Search result: Catalogue data in Autumn Semester 2020

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, Number Thy, Topology, Discrete Mathematics, Logic
NumberTitleTypeECTSHoursLecturers
401-3119-70Lp-Adic NumbersW4 credits2VP. Bengoechea Duro
AbstractThis course is an introduction to the p-adic numbers. We will see how the field of p-adic numbers Q_p is build. We will explore the (strange) topology and the arithmetic of Q_p, as well as some elementary analytic concepts such as functions, continuity, integrals, etc. We will explain an algebraic and an analytic reasons of interest for the existence of p-adic numbers.
Objective
Content- Absolute values on Q and Completions
- Topology and Arithmetic of Q_p, p-adic Integers
- Equations over p-adic numbers and Hensel's Lemma
- Local-global principle
- Hasse-Minkowski's Theorem on binary quadratic forms
- Elementary Analysis in Q_p
- the p-adic Riemann zeta function
Literature"p-adic Numbers. An Introduction", Fernando Q. Gouvea (Springer)
"p-adic Numbers, p-adic Analysis, and Zeta-Functions", Neal Koblitz (Springer)
"p-adic numbers and Diophantine equations", Yuri Bilu (online notes 2013)
Prerequisites / NoticeThe courses Topology, Measure and Integration, Algebra I/II are required prerequisites.
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.
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