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System komputerowy Mizar narzędziem do komputerowego wspomagania nauczania w szkole wyższej

100%

Borak E.

Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia

2010

tom 3

21-40

The MIZAR system is a computer system for representing mathematical proofs in such a way that the computer checks their correctness. The texts written in the MIZAR language are called Mizar articles and are organized into the Mizar Mathematical Library (MML). Since the very beginnig of the development of the MIZAR system, experiments using MIZAR as a tool for teaching mathematics have been conducted. Numerous courses were organized which were based on different versions of the system: starting from the first implementation of its processor, through MIZAR-MSE, MIZAR-4 and PC-MIZAR, up till its current version. The first MIZAR-aided classes were introduced in 1975. In this paper we present the MIZAR system and the Mizar language and discusse courses conducted in the Institute of Informatics at the Univesity of Białystok. These courses employ MIZAR as the main tool of instruction.

Extended finite operator calculus-an example of algebraization of analysis

63%

Kwaśniewski A., Borak E.

Open Mathematics

2004

tom 2

nr 5

767-792

“A Calculus of Sequences” started in 1936 by Ward constitutes the general scheme for extensions of classical operator calculus of Rota-Mullin considered by many afterwards and after Ward. Because of the notation we shall call the Ward's calculus of sequences in its afterwards elaborated form-a ψ-calculus. The ψ-calculus in parts appears to be almost automatic, natural extension of classical operator calculus of Rota-Mullin or equivalently-of umbral calculus of Roman and Rota. At the same time this calculus is an example of the algebraization of the analysis-here restricted to the algebra of polynomials. Many of the results of ψ-calculus may be extended to Markowsky Q-umbral calculus where Q stands for a generalized difference operator, i.e. the one lowering the degree of any polynomial by one. This is a review article based on the recent first author contributions [1]. As the survey article it is supplemented by the short indicatory glossaries of notation and terms used by Ward [2], Viskov [7, 8], Markowsky [12], Roman [28–32] on one side and the Rota-oriented notation on the other side [9–11, 1, 3, 4, 35] (see also [33]).

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1 Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia

1 Open Mathematics

2 Borak E.

1 Kwaśniewski A.

1 2010

1 2004

Wyniki wyszukiwania

System komputerowy Mizar narzędziem do komputerowego wspomagania nauczania w szkole wyższej

Extended finite operator calculus-an example of algebraization of analysis