Artykuły naukowe (WMFT): Recent submissions
Wyświetlanie pozycji 1-20 z 767
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The role of visualisation in the process of generalisation
(2015)In my paper, I discuss the results of individual observations of pupils aged 13-14. These children undertook an attempt to solve problems which were designed in order to bring about an inductive type of generalizing. The ... -
High School Identities
(2015)In 1969, Polish mathematician and logician, Alfred Tarski asked if all the identities true in the set of natural numbers involving the constant 1, addition, multiplication, and exponentiation can be derived from the ... -
O zjawisku zniekształcania obrazu matematyki
(2015)In this paper, we identify the phenomenon of false conviction. We analyze the definition of false conviction and provide the typology of false convictions, including their logical, geometric, cognitive and methodological types. ... -
Quasi-arithmetic means
(2015)We present a list of geometric problems with solutions that lead to known or less known means. We also prove, by elementary means, some property for so-called quasi-arithmetic means. We use the proved result to justify ... -
Iterations of homographic functions and recurrence equations involving a homographic function
(2015)The formulas for the $m$-th iterate $(m \in N)$ of an arbitrary homographicfunction $H$ are determined and the necessary and sufficient conditions for a solution ofthe equation $y_{m+1} = H(y_m)$, $m \in N$ to be an ... -
Fibonacci polynominals of order $k$
(2014)In this paper we give formulas determining the Fibonacci polynomials of order $k$ using the so-called generalized Newton symbols, i.e., the coefficients in the expansion of $(1+z +z^2 +. . .+z^{k−1})^n$ with respect to ... -
Calculus without the concept of limit
(2014)There are two different approaches to nonstandard analysis: semantic (model-theoretic) and syntactic (axiomatic). Both of these approaches require some knowledge of mathematical logic. We present a method based on an ... -
Nowe cechy równoboczności trójkątów
(2014)In this paper the authors formulate and prove several conditions for triangle to be equilateral. These conditions are associated with Gergonne, Nagel and Torricelli points and were obtained by composing and solving the ... -
Approximation by some combinations of the Poisson integrals for Hermite and Laguerre expansions
(2013)The aim of this paper is the study of a rate of convergence of some combinations of the Poisson integrals for Hermite and Laguerre expansions. We are able to achieve faster convergence for our modified operators over ... -
Congruences characterizing twin primes
(2012)Inspired by P.A. Clement’s results in [2], we give new necessary and sufficient conditions for two prime numbers to be twin primes. -
On stability of some functional equations and topology of their target spaces
(2012)Some remarks about the coherence of the stability of several functional equations with topology of their target spaces are given. The equations in question are: homogeneity (first of all) and quadratic ones, as well as ... -
Kształcenie przyszłych nauczycieli matematyki - wyzwanie edukacyjne
(2012)The purpose of this paper is to draw attention to the still current (as compared to the reform of higher education) issue: how should we train mathematics teachers in order to attain the desired outcomes? The article presents ... -
Z badań nad trudnościami studentów w rozumieniu pojęcia miary i całki
(2012)Measurement is an important form of human activity. It appears at all levels of secondary school education, while discussing the length of a segment, the area of a plane figure and the volume of a solid. The definition ... -
Przyczynek do badań nad twórczą postawą studentów podczas rozwiązywania zadań matematycznych
(2012)In this paper, we understand the term "creative attitude" to denote an action of the learner which consists in undertaking creative activity. This activity can take different forms, such as: discovery, invention, a ... -
O nieskończonych ciągach liczb parami względnie pierwszych raz jeszcze
(2012)In this paper the authors, using general formulas, determine and describe a class of infinite sequences of natural numbers, pairs of which are relatively prime. This result was obtained using the theory of Lucas sequences ... -
Cechy równoboczności trójkątów
(2012)The paper presents some non-standard (in the sense: not yet presented in the literature), necessary and sufficient conditions for a triangle to be isosceles. -
Od hipotezy do twierdzenia
(2012)In this paper, on the basis of elementary geometrical content, the authors present examples of students' reasoning, which permits, in the first place, to formulate a hypothesis, and further to find a proof. The essential ... -
O pewnym sposobie kontroli rozumienia wybranych pojęć z analizy matematycznej przez studentów studiów matematycznych
(2012)In the last years in Poland new standards for the matriculation examination have been established, especially in mathematics. Subsequently, for many years at the Pedagogical University of Krakow research has been conducted ... -
Przykłady zagadnień z różnych działów matematyki niezbędnych do studiowania teorii miary
(2012)In the education of mathematicians, including teachers of mathematics, the measure theory plays an important role. From the experience in and research on teaching the measure theory it follows that one of the important ... -
O ciałach uporządkowanych
(2012)In this paper, we present some basic facts concerning ordered fields. We review definitions of an ordered field, give an example of a field that admits many orderings, and present equivalent definitions of the axiom of ...