| ALSEKSEK Yasmina (AE), GRIRA Sofiane (AE) " The Role of Statistics Softwarein Improving Student’s Learning of Statistics " - from the section: New Trends in Mathematical Education A statistics course is fundamentally intended to enable students comprehend and manipulate statistical data then analyse results; based on these skills they shall make critical decisions in their future professions. Teaching students core statistical concepts using the right approach is a quite important aspect; it either sets off a clear background or induces confusion. Therefore, in order to satisfy the purpose of the course, various teaching styles should be implemented and results compared to maximize efficiency of teaching time and students’ perception. This paper anticipates the impact of using statistical software, StatCrunch, in statistics courses on students’ academic performances. |
| ANTOŠ Karel (CZ) " Possibilities and Strategies for Solving Problems in High School Mathematics " - from the section: Mathematics and Art The article shows that the use of heuristic teaching methods can help to improve the students' ability to solve problems and their ability to learn independently. The aim of the article is to explain how to include problem solving in mathematics teaching and how to apply experimentation as a method of solving problems. Examples of using typical heuristic strategies to solve problems in teaching mathematics are given here. |
| BALLOVÁ Dominika (SK) " The Achievement of Students in Mathematics and the Influence of Mathematics on the Study of Civil Engineering " - from the section: Statistical Methods in Technical and Economic Sciences and in Practise In civil engineering and technology itself (applied) mathematics often occurs. Therefore, first we evaluated the success of students during two semesters in the first year of their studies. In this paper we used several statistical tools to analyse and describe the results of the examination of the subjects Mathematics 1 and Mathematics 2. The core of these subjects is to deal with matrices, limits, derivatives, integrals and their application in civil engineering. Next aim was to described the impact of mathematical knowledge on successful graduation at the Faculty of civil engineering. This was carried out by means of logistic regression based on the results of previous graduates. Based on the obtained model we predicted successful or unsuccessful completion of studies for current freshmen. These days a very often discussed aspect is the importance of upper secondary school examination from the subject Mathematics. The effect of this factor on successful graduation is also determined. |
| BARTOŠOVÁ Jitka (CZ), BÍNA Vladislav (CZ) " Determinants of an Ability to Make Ends Meet In the Case of Czech Households " - from the section: Statistical Methods in Technical and Economic Sciences and in Practise The paper concerns an analysis of differences in subjective assessment of the financial situation in Czech households. It focuses on determinants influencing the ability of households to make ends meet. The aim of the paper is to choose from the group of household characteristics and to identify factors statistically significant for the assessment of the financial situation. The paper uses the newest data files from the EU-SILC 2017 sample survey concerning Czech households. |
| BENEŠ Michal (CZ), VACKOVÁ Petra (CZ), KUČERA Petr (CZ) " Existence and Regularity of the Stokes System with the Do-Nothing and Navier’s Boundary Conditions " - from the section: Differential Equations, Dynamic Systems and Their Applications In this paper we study qualitative properties of weak solutions of the Stokes equations with the mixed boundary conditions in bounded domains. We prescribe "do– nothing" boundary conditions and Navier’s boundary conditions in two different parts of the boundary. Our aim is to study regularity of solutions in the neighbourhood of points in which boundary conditions change their type. |
| BERAN Filip (CZ) " Geometric Transformations as a Gateway into Mathematical Structures: Constructivist Approach " - from the section: New Trends in Mathematical Education Linear algebra and generally abstract algebra are considered as one of the most difficult domains among university freshmen. This article briefly suggests how a gradual and creative exploration of the world of geometric transformations can provide insightful background for introducing crucial concepts of abstract algebra and other structural disciplines. |
| BEREZOVSKII Volodymyr (UA), MIKEŠ Josef (CZ), RÝPAROVÁ Lenka (CZ) " Conformal and Geodesic Mappings onto Ricci Symmetric Spaces " - from the section: Algebra and Geometry and Their Applications In this paper, we consider the conformal and geodesic mappings onto Ricci symmetric spaces. We obtained fundamental equations in the Cauchy type form, which depend on finite real parameters. |
