | 2V + 1U | E. Kowalski | |

Abstract | The 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. | |||||

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Content | The 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. | |||||

Literature | H. 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 | |||||

401-4209-66L | Group and Representation Theory: Beyond an Introduction | W | 8 credits | 3V + 1U | T. H. Willwacher | |

Abstract | The 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. | |||||

Objective | Despite 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. | |||||

401-3059-00L | Combinatorics IIDoes not take place this semester. | W | 4 credits | 2G | N. Hungerbühler | |

Abstract | The course Combinatorics I and II is an introduction into the field of enumerative combinatorics. | |||||

Objective | Upon completion of the course, students are able to classify combinatorial problems and to apply adequate techniques to solve them. | |||||

Content | Contents 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. | |||||

401-4145-66L | Reading Course: Abelian Varieties over Finite Fields | W | 2 credits | 4A | J. Fresán, P. S. Jossen | |

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