# Computational Mathematics

The group Computational Mathematics performs mathematical research in geometrical modeling, partial differential equations, numerical analysis, combinatorics and optimization. A lot of the activity is motivated by applications, and very central is the development of numerical *algorithms* and related theory.

## About the group

A core in the group's research is the interaction: THEORY - ALGORITHMS - APPLICATIONS. The mathematical foundation lies within analysis, linear algebra, differential equations and optimization, including a computational approach.

In **geometrical modeling** one works with problems related to digital geometrical models. Such models are used in industrial design, animation, computer games and other areas. Splines are functions defined via polynomials and they are very important in order to represent geometrical objects and functions in a flexible and efficient way.

**Mathematical optimization** is an important part of applied mathematics where one studies min- and max-problems. Many interesting problems lie at the borderline of optimization and combinatorics; there are lots of applications, and nice mathematics like polyhedral theory and combinatorial matrix theory. Several problems in industrial engineering, mathematical finance and economics may be studied and solved using optimization.

**Partiel differential equations** (PDE) are used in a wide range of applications like weather and climate models, modeling of oil flow in reservoars and pipelines, and removing noise from digital images. For instance, a PDE may describe how the temperature of an object will develop during time when its boundary is heated up. The group works on the mathematical anlysis of PDEs and the development of numerical methods for solving such equations. A central topic is to understand the properties of such solution methods. The activity intersects with the research at the group *Partial differential equations*.

The group has at the moment 6 permanent faculty positions and a number of PhD students, postdocs and visitors.

## Cooperation

The members in the group collaborate with several research groups at different universities internationally and in Norway. Moreover there is a close cooperation with SINTEF Applied mathematics in Oslo, both in geometry and optimization.

## Academic programmes and courses

The group memeber may supervises students at both Master and PhD level. For the Master's degree the main programs are Mathematics, and Applied Mathematics. The group is also very central in the work on the CSE project at the Faculty of Mathematics and Science; this project is focused on introducing an overall computational perspective in science.

Persons in the group often teach MAT-INF1100 Modeling and computations as well as MAT1120 Linear algebra, and otherwise the groups is responsible for the following courses:

- MAT-INF2360 - Applictions of linear algebra (10 studiepoeng)
- MAT-INF3360 - Partial differential equations (10 studiepoeng)
- MAT-INF3100 - Linear optimization (10 studiepoeng)
- MAT-INF4130 - Numerical linear algebra (10 studiepoeng)
- MAT-INF4360 - Topics in geometric modelling
- MAT-INF4170 - Spline methods (10 studiepoeng)
- MAT-INF4140 - Numerical analysis (10 studiepoeng)
- MAT-INF4110 - Mathematical optimization (10 studiepoeng)
- MAT-INF9170 - Spline methods (10 studiepoeng)
- MAT-INF9140 - Numerical Analysis (10 studiepoeng)
- MAT-INF9110 - Mathematical Optimization (10 studiepoeng)