M81B0 Mathematical models in biology

Faculty of Science
Spring 2023
Extent and Intensity
2/0/0. 2 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: k (colloquium).
Teacher(s)
Mgr. Ondřej Pokora, Ph.D. (lecturer)
Guaranteed by
doc. Mgr. Jan Koláček, Ph.D.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Tue 8:00–9:50 M6,01011
Prerequisites
Prerequisites: theoretical knowledge and practise in the scope of undergraduate courses of probability, mathematical statistics, calculus and software R.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
Selected methods of deterministic and stochastic modeling are presented and developed, with applications to some phenomena in biochemistry, biophysics, neurophysiology and medicine. Each part is supplemented by a summary of applied mathematical procedures and implemented in R software.
Learning outcomes
After passing the course, the student will be able:
to define and interpret the basic notions used in the basic parts of deterministic and stochastic mathematical modeling and to explain their mutual context;
to formulate relevant mathematical theorems and statements and to explain methods of their proofs;
to use effective techniques utilized in basic fields of mathematical modeling;
to apply acquired pieces of knowledge for the solution of specific problems including problems of applicative character.
Syllabus
  •  
  • Michaelis-Menten biochemical model of enzymatic kinetics.
  • Diffusion model.
  • Pharmacokinetical model.
  • Epidemiological models.
  • Models of a neuron.
Literature
  • MURRAY, J. D. Mathematical biology. 3rd ed. New York: Springer, 2003, xix, 811. ISBN 0387952284. info
  • Stochastic Models in Biology. 2004th ed. 2004. ISBN 978-1930665927. info
  • TUCKWELL, Henry C. Introduction to theoretical neurobiology. Cambridge: Cambridge University, 1988, xi, 265. ISBN 0521352177. info
Teaching methods
Lectures and discussions and practise in R software: 2 hours a week.
Assessment methods
Active discussion during lectures. To conclude the term, one has to do the homeworks and to prove understanding the topics, terms and models during the final infividual talk.
Language of instruction
Czech
Further comments (probably available only in Czech)
Study Materials
The course is taught annually.
Teacher's information
https://is.muni.cz/auth/el/sci/jaro2023/M81B0/index.qwarp
The lessons are usually in Czech or in English as needed, and the relevant terminology is always given with English equivalents.

The target skills of the study include the ability to use the English language passively and actively in their own expertise and also in potential areas of application of mathematics.

Assessment in all cases may be in Czech and English, at the student's choice.

The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2024, Spring 2025.
  • Enrolment Statistics (Spring 2023, recent)
  • Permalink: https://is.muni.cz/course/sci/spring2023/M81B0