Course: Discrete Mathematics

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Course title Discrete Mathematics
Course code UMKM/PDIM
Organizational form of instruction Lecture + Lesson
Level of course Master
Year of study not specified
Semester Winter
Number of ECTS credits 3
Language of instruction Czech
Status of course Compulsory, Optional
Form of instruction Face-to-face
Work placements This is not an internship
Recommended optional programme components None
Lecturer(s)
  • Zahrádka Jaromír, RNDr. Ph.D.
Course content
Numeration systems, numeration in the floating point, standard IEEE. Congruence and its aplications. Mathematical logic, disjunctive and conjunctive forms. Boolean algebra. Combinatorics, the binomial and multinomial theorem. Sets, principle of inclusion-exclusion. Undirected and directed graphs. Paths and circuits in the graph. Metric of graph, searching for the shortest or optimum way. Trees, spanning tree, cryptography, Kruskal's algorithm. Graphs coloring. Numerical methods for solving linear and nonlinear equations and systems. Numerical methods for calculating derivations, partial derivations and particular integrals. Numerical solving of differential equations.

Learning activities and teaching methods
unspecified, Monologic (reading, lecture, briefing), Methods of individual activities, Projection, Skills training
  • unspecified - 42 hours per semester
  • unspecified - 18 hours per semester
  • unspecified - 18 hours per semester
  • unspecified - 12 hours per semester
Learning outcomes
To follow up with the previous mathematical and mathematic-economical courses and acquaint the students with the topics of mathematical sets and logic, graphs theory and numerical methods with the view to economics and informatics.
Students will be able to solve basic as well as follow-up applied problems in the area of mathematical sets, logic, theory of graphs and numerical methods by the use of EXCEL programming environment.
Prerequisites
Basic mathematical knowns and skills of the mathematics of the middle schools, subjests PMT1 and PMT2 of bachelor study and EXCEL programing language.

Assessment methods and criteria
Home assignment evaluation, Student performance assessment, Work-related product analysis, Systematic monitoring

Assignment - two successful written exams and six semestr projects.
Recommended literature
  • Brázdová, Markéta. Operační výzkum I : úlohy.. Pardubice: Univerzita Pardubice, 1998. ISBN 80-7194-156-5.
  • Goodaire, Edgar G. Discrete mathematics with graph theory. Upper Saddle River: Prentice Hall, 2002. ISBN 0-13-092000-2.
  • Leader, Jeffery J. Numerical analysis and scientific computation. Boston, 2004. ISBN 9780321223357.
  • Matoušek, J., Nešetřil, J.H. Kapitoly z diskrétní matematiky. Praha, 2000. ISBN 80-246-0084-6.
  • Moler, Cleve B. Numerical computing with MATLAB. Philadelphia, 2004. ISBN 9780898716603.
  • Uri Ascher, Chen Greif. A First Course in Numerical Methods. Philadelphia, 2011. ISBN 978-0-898719-97-0.
  • Volek, Josef. Operační výzkum I. Pardubice: Univerzita Pardubice, 2002. ISBN 80-7194-410-6.
  • Walkenbach, John. Microsoft Excel : vzorce a funkce. Praha: Mobil Media, 2001. ISBN 80-86593-01-0.
  • Zahrádka, J. Diskrétní matematika pro SII - diskretizační metody numerické matematiky. Pardubice, 2014. ISBN 9788073958411.


Study plans that include the course