Wydział Nauk Ścisłych i Przyrodniczych (WMFT)
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Wybrane uwagi na temat roli zadań matematycznych w procesie nauczania-uczenia się matematyki
(2016)The paper presents the comments relating to the role of tasks in the process of teaching and learning of mathematics in the context of education of students studying to become teachers. In the considerations part, ... -
O pewnej implikacji
(2016)The purpose of this paper is to show how the process of proving a theorem in different ways or proving generalized versions of the theorem, after learning one its proofs, influences the development of the skills of ... -
Propozycja wyzwalania twórczości matematycznej studentów przy pomocy pewnej nierówności funkcyjnej
(2016)T. Szostok and Sz. Wąsowicz in (Szostok, Wąsowicz, 2011) studied the following functional inequality: $\vert F \left( y \right)-F\left( x \right)-\left( y-x \right)f\left(\frac{x+y}{2} \right)\vert \le \varepsilon$ stemming ... -
Twórcza aktywność matematyczna uczniów związana z rozwiązywaniem pewnych zadań na zastosowanie wzorów Viète’a
(2016)In this article we propose ways of developing the active and creative attitude of students towards solving mathematical problems. The tasks were sourced from various mathematical competitions for secondary school students, ... -
A Purely Algebraic Proof of the Fundamental Theorem of Algebra
(2016)Proofs of the fundamental theorem of algebra can be divided up into three groups according to the techniques involved: proofs that rely on real or complex analysis, algebraic proofs, and topological proofs. Algebraic proofs ... -
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 ... -
Geometric properties of arrangements of low-degree curves
(2026-07-13)This thesis investigates geometric properties of arrangements of low-degree plane algebraic curves in the complex projective plane. The primary focus is on configurations of lines, conics, and cubics, with particular ... -
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 ... -
Podstawy informatyki w kierunku twórczej aktywności ucznia
(Wydawnictwo Naukowe Uniwersytetu Pedagogicznego, Kraków, 2019)Skrypt jest przeznaczony dla studentów przygotowujących się do roli nauczyciela informatyki ze szczególnym uwzględnieniem pracy w technikum informatycznym. Może być także przydatny dla uczniów kierunku technik informatyk. ... -
Fregean fragments of Intuitionistic Propositional Calculus with mixed conguence type
(2025-11-27)We are investigating classes of subreducts of Heyting algebras, which form congruence permutable Fregean (quasi-) varieties. We are interested in classes that contain algebras of a mixed type according to Tame Congruence ... -
Wpływ temperatury i pola elektrycznego na właściwości monokrystalicznego tytanianu sodowo-bizmutowego $Na_{0,5}Bi_{0,5}TiO^3$
(2025-06-18)Na przestrzeni ostatnich dwóch dekad jesteśmy świadkami rewolucji naukowo-technicznej, polegającej na miniaturyzacji oraz wielofunkcyjności wielu urządzeń technicznych, której dzieckiem jest m.in. sztuczna inteligencja, ... -
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 ...
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