Mathematics in Neuroscience and Ecology

Mathematics for Neuroscience

Neural systems are one of nature’s neuroscience 2most impressive designs

They exhibit both computational power and the capacity to adapt to instantaneous changes in the environment. In contrast to human-made devices, their elementary mechanisms, i.e. neuronal cells, are non-identical, slow, and unreliable. Despite the poor performance of their elements, as networks like the human brain, they demonstrate superior performance and versatility as compared to existing artificial intelligent machines.

How do neural systems compute successful decisions in an uncertain and changing environment using slow, unreliable elementary processors? What are the basic principles behind such computation? Why are these systems exceptionally robust while being extremely flexible?

These questions constitute the frontier of research in mathematical neuroscience. Understanding the principles behind computation and flows of information in neural systems has a great impact in wider areas of science and biology.  For example, such knowledge is necessary for building machine-brain interfaces.

It is essential when inventing new cures for the neurological diseases caused, for example, by strokes. It is also useful in developing non-invasive tools for enhancing/controlling performance of human brain.

The program offers opportunities to study mathematical modelling of neural dynamics – from the basic principles of generation of the evoked potential in the membranes of neural cells to the dynamics of ensembles of neurons.

Mathematics in Ecology

Mathematics plays a ecologyremarkable role in contemporary population ecology and epidemiology

There are several reasons for that. Dealing with ecological systems, often available field data are scarce and regular experimental study is expensive. Moreover, a field study can be dangerous for the environment and, potentially, for the human population: Just imaging a study on a spatial spread of a very harmful pest which, instead of attempting to eradicate the species, would bring and release more and more of it! Obviously, the same concern applies also to studies of disease dynamics.

Moreover, replicated experiments (which create the basis of any empirical science) are hardly possible at all in ecology because of a virtual impossibility to reproduce the initial and environmental conditions. In all these situations, mathematical modelling and computer simulations provide an effective and convenient tool to reveal the role of various natural factors, to test or verify hypotheses and, finally, to significantly enhance our understanding of relevant issues.

Application of mathematics in ecology deals with a very broad variety of problems coming from living nature, such as:

  • How to fight pests without pesticides?
  • How many trees in a forest can be cut without disrupting animals’ and birds’ life?
  • How many fish are left in the North Sea?
  • Do genetically modified crops spread long distances or remain localized?
  • How fast does an infectious disease spread?

These are only a few examples, the actual applications span over the whole range of ecological phenomena.

Our MSc course in Mathematical Modelling in Biology is designed to not only to introduce the students to the basic ideas of mathematical ecology and ecological modelling but also bring them up to date. An account about recent theoretical advances in studies and understanding of the dynamics of ecological systems makes an important part of this course and is taught in a comprehensive and self-consistent way.

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