CORE114 Biological Mathematics

Faculty of Science
Spring 2025
Extent and Intensity
2/0/0. 3 credit(s). Type of Completion: k (colloquium).
In-person direct teaching
Teacher(s)
prof. Ing. Jiří Holčík, CSc. (lecturer)
Guaranteed by
prof. Ing. Jiří Holčík, CSc.
RECETOX – Faculty of Science
Contact Person: RNDr. Pavel Lízal, Ph.D.
Supplier department: RECETOX – Faculty of Science
Prerequisites
!TYP_STUDIA(ND) && !FORMA(C) && (!PROGRAM(B-UCB) && !PROGRAM(B-UCC) && !PROGRAM(B-UCF) && !PROGRAM(B-UCM) && !PROGRAM(B-UCZ) && !PROGRAM(B-LGM))
We assume the course open for all the students of bachelor programmes at the Masaryk University (apart from Teacher Training programmes and the study programme LGM) with positive relationship to mathematics who are expected to have an active interest in the course issues. In any case, the course will enable students of mathematical study programmes to get knowledge above framework of their main study programme.
Course Enrolment Limitations
The course is offered to students of any study field.
The capacity limit for the course is 50 student(s).
Current registration and enrolment status: enrolled: 0/50, only registered: 28/50, only registered with preference (fields directly associated with the programme): 0/50
Course objectives
The aim of the course is: • to get students acquainted with character of mutual interaction between various scientific disciplines not only but mainly on example of biology, medicine, and mathematics or informatics. • to draw attention of students to examples of inspiring influence of selected biological phenomena to development of new mathematical methods/algorithms. • to give students a lead to critical assessment of the developed mathematical methods. • eventually, to teach students how to express their opinion in formal (written) way on methods explained in the course or to other examples of mutual inspiration of various disciplines according to student’s interest.
Learning outcomes
At the end of the course, students should be able to: • identify particular common features of scientific disciplines (esp. biology and mathematics), seek them out and apply. • understand principles of selected mathematical methods and formulate their strengths and weaknesses. • formulate their own opinions dealing with the course content.
Syllabus
  • 1. Introductive lecture, the course administration, mutual relationship of various disciplines in time and place – first on example of fine art, latter specifically for biology and mathematics, how to write technical papers and/or reports. 2. Artificial life – basic principles, Conway’s game “Life”, artificial virtual ant, swarm intelligence. 3. Adaptation and control in natural and artificial systems – cybernetics. 4. Cellular automata (CA) – basic principles – tissue, automaton, definition of CA, CA as mathematical discipline, practical application of the CA, mathematical models of spreading infection diseases by means of CA. 5. 1st partial test. 6. Artificial neural networks (ANN) I – neural system, neuron and its mathematical models, ANN – feedforward and feedback structures. 7. Artificial neural networks II – perceptrons, Hopfield ANN, learning ANN, applications. 8. Genetic algorithms (GA) – fundamental of genetics, natural selection, optimization methods, principles of genetic algorithms, applications. 9. 2nd partial test. 10. Artificial immune systems (AIS) – basic principles, artificial immune system – definition, types of AIS implementation, application. 11. Deterministic chaos – fundamentals of modelling population dynamics, discrete models of single population, variability in behaviour of discrete logistic equation, universality of the chaos, fractals. 12. Catastrophe theory – basic principles and examples, basic types of mathematical catastrophes, examples of models using butterfly catastrophe. 13. 3rd partial test.
Literature
  • Handbook of Natural Computing. Rozenberg, G., Bäck, T., Kok, J.N. (eds.), Spinger-Verlag, Berlin Heidelberg 2012.
Teaching methods
Lectures supported by Power Point presentations. Understanding principles, methods and algorithms is emphasized. Students are continuously encouraged to be in an interaction with a lecturer to check up their understanding of the lectured topics and to provoke their activity in solving problems.
Assessment methods
The course will be completed by a colloquium. The credits will be given in case of at least 50% of correct answers from all possible answers of the three partial written tests (selection of the correct answer from a list of possible answers). An alternative possibility for getting the credits is to write and successfully defend an essay dealing with either some discipline/method from those lectured in the course, some other forms of mutual inspiration of biology and mathematics or some other mutually influenced disciplines close to students’ orientation. The essay is to be of the standard form of scientific/technical paper. Students will take up with the form during the first lecture.
Language of instruction
Czech
Further Comments
The course is taught each semester.
The course is taught: every week.
The course is also listed under the following terms Autumn 2024.
  • Enrolment Statistics (recent)
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