Department of Mathematics and Statistics at the University of Turku is particularly well-known for the high level of research in Discrete Mathematics. Discrete Mathematics studies finite or denumerable phenomena. Denumerable infinity means that things can be put in line one after the other. Research of discrete Mathematics in Turku specializes in areas that arise from Information Technology and Telecommunications. One could mention the following research areas: In Cryptography one studies how information can be concealed, in Coding Theory how errors in transferred data can be corrected and in Number theory the attributes of natural numbers. Four research groups study Discrete Mathematics at University of Turku.
The foundations of Analysis lay on the concepts of continuity and limit. Analysis consists of tens of different subgroups that use similar methods. The study objects of the research are e.g. functions, measures and differential equations. Many physical phenomena such as thermal conductivity and the movement of the glacier can be modeled with differential equations. In Geometrical Function Theory one studies the geometric qualities of functions. In Theory of Differential Equations one studies which differential functions have solutions and what kind of qualities these solutions have.
In Biomathematics one studies the modeling of natural phenomena such as changes in the population size. The modeling is often done by by using a suitable differential equation. In Biomathematical research one aims at finding a differential equation that represents the phenomenon as accurately as possible and in what way the phenomenon's behavior changes in the progress of time.
Optimization strives to find the best solution with given boundary conditions. Optimization is used in many practical applications; industrial paper machines can be made more efficient, the best shape for airplane wing or vessel propeller can be found or search for the best structures of medical molecules.
Statistics is a mathematical science separate from theoretical and applied mathematics that studies all the aspects of data analysis. In the heart of statistical analysis are probability representations as statistical models describing for instance data collection processes, data missingness mechanisms and dependency structures allowing the distinction between information and noise. These often complex models can still generally be described by relatively few interpretable parameters that are subject to statistical inference and estimation using the observed data.
The main lines of research on statistical methodology in Department of Mathematics and Statistics are on
· Nonparametric and robust multivariate methods
· Latent variable models for correlated and other structural data
· High dimensional problems such as cancer cell image analysis and “omics” data
· Bayesian approaches and applications in brain imaging
Our researchers closely collaborate with external parties such as Turku Brain and Mind Center, VTT/CEA and DattaLab (university of Louisville), and provide statistical expertise to large medical studies such as LASERI, FinnBrain and DIPP.