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Lecturer(s)
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Černý Jan, prof. RNDr. DrSc.
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Bulíček Josef, doc. Ing. Ph.D.
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Course content
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The overview of often utilised mathematical models in transport and telecommunications. Linear deterministic methods. Non-linear and dynamic deterministic models. Probabilistic models. Discrete mathematical structures. Combinatorial structures. Location into finite set of positions and relations. Dimension of combinatorial structures. Combinatorial equalities and recurrent relations. Graphs. Modelling of transport networks by evaluated graphs. Controlling of problems of location, routes and flows, determining of singular components graphs. Algorithms. Schedules. Types of scheduling problems. Transport applications, space schedules, time schedules, circulatory schedules. Problems of decision-making. Methods of game theory, utilising for solution of conflict situations. Problems of decision-making with risk and uncertainty. Probability and mathematical statistics. The most important random quantities in the point of view of applications in transport and telecommunications. Random vectors and random progressions. Limit characteristics. Markov processes, utilizing on the mass operation systems. Selected problems of the subject in accordance with specialization of student and the theme of dissertation.
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Learning activities and teaching methods
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Dialogic (discussion, interview, brainstorming)
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Learning outcomes
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The aim of the subject is to inform students about often utilised mathematical models in transport and communications.
Student is able to utilize of knowledge from the subject in dissertation work.
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Prerequisites
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unspecified
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Assessment methods and criteria
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Oral examination
The examination (form, content, duration) is set in accordance with the Educational and Examinational Code of the University of Pardubice.
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Recommended literature
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BERMAN, G. Introduction to combinatorics. New York : Academic Press, 1972.
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BLUMENTHAL, R.M. - GETOOR, R.K. Markov processes and potential theory. 1968.
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Cenek, Petr. Optimalizace dopravních a spojových procesů. Žilina: Vysoká škola dopravy a spojov, 1994. ISBN 80-7100-197-X.
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Cole, Stuart. Applied transport economics. London: Kogan Page, 2005. ISBN 0-7494-3964-5.
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Golumbic, Martin Charles. Algorithmic graph theory and perfect graphs. Amsterdam: Elsevier, 2004. ISBN 0-444-51530-5.
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Häggström, Olle. Finite Markov chains and algorithmic applications. Cambridge: Cambridge University Press, 2002. ISBN 0-521-89001-2.
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Hillier, F. S., Lieberman, G. J. Introduction to Operations Research. Mc Graw-Hill, Boston, 2001. ISBN 0-07-121744-4.
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Hosmer, David W.. Applied logistic regression. New York: John Wiley & Sons, 2000. ISBN 0-471-35632-8.
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Montgomery, Douglas C. Applied statistics and probability for engineers. Hoboken: John Wiley & Sons, 2003. ISBN 0-471-73556-6.
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Ortúzar Salas, Juan de Dios. Modelling transport. Chichester: John Wiley & Sons, 2001. ISBN 0-471-86110-3.
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Padberg, Manfred. Linear optimization and extensions. Berlin: Springer, 1999. ISBN 3-540-65833-5.
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