English

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The students will improve their knowledge of the algebraic structures that are most often employed in informatics. These will be mathematical logic, algebra, functional alalysis and graph theory. This will enable them to better understand the theoretical foundations of informatics and also conduct research work in the field.

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The aim of the subject is to improve the students' knowlende of the basic mathematical structures that are often utilized in different branches of informatics. In addition to universal algebra and the classical algebraic structures, foundations will be discussed of the mathematical logic, the theory of Banach and Hilbert spaces, and the theory of both udirected and directed graphs.

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Biggs, N.L.: Discrete Mathematics, 2nd ed., Oxford University Press, 2003, ISBN 978-0198507185 (EN)
Mendelson, E.: Introduction to Mathematical Logic, Chapman and Hall/CRC, 2015, ISBN 9781482237726 (EN)
Robinson, J.C.: An Introduction to Functional Analysis, Cambridge University Press, 2020, ISBN 9781139030267 (EN)

Farenick, D.: Fundamentals of Functional Analysis, Springer-Verlag, 2016, ISBN 978-3-319-45633-1 (EN)
Lang, S.: Undergraduate Algebra, Springer-Verlag, New York , 2005, ISBN 978-0-387-22025-3 (EN)
Nerode, A., Shore, R.A.: Logic for Applications, 2nd. ed., Springer-Verlag, 1997, ISBN 978-0-387-94893-5 (EN)
Shoham, Y.: Reasoning about Change, MIT Press, Cambridge, 1988, ISBN 0262192691 (EN)
Van der Waerden, B.L.: Algebra I, II, Springer-Verlag, Berlin - Heidelberg - New York, 1971, Algebra I. ISBN 0387406247, Algebra II. ISBN 0387406255 (EN)