The subject, Foundations of Mathematics I, contains three chapters dealing
with linear algebra, analytic geometry in E3 and an introduction into the
differential calculus of a function of one real variable.
The goal of the first chapter is to introduce, by suitable motivations, terms
of the n-dimensional arithmetic vector and the vector space, to make the
student familiarized with other basic terms and with the solution of systems of
linear equations.
The second chapter deals with the analytical expressions of a plane and a
line in E3 and the basic positional and metric tasks.
The third chapter deepens the knowledge obtained in secondary schools
regarding the real-valued function of a real variable. The basic term of the
differential calculus – the term of derivation is motivated geometrically as
well as physically. The knowledge of examining the behaviours of functions is
used also in the solution of practical problems.