Course detail

Mathematical Foundations of Risk Analysis

ÚSI-RSMATAcad. year: 2019/2020

The course is based on mathematical modelling 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: Statistics, Minitab, Mat lab, and Excel.

Language of instruction

Czech

Number of ECTS credits

5

Mode of study

Not applicable.

Guarantor

doc. RNDr. Zdeněk Karpíšek, CSc.

Department

Institute of Forensic Engineering (ÚSI)

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, numerical methods), and computer technology for application software use.

Co-requisites

Not applicable.

Planned learning activities and teaching methods

Teaching is carried out through lectures and seminars. Lectures consist of interpretations of basic principles, methodology of given discipline, problems and their exemplary solutions. Seminars particularly support practical mastery of subject matter presented in lectures or assigned for individual study with the active participation of students.

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 (5 tasks), a theoretical part (5 tasks); ECTS evaluation used.

Course curriculum

1. Fundamental mathematical concepts of risk engineering.
2. Selected deterministic models for economic and financial 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 modelling, 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 multiple 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

ANDĚL, Jiří. Základy matematické statistiky. Praha: Matfyzpress, 2011. ISBN 978-80-7378-162-0. (CS)
CIPRA, Tomáš. Riziko ve financích a pojišťovnictví: Basel III a Solvency II. Ekopress 2015. ISBN 978-80-87865-24-8.
KARPÍŠEK, Zdeněk. MATEMATIKA IV: Statistika a pravděpodobnost. Akademické nakladatelství CERM s.r.o., Brno 2014. ISBN 978-80-214-4858-2.
MONTGOMERY, Douglas C., RUNGER, George. Applied Statistics and Probability for Engineers. 5th ed. New York: John Wiley & Sons, 2010. ISBN 978-0-470-05304-1. (CS)

Recommended reading

AGRESTI, Alan. Categorical Data Analysis. 3rd ed. New York: John Wiley & Sons, 2013. ISBN 0-470-46363-5.
BROCKWELL, Peter J., DAVIS, Richard, A. Introduction to Time Series and Forecasting. 2nd ed. New York: Springer-Verlag, 2002. ISBN 0-387-95351-5
KLIR, George J., YUAN, Bo. Fuzzy Sets and Fuzzy Logic - Theory and Applications. New Jersey: Prentice Hall, 1995.

Classification of course in study plans

  • Programme RRTES_P Master's

    specialization RRES , 1 year of study, winter semester, compulsory
    specialization RRTS , 1 year of study, winter semester, compulsory

Type of course unit

 

Lecture

26 hod., compulsory

Teacher / Lecturer

doc. RNDr. Zdeněk Karpíšek, CSc.

Syllabus

1. Fundamental mathematical concepts of risk engineering.
2. Selected deterministic models for economic and financ 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 multidimensional 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.

Exercise

26 hod., compulsory

Teacher / Lecturer

doc. RNDr. Zdeněk Karpíšek, CSc.

Syllabus

1. Fundamental mathematical concepts of risk engineering.
2. Selected deterministic models for economic and financ 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 multidimensional 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.