# Mathematical Sciences

The Centre for Mathematical Sciences is a joint department covering all areas of mathematical sciences. The scope is broad regarding both content and area of application, ranging from highly theoretical to extremely applied. Several research projects at LTH have resulted in spin-off companies; advanced mathematical innovations are often the basis for products and services.

About 100 employees work at the Department, most of them in mathematics. The Department belongs to both the Engineering and Science faculties. The Department is responsible for a great deal of teaching, in almost all the programmes at LTH.

## Research is made in the following areas:

## Mathematical Statistics

Mathematical Statistics involves most areas associated with probability and chance. Theoretical research is directed towards probability theory and statistical theory and methods. Applied research is carried out in the following areas.

*Biology, medicine*: research in bioinformatics deals with methods of analysing genetic relations to, for example, inherited diseases. Statistical signal processing and statistical image analysis are being investigated for use in diagnostics, for example, in neurology.

*The environment, climate and risk*: climate and weather are typical examples of natural processes that develop in a random way. One important area of research is concerned with how a slow change in climate can lead to extreme weather conditions. Research in statistical risk management includes models for wear, fatigue and the safety of constructions.

*Economics*: in the field of financial statistics methods are being developed for risk management, optimization and pricing in, for example, the electricity generation industry and market, and for various economic prognoses.

*Keywords: biostatistics, statistical signal processing, statistical extreme weather theory, risk analysis, stochastic fatigue, financial risks, Makarov processes, stochastic differential equations, economic prognoses, extreme climate and weather, experimental design, chemometrics, clinical trials, marine safety, medical statistics*

## Mathematics

Mathematics is a basic, applied and interdisciplinary subject. The traditional, but coarse division can be made into algebra, analysis and geometry, where development is driven by both scientific and applied problems.

Most of the research at LTH is carried out within applied mathematics, especially image analysis and computer vision. Methods based on sequences of images are developed for recognition, reconstruction and analysis of motion. Applications can be found in IT, medical engineering, robotics, metrology and computer-aided decision support.

In Lund there is a strong tradition in partial differential equations, which forms the basis for many widely differing areas of application. One of the expanding areas at LTH is that of dynamic systems, where studies are being carried out on the general principles of evolutionary processes. Other areas include harmonic analysis, operator theory, computer algebra, optimization and complex analysis.

*Keywords: algebra, mathematical analysis, geometry, applied mathematics, mathematical image analysis, differential equations, harmonic analysis, dynamic systems, chaos, operator theory, optimization*

## Numerical Analysis and Scientific Computing

Numerical Analysis and Scientific Computing is concerned with developing methods of solving complicated mathematical problems with the aid of computers. Algorithms that must be accurate and efficient are designed, analysed and programmed. Problems are often taken from industry or the areas of science and technology. Computations are performed on every subject from planetary orbits, solid mechanics and fracture, hip and knee replacements, to complicated fluid mechanics. *Keywords: numerical analysis, scientific computing, stress calculations, composite materials, integral calculus, potential theory, multipole methods, simulation of dynamic systems, numerical simulation of shockwaves/giant waves, adaptive high-resolution algorithms.*