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This entry is from Winter semester 2021/22 and might be obsolete. No current equivalent could be found.

Wavelet Analysis II
(dt. Waveletanalysis II)

Level, degree of commitment Specialization module, compulsory elective module
Forms of teaching and learning,
workload		 Lecture (3 SWS), recitation class (1 SWS),
180 hours (60 h attendance, 120 h private study)
Credit points,
formal requirements		 6 CP
Course requirement(s): Successful completion of at least 50 percent of the points from the weekly exercises.
Examination type: Written or oral examination
Language,
Grading		 German,
The grading is done with 0 to 15 points according to the examination regulations for the degree program M.Sc. Mathematics.
Duration,
frequency		 One semester,
Regularly alternating with other specialization modules
Person in charge of the module's outline Prof. Dr. Stephan Dahlke

Contents

Construction of multivariate wavelets for general scaling, construction of biorthogonal wavelets, characterization of function spaces using wavelets, continuous wavelet transformation.


Qualification Goals

The students shall

  • get to know advanced starting points of wavelet analysis by concrete examples,
  • Understand various advanced constructions and deepen the analytical tools used,
  • to recognize exemplarily the theoretical background and the concrete applications of analytical methods,
  • follow recent developments in a current field of mathematics,
  • practice mathematical working methods (development of mathematical intuition and its formal justification, training of the ability to abstract, proof techniques),
  • improve their oral communication skills in the exercises by practicing free speech in front of an audience and during discussion.

Prerequisites

None. The competences taught in the following module are recommended: Wavelet Analysis I.


Applicability

Module imported from M.Sc. Mathematics.

It can be attended at FB12 in study program(s)

  • B.Sc. Mathematics
  • B.Sc. Business Mathematics
  • M.Sc. Computer Science
  • M.Sc. Mathematics
  • M.Sc. Business Mathematics

When studying B.Sc. Business Mathematics, this module can be attended in the study area Specialization Modules.

The module is assigned to the focus area Numerics/Optimisation. Further information on eligibility can be found in the description of the study area.


Recommended Reading

  • Daubechies, I.: Ten lectures on Wavelets, CBMS-NSF Regional Confe-rence Series in Applied Mathematics, 61 SIAM Press, Philadelphia;
  • P. Wojtaszczyk. A mathematical introduction to wavelets, Cambridge
  • University Press 1997



Please note:

This page describes a module according to the latest valid module guide in Winter semester 2021/22. Most rules valid for a module are not covered by the examination regulations and can therefore be updated on a semesterly basis. The following versions are available in the online module guide:

The module guide contains all modules, independent of the current event offer. Please compare the current course catalogue in Marvin.

The information in this online module guide was created automatically. Legally binding is only the information in the examination regulations (Prüfungsordnung). If you notice any discrepancies or errors, we would be grateful for any advice.