Abstract. We study finitely additive measures on the set N which extend the asymptotic density (density measures). We show that there is a one-toone correspondence between density measures and positive functionals in ℓ * ∞ , which extend Cesàro mean. Then we study maximal possible value attained by a density measure for a given set A and the corresponding question for the positive functionals extending Cesàro mean. Using the obtained results, we can find a set of functionals such that their closed convex hull in ℓ * ∞ with weak * topology is precisely the set of all positive functionals extending Cesàro mean. This also describes a set of density measures, from which all density measures can be obtained as the closed convex hull.

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Analysis of the experimental results presented in the following chapter reveals experiences with introduction of active learning methods in basic mathematics courses at the Faculty of Mechanical Engineering, Slovak University of Technology in Bratislava. Experiment was implemented in the academic year 2018/19, in basic courses Mathematics I and Mathematics II scheduled in the first year of bachelor study programs and in subject Basics of Statistical Analysis for bachelor students in the second year of their studies. The aim of the experiment was to find achieved level of knowledge acquisition and to compare abilities of students to solve mathematical problems individually or by collective work and collaboration in small groups. Anonymous questionnaire answered by students after completion of the experiment provided rich feedback and overview of their opinions, from which their attitudes towards different teaching methods applied in 3 compulsory subjects from their study programs could be deduced and summarised. Based on received data, research analysed also results that students achieved comparing their achievement from the secondary schools and in both maths courses at the university.