Studium
Bachelor/Master Projekte
Am Institut für Numerische und Angewandte Mathematik arbeiten die Professoren*innen in verschiedenen Arbeitsgruppen und vergeben Bachelor- und Masterarbeiten. Wenn Sie den entsprechenden Links unten folgen, gelangen Sie zu Beschreibungen der Forschungsgebiete. Sie können die entsprechenden Professoren immer in den ausgewiesenen Sprechzeiten aufsuchen (gern persönlich vorbeischauen oder per Mail kontaktieren).
Bachelor/Master projects
At the Institute of Numerical and Applied Mathematics, the professors work in various research groups and award Bachelor's and Master's theses. If you follow the corresponding links below, you will find descriptions of the research areas. You can always visit the respective professors during the designated consultation hours (feel free to drop by in person or contact them by e-mail).
- Inverse Probleme (Prof. Dr. T. Hohage)
- Berechnung partieller Differentialgleichungen (Prof. Dr. C. Lehrenfeld) Many physical processes can be modeled by partial differential equations (PDEs) which typically need to be solved numerically. Our research efforts concentrate around the development and analysis of modern finite element methods for PDEs. If you are interested in a thesis topic or a student project, please take a look here. A selection of finished thesis projects can be found here.
- Kontinuierliche Optimierung und Variationelle Analysis (Prof. Dr. R. Luke) AG Variational Analysis and Continuous Optimizaton:
- Optimierung auf glatten Mannigfaltigkeiten (Jun. Prof. M. Pfeffer) Required lectures: Numerics I & II, either Optimisation or Scientific Computing
- Mathematische Signal- und Bildverarbeitung (Prof. Dr. G. Plonka-Hoch) Topics of Bachelor/Master theses are from the following fields:
- Diskrete Differential-Geometrie (Prof. Dr. M. Wardetzky)
- Angewandte Mathematik in den Naturwissenschaften (Jun.-Prof. Dr. A. Wald) The focus of the research in the group Applied Mathematics in the Natural Sciences is related to problems arising in the applied sciences, particularly in physics. Typical goals are the evaluation of indirect measurement data as well as modelling aspects, which often require the (numerical) solution of inverse problems. Some of our current applications are
Consultation Hours: Tuesday 12:00-14:00
Contact: lehrenfeld@math.uni-goettingen.de
Optimization has played a central role in applied mathematics with applications spanning both the social and natural sciences as well as engineering and finance. Continuous optimization is often associated with branches of analysis and its central theoretical contributions concern the analysis of nonsmooth and set-valued objects. The tools of classical analysis, including derivatives, integrals and resolvents, are contained in the more modern language of variational analysis which comprises the theoretical foundation of mathematical optimization. If you are considering writing a bachelors or masters thesis in optimization, it is expected that you have had a fundamentals of optimization or operations research lecture, and have attended at least one of the seminars offered regularly by Prof. Luke. Masters students are expected to have attended at least one semester of Prof. Luke's special lectures on variational analysis/numerical optimization. Topics are determined on an individual basis, depending on the students' background and the current research activity of the Working Group on Variational Analysis.
You are invited to speak with Prof. Russell Luke during office hours:
Consultation Hours: Tuesday 10:00 - 12:00
Contact: luke@math.uni-goettingen.de
Consultation Hours: Tuesday 14:00 - 15:00
Contact: m.pfeffer@math.uni-goettingen.de
- Numerical Linear Algebra (e.g. fast algorithms in linear algebra with applications, special matrices, eigenvalues)
- Numerical Analysis (in particular approximation theory, quadrature formulas, stable algorithms)
- Numerical Fourier Analysis (e.g. fast algorithms for Fourier transforms, trigonometric transforms, wavelets, etc.)
- Applications in Signal and Image Processing (e.g. signal- and image denoising, signal compression)
- Inverse Problems in Signal and Image Processing
- Mathematical Background of Deep Learning
- Applications of Signal and Image Processing in cooperation with industrial partners or interdisciplinary topics
Topics for Bachelor and Master thesis are provided individually depending on the mathematical background and the interest of the candidate.
Examples of previous Bachelor and Master thesis topics can be found here:
https://na.math.uni-goettingen.de/index.php?section=gruppe&subsection=absolve&master=1
Needed prerequisites: Successful completion of the following lectures
For a Bachelor thesis:
- Numerical Mathematics I
- Numerical Mathematics II or Functional Analysis or one lecture of the lecture series Image and Geometry Processing (e.g. Fourier Analysis)
For a Master thesis:
- at least two of the lectures Numerical Mathematics II, Functional Analysis, lectures of the lecture series “Image and Geometry Processing” (Fourier Analysis, Numerical Methods in Signal and Image Processing, Computer Tomography), Approximation Theory
For more information on the Lectures see:
Consultation Hours: Friday 10:30 - 11:30
Contact: plonka@math.uni-goettingen.de
• identification of material parameters and forces in active matter,
• traction force microscopy and inverse problems in elasticity,
• dynamic computerized tomography, particularly on the nano scale,
• terahertz tomography for nondestructive testing.
In strong connection to these applications, we work on
• (fast) regularization techniques,
• parameter identification problems for partial differential equations,
• combinations of machine learning techniques and regularization schemes.
More details can be found on the group’s website.
Topics of Bachelor and Master theses are usually selected based on the background and interests of the students. The successful completion of the lectures in Numerical Mathematics are necessary for both Bachelor and Master theses. Apart from this, it is helpful (but not necessary) to have a background in inverse problems, optimization, functional analysis, (numerical methods for) partial differential equations, scientific computing, or deep learning.
Consultation hours: Wednesday 11:00 - 12:00 (please send an eMail in advance!)
Contact: a.wald@math.uni-goettingen.de
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