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PřF:M7111 Topics on mathematical modelli - Course Information

## M7111 Topics on mathematical modelling

**Faculty of Science**

Autumn 2020

**Extent and Intensity**- 2/0/0. 2 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: k (colloquium).

Taught online. **Teacher(s)**- doc. RNDr. Petr Lánský, DrSc. (lecturer)

Mgr. Ondřej Pokora, Ph.D. (lecturer) **Guaranteed by**- doc. PaedDr. RNDr. Stanislav Katina, Ph.D.

Department of Mathematics and Statistics - Departments - Faculty of Science

Supplier department: Department of Mathematics and Statistics - Departments - Faculty of Science **Timetable**- Thu 14:00–15:50 M6,01011
**Course Enrolment Limitations**- The course is offered to students of any study field.
**Course objectives**- Selected methods of mathematical modeling are presented and developed. A comparison between deterministic and stochastic approaches is followed in detail. New trends in mathematical modeling are introduced and reviewed. Each chapter is supplemented by a summary of applied mathematical procedures.
**Learning outcomes**- After passing the course, the student will be able:

to define and interpret the basic notions used in the basic parts of 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**- Program is modified with respect to models under consideration 1) Hypergeometric probability distribution 2) Poisson probability distribution 3) Random variable simulation 4) Poisson process, in time and space 5) Sequences of random variables 5) Information coding 6) Birth-and-death processes 7) Deterministic population models 8) Diffusion processes 9) Stochastic differential equations

**Literature**- TUCKWELL, Henry C.
*Elementary applications of probability theory : with an introduction to stochastic differential equations*. 2nd ed. London: Chapman and Hall, 1995. xv, 292. ISBN 0412576201. info

- TUCKWELL, Henry C.
**Teaching methods**- Lectures and discussion
**Assessment methods**- Active discussion during lectures, cooperation during classes. To conclude the term, one has to prove understanding the topics, to be able to create new concepts and this has to be shown in the homeworks and discussion in them. The discussion can take place in person or in remote-online form.
**Language of instruction**- Czech
**Further Comments**- Study Materials

The course is taught annually.

- Enrolment Statistics (recent)

- Permalink: https://is.muni.cz/course/sci/autumn2020/M7111