Course detail

Mathematical Foundations of Risk Analysis

ÚSI-2SAMZAcad. year: 2011/2012

The course is based on mathematical modeling and its applications in risk engineering. The explanation is oriented on explication of fundamental ideas and notions, especially by means of suitable examples, on their applicability and on unifying view of mathematical principles. Related mathematical methods of solutions for individual areas will be presented with the use of suitable the software: Statistica, Minitab, Matlab, and Excel.

Language of instruction

Czech

Number of ECTS credits

6

Mode of study

Not applicable.

Learning outcomes of the course unit

Fundamental concepts, methods and analytical techniques related to risk modelling will be studied. Specific ways of reasoning, typical for risk analysis and related model building will be developed and enhanced.

Prerequisites

Basic knowledge of undergraduate mathematics (linear algebra, differential and integral calculus, probability and statistics, numarical methods), and computer technology for application software use.

Co-requisites

Not applicable.

Planned learning activities and teaching methods

Teaching methods depend on the type of course unit as specified in the article 7 of BUT Rules for Studies and Examinations.

Assesment methods and criteria linked to learning outcomes

Course-unit credit requirements: active participation in seminars, mastering the subject matter, and delivery of semester assignment. Examination (written form): a practical part (4 tasks), a theoretical part (4 tasks); ECTS evaluation used.

Course curriculum

1. Fundamental mathematical concepts of risk engineering.
2. Selected deterministic models for economic and financal computations.
3. Selected deterministic models for numerical and engineering approaches, sensitivity analysis.
4. Uncertainty in problems of risk engineering - stochastic and fuzzy models.
5. Problems of systems reliability and risks evaluations modeling, simulation approach.
6. Elementary models of decision making under uncertainty.
7. Selected estimation methods of models parameters probability distributions. Statistical software.
8. Advanced mathematical statistics methods - linear and nonlinear multivariet regression analysis.
9. Elements of categorical, factor and cluster analysis.
10. Parametric and nonparametric statistical hypotheses tests.
11. Models for dynamic problems - introduction to Markov chains (applications in production systems).
12. Elements of time series analysis.
13. Basic models for quality control of production and produces.

Work placements

Not applicable.

Aims

Students will learn useful knowledge of mathematical models focusing on risk modelling. They will also learn how apply studied models and methods within the framework of engineering processes.

Specification of controlled education, way of implementation and compensation for absences

Attendance at seminars is controlled and the teacher decides on the compensation for absences.

Recommended optional programme components

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

CIPRA, T.: Finanční matematika, MatFyzPress, 1993, ISBN 80-901495-1-0
HNILICA, J., FOTR, J.: Aplikovaná analýza rizika ve finančním managementu a investičním rozhodování. Praha : Grada, 2009, ISBN 978-80-247-2560-4.
KLAPKA A KOL.: Metody operačního výzkumu, VUTIUM 2001, ISBN 80-214-1839-7
ANDĚL, J.: Základy matematické statistiky. Praha : Matfyzpress, 2005.
CIPRA, T: Modely časových řad, SNTL, 1998.

Recommended reading

KARPÍŠEK, Z.: Statistika a pravděpodobnost, CERM 2003, ISBN 80-214-2522-9
MONTGOMERY, D. C., RENGER, G.: Applied Statistics and Probability for Engineers. New York : John Wiley & Sons, 2003.
WILLIAMS, H. P.: Model Building in Mathematical Programming, Wiley 1993, ISBN 0471941115.

Classification of course in study plans

  • Programme MRzI Master's

    branch RFI , 1 year of study, winter semester, compulsory
    branch RCH , 1 year of study, winter semester, compulsory
    branch RSK , 1 year of study, winter semester, compulsory
    branch RSZ , 1 year of study, winter semester, compulsory
    branch RIS , 1 year of study, winter semester, compulsory
    branch REZ , 1 year of study, winter semester, compulsory

Type of course unit

 

Lecture

26 hod., optionally

Teacher / Lecturer

Exercise

26 hod., compulsory

Teacher / Lecturer