Numerical methods

proseminars

Numerical methods for solving certain problems in applied sciences.

We focus on the numerical solution of problems in applied mathematics. We consider problems which are interesting not only from the mathematical point of view, but also in view of a possible future work of participants. Example topics may include:

• Monte Carlo methods with applications in finance (e.g. option pricing),
• methods of numerical optimization,
• application of Fourier transform to signal processing and compression,
• numerical solution of equations modelling physical, economic or social processes.

We want to show how we can solve specific problems using and expanding our knowledge. The solution process can be split into the following stages:

• mathematical formulation (model),
• algorithmic and theoretical investigation,
• finding adequate numerical method(s),
• implementation, visualization, discussion, conclusion(s).

While we encourage the participants to pay specific attention to the last stage, fully theoretical analysis/discussion of numerical methods is also warmly welcome.

References will be given at the first meeting.

Knowledge and skills:

The students:

1. understand the role of a mathematical theory in connection with solutions of problems in other sciences;
2. can apply the theory to find practical solutions for specific problems;
3. can apply numerical methods which are adequate for specific problem;
4. can give a speech;
5. can write a licentiate thesis.

Competence:

The students:

1. can comprehensibly reframe mathematical issues in speech and writing;
2. are aware of own limitations and the need for further education;
3. can unassisted search information in the literature, also in foreign languages;
4. understand and appreciate the importance of intellectual integrity in their own and others' activities; behave ethically.

Grading based on the licentiate thesis.