| BÍLKOVÁ Diana (CZ) " Elasticity of Four-Parameter versus Three-Parameter Lognormal Curves: Comparative Analysis " - from the section: Statistical Methods in Technical and Economic Sciences and in Practise This paper deals with the construction of wage distribution models using four-parameter and three-parameter lognormal curves. The main objective of the research is to compare the accuracy using both types of lognormal distribution as wage distribution models. Gross monthly nominal wage is the main research variable. The results in terms of the accuracy of both types of lognormal curves are approximately the same in only a few cases. However, the differences are not critical. |
| BÍMOVÁ Daniela (CZ), BŘEHOVSKÝ Jiří (CZ), PIRKLOVÁ Petra (CZ) " Creation of Geometric Solids in GeoGebra " - from the section: New Trends in Mathematical Education Spatial visualisation and spatial geometric thinking belong among the innate abilities of a man. Every man borns with certain assumptions of both of them. If spatial visualization is trained by appropriate stimuli, the man can improve its level. It’s possible to train the spatial visualization in all the levels of school attendance. The contribution shows the possibility of practising it via GeoGebra dynamic applets inserted into the GeoGebra book “Creation of Geometric Solids” at the university. |
| BOLOGNA Francesco (IT), PERROTTA Anna (IT), ROGORA Enrico, VERONESI Ilaria (IT) " Using Graphing Calculators at University " - from the section: New Trends in Mathematical Education In the last few years, we made use of graphing calculators in many different teaching/learning contexts at University. This is a report about these experiences with some considerations on the suitability of graphing calculators for teaching/learning Mathematics at University. We shall report activities with five different groups of learners: prospective university students in mathematics; first year university students in science; students working for Master’s Degree Projects; prospective teachers of Mathematics; in-service teachers of Mathematics. |
| BONANZINGA Vittoria (IT), CISTO Carmelo (IT), MICELI Edwige (IT) " Blended Learning: An Experience Withuse of Mobile Devices for the Course “Fundamentals of Mathematics for Basic Education” " - from the section: New Trends in Mathematical Education In this paper we show an experience of Blended Learning for the course of “Fundamentals of Mathematics for Basic Education”, held at the University of Reggio Calabria (Italy). The main feature of this experience was the use of the university e-learning platform to enable students to take tests both in and outside of the lecture hall, above all, using mobile devices. |
| BRANDI Primo (IT), PUCCI Mario Angelo (IT), SALVADORI Anna (IT) " Elementary Mathematical Models in Chemical Kinetics " - from the section: Mathematics and Art We wish to present some opportunities offered by Chemistry to Mathematics in the context of an interdisciplinary approach to education for pre-university studies. A double voice on the same topic has important advantages for both disciplines. Mathematics has the opportunity to deepen some fundamental concepts and to introduce the students to basic elements of mathematical modeling. Chemistry, by delegating the more technical elements of modeling to Mathematics, can concentrate on the peculiar aspects of the discipline. The result is certainly a strengthening in the education for both the disciplines. |
| BRANNY Michael (CZ), FERDIÁNOVÁ Vera (CZ) " Mascheroni Constructions of Line Segments of Different Square Roots " - from the section: Mathematics and Art Mascheroni constructions are constructions with restricted means, more specifically only with a compass. The paper is a follow-up to previous articles [1] and [2] discussing the topic. New constructions of line segments will be presented; this time of a given length of various square roots. |
| BRUNETTI Federico Alberto (IT) " Unity in Multiplicity the New Bocconi Urban Campus, Designed by Sanaa Shapes, Surfaces, Perceptions in a Curvilinear Building Group. " - from the section: Mathematics and Art The realization of a particularly innovative project designed to house the new urban campus of the Bocconi University of Milan was recently inaugurated. The morphological, typological and technological characteristics of the project, designed by Kazuyo Sejima and Ryue Nishizawa's Sanaa architectural firm in Japan, are such as to merit a careful description also from the point of view of the adopted topological methodology. The constant curvilinear shape of the forms in the overall composition of the plan creates a space where the physical and perceptive continuity of some elementary forms that modulate and collide, creating a particularly characterized, innovative and surprising environment. The structure of the complex of buildings is organized - into the former Centrale del Latte industrial food plant abandoned area - distributing the various functions required by the University's customer through a system of planimetric forms derived from an original circular shape, but progressively altering the initial symmetry with different dilatations and internal voidings, which seems to refer to generative topologies or homeostatic morphologies. |
