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1

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

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2014

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Vol. 19

11--24

EN

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.

2

On ∞-entropy points in real analysis

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

Opuscula Mathematica

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2014

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Vol. 34, no. 4

799--812

EN

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.

3

Programowanie w C+ + a metoda projektu

Korczak E., Loranty A., Pawlak R. J., Walczak S. M.

Zeszyty Naukowe Wyższej Szkoły Informatyki

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2004

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Vol. 3, Nr 1

93-105

4

Rola i znaczenie kontekstów realistycznych w procesie budowania dojrzałości matematycznej na różnych szczeblach edukacji

Pawlak R. J.

Matematyka Stosowana : matematyka dla społeczeństwa

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2003

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Nr 4

139-153

5

On Baire one point of funtions

Pawlak R. J., Świątek B.

Demonstratio Mathematica

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2003

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Vol. 36, nr 1

53--64

EN

We show that the subspace of the space of almost continuous first recoverable with respect to some trajectory {xn} functions, consisting of first return continuous functions with respect to {xn}, is porous at each point of whole space. Next we define a class of strongly F-almost everywhere first return recoverable functions and we describe some properties of these functions. We also prove that the subspace of the space of strongly F-almost everywhere first return recoverable functions consisting of measurable functions is superporous at each point of whole space.

6

On the Set D in the Space D R1

Pawlak R. J.

Zeszyty Naukowe Wyższej Szkoły Informatyki

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2001

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Vol. 1, Nr 1

27-33