Mathematical models in biology and social sciences 1000-1D10MBS
We will discuss mathematical models and methods used in natural and social sciences. We will analyze complex processes in Physics, Biology, Medicine, and Social Sciences that can be described by discrete and continuous dynamical systems both deterministic and stochastic ones. Special attention will be given to time delays, diffusion in space and stochastic fluctuations. The description will be on microscopic level (kinetic equations, Markov chains, birth and death processes) on macroscopic level (ordinary and partial differential equations) and in the framework of game theory. We will investigate asymptotic behavior for large time, stability and existence of attractors (including the strange attractors).
Type of course
Prerequisites
Course coordinators
Term 2024: | Term 2025: |
Learning outcomes
Knowledge and skills:
0. Can write a thesis.
1. Knows the basic mathematical models (appropriate mathematical structures) of biological, medical and social processes.
2. Can construct mathematical models on the basis of literature in natural and social sciences.
3. Can perform a mathematical analysis of the model.
4. Knows the basic techniques of mathematical model analysis.
5. Knows how to prepare and deliver presentations of varying degrees of generality regarding mathematical details as well as biological, medical and social foundations.
6. Can prepare (also in English) a scientific report regarding selected field of mathematics.
7. Has language skills in the field of mathematics in accordance with the requirements specified for the B2 + level of the European System for the Description of Languages.
8. Can define the directions of further learning and realise the process of self-education.
Social competence:
1. Is able to establish a dialogue with representatives of natural and social sciences.
2. Can promote mathematics as a tool to describe the reality.
Assessment criteria
1st year: Class attendance, 2 presentations.
2nd year: Class attendance, 2 presentations, submitted MA thesis.
Bibliography
References will be given at the first meeting.
Additional information
Information on level of this course, year of study and semester when the course unit is delivered, types and amount of class hours - can be found in course structure diagrams of apropriate study programmes. This course is related to the following study programmes:
Additional information (registration calendar, class conductors, localization and schedules of classes), might be available in the USOSweb system: