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2 2014

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Elements of mathematical epistemology - elements of the philosophy of teaching mathematics

Pawlak R. J., Korczak-Kubiak E.

Scientific Issues of Jan Długosz University in Częstochowa. Mathematics

2014

Vol. 19

11--24

In the paper we present the main idea of the concept which we have called confrontational concept of mathematical epistemology. We refer it to philosophy of mathematics (in the context of epistemology of research) as well as to didactic problems (in the context of teacher preparation). Although we tried not to involve our discussion directly with any existing concepts of the philosophy of mathematics, however, in the paper one can notice some elements of modern formalism as well as Lakatos quasi-empiricism or a modern approach to structuralism.

On ∞-entropy points in real analysis

Korczak-Kubiak E., Loranty A., Pawlak R. J.

Opuscula Mathematica

2014

Vol. 34, no. 4

799--812

We will consider ∞-entropy points in the context of the possibilities of approximation mappings by the functions having ∞-entropy points and belonging to essential (from the point of view of real analysis theory) classes of functions: almost continuous, Darboux Baire one and approximately continuous functions.