Course detail

Discrete Mathematics

FEKT-BPC-DMAAcad. year: 2023/2024

The sets, relations and mappings. Equivalences and partitions. Posets. The structures with one and two operations. Lattices and Boolean algebras.The propositional calculus in the context of the formulae classes of the predicate calcullus. The normal forms of formulas. Matrices and determinants. Vector spaces. Systems of linear equations.The elementary notions of the graph theory. Connectedness. Subgraphs and morphisms of graphs. Planarity. Trees and their properties. Simple graph algorithms.

Language of instruction

Czech

Number of ECTS credits

Mode of study

Not applicable.

Guarantor

doc. RNDr. Martin Kovár, Ph.D.

Department

Department of Mathematics (UMAT)

Entry knowledge

The knowledge of the content of the subject BMA1 Matematika 1 is required. The previous attendance to the subject BMAS Matematický seminář is warmly recommended.

Rules for evaluation and completion of the course

The semester examination is rated at a maximum of 70 points. It is possible to get a maximum of 30 points in practices, 10 of which are for written tests and 20 points for 2 project solutions.
The content and forms of instruction in the evaluated course are specified by a regulation issued by the lecturer responsible for the course and updated for every academic year.

Aims

The modern conception of the subject yields a fundamental mathematical knowledge which is necessary for a number of related courses. The student will be acquainted with basic facts and knowledge from the set theory, topology and especially the discrete mathematics with focus on the mathematical structures applicable in information and communication technologies.
The students will obtain the necessary knowledge in discrete mathematics and an ability of orientation in related mathematical structures.

Study aids

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

Johnsonbaugh, R., Discrete mathematics, Macmillan Publ. Comp., New York, 1984. (EN)
Kolář, J., Štěpánková, O., Chytil, M., Logika, algebry a grafy, STNL, Praha 1989. (CS)
Kolibiar, M. a kol., Algebra a príbuzné disciplíny, Alfa, Bratislava, 1992. (CS)
Preparata, F.P., Yeh, R.T., Úvod do teórie diskrétnych štruktúr, Alfa, Bratislava, 1982. (CS)

Recommended reading

Acharya D. P., Sreekumar, Fundamental Approach to Discrete Mathematics, New Age International Publishers, New Delhi, 2005. (EN)
Anderson I., A First Course in Discrete Mathematics, Springer-Verlag, London 2001. (EN)
Chartrand G., Zhang Ping, Discrete Mathematics, Waveland Pr Inc, 2011. (EN)
Garnier R., Taylor J., Discrete Mathematics for New Technology, Institute of Physics Publishing, Bristol and Philadelphia 2002. (EN)
Grossman P., Discrete mathematics for computing, Palgrave Macmillan, New York 2002. (EN)
Grimaldi R. P., Discrete and Combinatorial Mathematics, Pearson Addison Valley, Boston 2004. (EN)
Kolman B., Busby R. C., Ross S. C., Discrete Mathematical Structures, Pearson Education, Hong-Kong 2001. (EN)
Lipschutz, S., Lipson, M.L., Theory and Problems of Discrete Mathematics, McGraw-Hill, New York, 1997. (EN)
Lovász L., Pelikán J., Vesztergombi, Discrete Mathematics, Springer-Verlag, New York 2003. (EN)
Matoušek J., Nešetřil J., Kapitoly z diskrétní matematiky, Karolinum, Praha 2000. (EN)
Matoušek J., Nešetřil J., Invitation to Discrete Mathematics, Oxford University Press, Oxford 2008. (EN)
O'Donnell, J., Hall C., Page R., Discrete Mathematics Using a Computer, Springer-Verlag, London 2006. (EN)
Rosen, K.H., Discrete Mathematics and its Applications, AT & T Information systems, New York 1988. (EN)
Rosen, K. H. et al., Handbook of Discrete and Combinatorial Mathematics, CRC Press, Boca Raton 2000. (EN)
Ross, S. M. Topics in Finite and Discrete Mathematics, Cambridge University Press, Cambridge 2000. (EN)

eLearning

eLearning: currently opened course

Classification of course in study plans