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# Course detail

## Mathematical Foundations of Risk Analysis

Subjet code : ÚSI-2SAMZ Institute of Forensic Engineering 2011/2012 Yes doc. RNDr. Zdeněk Karpíšek, CSc. Institute of Forensic Engineering Master's full-time study Czech 6 course-unit credit and examination 1 winter compulsory

The study programmes with the given course

 Objective of the course – aims of the course unit: 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. Objective of the course – learning outcomes and competences: 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. Course contents (annotation): 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. Teaching methods and criteria: 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. 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 reading: CIPRA, T.: Finanční matematika, MatFyzPress, 1993, ISBN 80-901495-1-0HNILICA, 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 80-214-1839-7ANDĚL, J.: Základy matematické statistiky. Praha : Matfyzpress, 2005.CIPRA, T: Modely časových řad, SNTL, 1998.KARPÍŠEK, Z.: Statistika a pravděpodobnost, CERM 2003, ISBN 80-214-2522-9MONTGOMERY, 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.Statistica, GAMS a Matlab

Type of course unit:
Lecture: 26 hours, optionally doc. RNDr. Zdeněk Karpíšek, CSc. 26 hours, compulsory doc. RNDr. Zdeněk Karpíšek, CSc.