The mathematics research at Tampere University covers selected areas from both pure and applied mathematics. Short descriptions of the research groups and the links to the dedicated websites can be found below. Mathematical topics are also studied in the Data Science group. Information regarding mathematics teaching can be found on the "Teaching" page. You can contact the research groups to ask about potential topics for bachelor's and master's theses.

## Algebra, geometry and topology

The research group's fields include applied algebraic topology, number theory, and discrete geometry. In the area of applied algebraic topology, the group is currently focused on studying the algebraic foundations of topological data analysis. Topological data analysis is a new branch of mathematics that allows the study of the shape of large data sets. It has quickly found applications ranging from medicine to materials science. Topological data analysis provides a remarkable example of how abstract mathematics can be applied in practice.

## Inverse Problems

An inverse problem starts with the effects and then calculates the causes, which is inverse of a forward problem, which starts with the causes and then calculates the effects. Inverse problems are by definition ill-posed either in the sense of solution existence and uniqueness, or stability. Traditionally, inverse problems are application oriented, although there are also pure mathematical problems that are considered to be inverse problems. The research of the group concentrates on the applications of inverse problems in Forest and ecological research, Geoscience (Radar tomography), and Biomedical Science (Brain imaging).

## Logic

The logic group's research interests relate to various fields of logic, including applications in theoretical computer science and discrete mathematics. Specific topics include answer-set programming, finite model theory, many-valued logics, computational complexity of reasoning problems (e.g., satisfiability, validity and model checking), explainability in AI, automated reasoning, knowledge representation, GUHA data mining, dependence logic and temporal logics.

## Mathematical Systems Theory and Functional Analysis

The Systems Theory Research Group studies the mathematical theory behind the dynamical behaviour of models involving ordinary and partial differential equations. Such "dynamical systems" arise from modelling physical phenomena in the nature and in engineering applications, and in particular involve dynamics of waves and vibrations, fluid flows, and evolution of temperature profiles. The research group focuses on the theoretical analysis of the long-term behaviour of such systems, as well as on developing the means to influence the behaviour of these models using dedicated control signals. The research belongs to the fields of mathematical control theory, functional analysis, and analysis of partial differential equations.

## Mathematics Education Research

We conduct research on mathematics education and learning, particularly at the university level. Our aim is to investigate how different pedagogical teaching and assessment methods impact students' studying, learning, and well-being. We also explore and develop educational technology, focusing on customized tasks and feedback tailored to students' needs.