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Some beautiful and powerful mathematical ideas are hard to present to students because of the involved abstract language (notation, definitions, theorems, proofs, formulas) and lack of time. Animation and “mathematical experiments” provide a remedy. In the field of stochastics, the Galton board experiment presents several fundamental stochastic notions: a random event, independent random events, the...
In this paper, we give the proposition of didactic discussion on the existence of solutions of some equations containing expressions with absolute value. We are interested in the possibility of applying the method of conceptual problem solving. Under this term we understand such a procedure, in which the solver is not limited to the automatic application of the definition of the absolute value, but...
In the presented paper we study some properties of preponderantly continuous functions and functions satisfying the property A1. For any family F of real-valued functions we define MAXF= {g: max{f,g} ∈ F for all f ∈ F} and MINF= {g: min{f,g} ∈ F for all f ∈ F}. The aim of the paper is to find MINFfor two discussed classes of functions.
The problem of general description of the group of automorphisms of any Witt ring W seems to be very difficult to solve. However, there are many types of Witt rings, which automorphism are described precisely (e.g. [1], [2], [4], [5], [6],[7], [8]). In our paper we characterize automorphisms of abstract Witt rings (cf. [3]) isomorphic to powers of Witt rings of quadratic forms with coefficients in...
In this paper, research in the field of modular computing structures defined on sets of Gaussians are presented. The basis of the qualitatively new technique for the organization of high-speed parallel computations in a complex plane is presented by quadratic minimum redundant modular number systems (QMRMNS).
We show that the one-sided regularizations of the generator of any uniformly continuous set-valued Nemytskij operator, acting between the spaces of functions of bounded variation in the sense of Schramm, is an affine function. Results along these lines extend the study [1].
The aim of the paper is to present some of the results of an analysis of educational needs which was carried out among students of the Primary school teacher training study programme at Palacký University Olomouc and which was focused on the mathematical and didactical competencies of those students.
In this paper we present the results of research which was conducted in years 2006/2007 and 2007/2008 on groups of students of Pedagogical University of Cracow. The results are related with the role of the computer in the process of solving the tasks on the functions with parameter, discovering some properties of functions, formulating statements describing observed regularity and finding the method...
In the school year 2009/10 a mathematics achievement test was conducted on a sample of 576 students in the 3th grade of school. A mathematical skills test examined the ability to complete both simple and complex tasks. It also tested their aptitude for the application of knowledge to practical and problematic situations. The skills checked were mastered at a level of about 65%. Skills in geometrics...
In this article we present some theoretical approaches in mathematics education, especially in Poland and Hungary, with practical examples. We also describe some aspects of using ICT in mathematics education and cooperative learning.
In this paper we establish an approximation of subquadratic functions, which satisfy the condition ∃ ϵ > 0 ∀ x ϵ X |ϕ(2x) - 4ϕ(x)| ≤ 3ϵ, by quadratic functions.
The problem of calculating routing probabilities in packet synchronous networks, such as optically-switched packet networks, involves enumerating packet arrangements. Previously we published a method for enumerating the most probable packet arrangements, and in this article we present its novel graph interpretation and evaluate the method for several stop conditions and for the Poisson and geometric...
In this paper we consider the Poisson integrals of functions of two variables for Hermite and Laguerre expansions in the spaces [wzór] and [wzór], respectively. We state some estimates of the rate of convergence of the Poisson integrals.
The investigation of strong automorphisms of Witt rings is a difficult task because of variety of their structures. Cordes Theorem, known in literature as Harrison-Cordes criterion (cf. [1, Proposition 2.2], [3, Harrison's Criterion]), makes the task of describing all the strong automorphisms of a given (abstract) Witt ring W = (G, R) easier. By this theorem, it suffices to find all such automorphisms...
The first step to make transitional systems more efficient is to minimize the number of their states. A bisimulation relation is a mathematical tool that helps in searching for equivalent systems, what is useful in the minimization of algorithms. For two transition systems bisimulation is a binary relation associating systems which behave in the same way in the sense that one system simulates the...
Over the past 25 years highly successful methods for geometry theorem proving have been developed. We will use elementary and understandable examples to show the nature of the techniques for verification of geometric constructions made with interactive geometry environment and for proving geometric statements. In addition to some informations about the WinGCLC software with specific language, we look...
The time-fractional heat conduction equation with the Caputo derivative of the order 0 ˂ α ˂ 2 is considered in a bounded domain. For this equation different types of boundary conditions can be given. The Dirichlet boundary condition prescribes the temperature over the surface of the body. In the case of mathematical Neumann boundary condition the boundary values of the normal derivative are set,...
Many changes in the curriculum of mathematics have been made during a few last years. Frequent changes carry certain consequences. Pupils which finish high school may possess different knowledge in different years. This is because they may have various ranges of educational material (different from those of their older or younger colleagues). Additionally, some parts of school mathematical material...
Electronic support of teaching is a prospect of future education, especially for students of tertiary education. Since 2005/2006 academic year the study at the Faculty of Education, University of Presov, has been implemented by the combination of methods. Mathematical disciplines have been taught in the form of contact classes and electronic support through LMS Moodle. The article analyzes the importance...
M/M/n/m queueing systems with identical servers are well known in queueing theory and its applications. The analysis of these systems is very simple thanks to the fact that the number of customers ɳ(t) in the system at arbitrary time instant t forms a Markov chain. The main purpose of this paper is to analyse the M/M/n/m system under assumption that its servers are different, i.e. they have different...
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