Wydział Nauk Ścisłych i Przyrodniczych (WMFT): Recent submissions
Wyświetlanie pozycji 301-320 z 944
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Kilka uogólnień reguł pewnej gry strategicznej
(2013)In the paper a set of strategy games is presented. It is shown how the “manipulative” developing of the winning strategy of a known and simple game can lead to conceptual reasoning based on reduction; then it is ... -
Around the Wilson's theorem
(2013)In this paper some known conditions and new congruences characterising prime numbers are given. Some of them are obtained by the generalised Wilson theorem given by Gauss. The elementary proof of this theorem is also presented. -
Twierdzenie Bézouta o przecięciu krzywych algebraicznych w pracach Eulera
(2013)In the paper an early history of the Bézout theorem on algebraic curves and effective methods in elimination theory is presented. The hypothesis, stated in 1665 by Newton, on the ”intersection number” of algebraic curves ... -
Uporządkowane struktury liczbowe
(2013)In this article we consider the ordered algebraic structures of the systems of natural numbers, integers, rational and real numbers. We present the ordered algebra of natural numbers, the ordered ring of integers, and ... -
O fałszywych przekonaniach obserwowanych na zajęciach z analizy matematycznej
(2009)In this paper we present the results of our research carried out among the students of the first, second and third years of mathematical studies in the years 2003-2006. The research was focused on the diffi- culties ... -
Diagnoza wiedzy uczniów szkół ponadgimnazjalnych i studentów matematyki na temat związku twierdzenia z jego dowodem
(2009)The paper presents results of research carried out on the two following levels of mathematics education: the high school level and the level of pre-service Mathematics teachers training. The subject of the research was ... -
O zastosowaniu sumowania według Eisensteina do pewnej sumy podwójnej
(2009)The lattice sum $S_2$ for the square array conditionally converges. Having used physical arguments, Rayleigh chose an order of summation in such a way that $S_2$ = π. The Eisenstein summation method applied to $S_2$ ... -
Wybrane problemy zadań konstrukcyjnych na płaszczyźnie euklidesowej i wykorzystanie do ich rozwiązywania twierdzeń geometrii rzutowej
(2009)The article gives examples of construction tasks of first and second degree on a Euclidean plane, which can be solved with the use of a simple ruler. For this purpose the theoretical backgrounds of projective geometry ... -
Idea czynnościowego wprowadzania pojęć geometrii elementarnej z pomocą kursu e-learningowego
(2009)The present article introduces a didactic proposal of supporting the process of teaching mathematics with blended learning. The authors discuss both benefits and dangers of this idea. Also, the concept of functional method ... -
Wprowadzenie funkcji trygonometrycznych przez szeregi Eisensteina
(2009)In the paper we describe how to introduce the trigonometric functions using their functional characteristics and the Eisenstein series. -
Rola programu komputerowego CABRI w rozwiązywaniu matematycznych problemów
(2009)CABRI is a didactic program which has won a very stable position and is probably the most popular one in teaching mathematics. The program is constructed in such a way that it not only accepts and carries out tasks but ... -
O nieskończonych ciągach liczb naturalnych, parami względnie pierwszych
(2009)In the first part of the paper the authors, using general formulas, determine and describe a class of infinite series of natural numbers pairs of which are relatively prime. The second part of the paper contains - as a ... -
Z badań nad sylwetką absolwenta matematycznych studiów w Akademii Pedagogicznej w Krakowie w latach 2001-2007
(2009)The main goal of our studies was eliciting the opinion of graduates and students of the last year of Master studies on the course for teachers of mathematics at the Pedagogical University of Cracow. The research method ... -
O różnych sposobach definiowania wartości bezwzględnej liczby rzeczywistej
(2009)In this article we present some didactic ideas of introducing the absolute value of a real number by means of functional equations and an inequality. The basic properties of the absolute value of a real number are written ... -
Ułamki algebraiczne i funkcje wymierne
(2009)The subject-matter of this article can be divided into three main parts. The first one includes the theoretical problems concerning the fields of algebraic fractions and rational functions. In the second part we deal with ... -
On a class of linear differential operators of first order with singular point
(1997)The aim of this paper is to give a background to study spectral properties of some operators occurring in differentiall geometry. We deal with the problem of existence and uniqueness of local solutions of partial ... -
The stability of a generalized quadratic functional equation
(1997)In the paper we consider the stability of the functional equation f ( x + y) + f ( x - y) + ||f ( x + y) - f (x - y)||u = 2f(x) + 2f(y), where f : G —> X, X is a normed space, u ϵ X such that ||u|| ≥ 1 and ||u|| ≠ 3 is ... -
Quasi-linear mappings
(1997)Let E[1], E[2] be real normed spaces and let ε ϵ [0,1). The paper deals with the system of inequalities || f(x + y) - f(x) - f(y)|| ≤ ε min{||f(x + y)||,||f(x) + f(y)||} for x , y ϵ E[1], II f(αx) - αf(x)|| ≤ ε min ...