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German original

Wavelet Analysis I
(dt. Waveletanalysis I)

Level, degree of commitment in original study programme Advanced 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: 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 study course M.Sc. Mathematics.
Original study programme M.Sc. Mathematik / Vertiefungsbereich Mathematik
Duration,
frequency		 One semester,
Regelmäßig im Wechsel mit anderen advanced moduleen
Person in charge of the module's outline Prof. Dr. Stephan Dahlke

Contents

Multi-scale analysis, construction of wavelets, regularity and approximation properties of wavelet bases and their application, for example, in signal processing


Qualification Goals

The students shall

  • get to know the starting point of wavelet analysis through concrete examples,
  • Understand different constructions and deepen the analytical tools used,
  • to understand exemplarily the theoretical background and the concrete application 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 modules are recommended: Measure and Integration Theory, Functional Analysis.


Recommended Reading

  • Daubechies, I.: Ten lectures on Wavelets, CBMS-NSF Regional Confe-rence Series in Applied Mathematics, 61 SIAM Press, Philadelphia;
  • Chui, C.: An Intriduction to Wavelets, Academic Press, 1992.



Please note:

This page describes a module according to the latest valid module guide in Wintersemester 2022/23. 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.