M7111 Topics on mathematical modelling

Faculty of Science
Autumn 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
Mon 18:00–19:50 M2,01021
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 offered to students of any study field.
Course objectives
Selected methods of stochastic modeling are presented and developed. New trends in mathematical modeling are introduced and reviewed. 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 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
  • Binomial, hypergeometric, Poisson and exponential probability distribution.
  • Poisson process.
  • Renewal processes.
  • Pure-birth process (Yule process), pure-death process, birth-and-death process.
  • Galton-Watson branching process.
  • Random walk.
  • Brownian motion (Wiener process).
  • Brownian motion with drift, First Passage Time.
  • Diffusion processes.
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
Teaching methods
Classes are in full-time form: lectures = 2 hours a week – lectures, problem solving, discussions.
Assessment methods
Discussions, homeworks and problem solving. 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 problem solving and by the final discussion.
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/podzim2023/M7111/index.qwarp
Detailed information, schedule of lectures and study materials for the current period are posted in the Interactive syllabus in IS.
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 2010 - only for the accreditation, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2019, Autumn 2020, autumn 2021, Autumn 2022, Autumn 2024.
  • Enrolment Statistics (Autumn 2023, recent)
  • Permalink: https://is.muni.cz/course/sci/autumn2023/M7111