The module consists of a lecture with tutorials that deals with the following topics:

1. Structures and functions
   
   • real and complex numbers
   • basic topological and metrical terms
   • Functions and mappings in Rⁿ, complex functions
2. Basics of infinitesimal calculus
   
   • Convergence of sequences, series
   • Function sequences and series  (e.g. Fourier series)
   • Limits of functions, continuity
3. Differential and integral calculus
   
   • Differentiation, rules of computing
   • Taylor development
   • Integral, rules of computing (improper integrals)
   • Fundamental theorem of differential and integral calculus
4. Linear spaces and linear mappings (finite-dimensional)
   
   • Vector spaces (Rⁿ/Cⁿ , basis, duality)
   • linear mappings and matrices calculus
   • linear equations

The module is a non-compensable obligatory module. It is passed and the credit points are awarded if the test is passed. Admission requirement for the test is the regular successful participation in tutorials, especially the successful process of the exercises. The docent announces how many exercises have to be passed successfully at the beginning of the semester. It is necessary to applicate to an exam. At the beginning of the following semester a re-examination will be offered. Another retry is possible in the next year. A non- passed exam can be repeated twice. In case of not passing the second re-examination the module is considered failed. This module is not marked and is evaluated with passed/ failed.

• Funding of logical and analytical thinking