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The course consists of several deeper results in a few mathematical disciplines. The idea is to help a student to read, with a certain comfort, the monographs in given lines of applied mathematics. The contents of the course are fundamental results (principles) of nowadays mathematics.
More specifically, the course concerns the Stone representation theorem for Boolean algebras (as applied in mathematical logics and probability theory), the Banach fixed-point theorem for complete metric spaces (as applied in numerical mathematics), the Tychonoff theorem on compact spaces (as applied in measure theory), the Riesz representation theorem for linear forms in a Hilbert space (as applied in the optimization theory), the Brower theorem for balls in $\R^n$ (as applied in linear algebra – the Perron theorem), the elements of category theory for a practical man, etc. The asset may be a certain encouragement in a student’s research.