| BUDÍK Ladislav (CZ), BUDÍKOVÁ Marie (CZ) " Comparison of Various Methods of Parameters Estimation of mLN5 Distribution Using Simulation Study " - from the section: Statistical Methods in Technical and Economic Sciences and in Practise In this paper, we present the results of a simulation study that was focused on investigating the properties of four methods for estimating the parameters of the cumulative frequency curve of a modified LN5 distribution. We assess the quality of estimates by deviations of estimated parameters or extrapolated values from theoretical values. The simulation study pointed to some problems that will be the subject of further research. |
| ČADKOVÁ Věra (CZ), KUBÁTOVÁ Dana (CZ) " Design of Experiment for Monitoring Influence of Selected Factors on the Core Roughness Depth " - from the section: Statistical Methods in Technical and Economic Sciences and in Practise The paper describes application of the Design of Experiment in area of surface quality. Two factors in more levels (type of software filter and type of standard) and their influence on the response value (the core roughness depth) were watched. The aim of the experiment was to determine whether the selected factors influence the value of core roughness depth or whether there is an interaction of these two factors. |
| CAPANNA Alessandra (IT), MELE Giampiero (IT) " The Shape of Continuity a Research Method " - from the section: Mathematics and Art The study of mathematical objects with the philosophical aspiration to true, beauty and right, are the center of the research that from 2016, we are carrying on as the appliance of a method for the project of renewal of buildings and historical sites, starting from the original unit of measurement. The research produced survey-and-design experiments of different nature. The first in Castri di Lecce, a small town in Puglia, culminated with an exhibition and published in a book that extensively illustrates the hypotheses of intervention on this ancient ducal palace. |
| CARIDADE Cristina M.R. (PT), RASTEIRO Deolinda M. L. D. (PT),
RICHTARIKOVA Daniela (SK) " Mathematics for Engineers: Assessing Knowledge and Competencies " - from the section: Algebra and Geometry and Their Applications This work follows from the RULES_MATH project which aims to describe and analyse ways to assess mathematics taught to future engineers through competencies. The eight mathematical competencies already identified are recognized in the assessment made to students. Thus, in this work the competencies for learning complex numbers are evaluated. The study was carried out in a group of 126 students of Linear Algebra from Biomedical, Electromechanical and Mechanical Engineering in Coimbra Institute of Engineering. The results obtained were satisfactory since at almost questions (7 out of 9) students were able to obtain a positive grade. The performed assessment test also permits to identify level differences between the courses were it was applied. Relating the test itself as a tool to assess competencies, we may conclude that it covers most of the competencies that we need to evaluate, and its difficulty is adequate to our students. |
| CATERINO Alessandro (IT), CEPPITELLI Rita (IT), HOLÁ Ľubica (SK) " On the Jointly Continuous Multi-Utility Representation Problem " - from the section: Statistical Methods in Technical and Economic Sciences and in Practise One of the main problems in Decision Theory is to represent preference relations (or preorders) by means of continuous utility functions. We are interested in the existence of the multi-utility representations, jointly continuous in consumption sets and preferences, of a family P of non-total (partial) preorders defined on closed subsets of a topological space X. Non-total preorders are usually considered in the context of decision-making under uncertainty and risk. The continuous multi-utility representation of a non-total preorder is more functional than the classical Richter-Peleg utility representation as it allows a complete characterization of the preorder. The research in this paper can be described as a jointly continuous multi-utility representation problem. Problems of this type are important in Mathematical Economics, where the closed subsets of X are the consumption sets and P can be considered as a family of preference relations {  i : i  I }, where I is a set of economics agents. |
| CAVAGLIÀ Matteo (IT), COCCHIARELLA Luigi (IT) " The Role of Geometry as a Link Between Graphics and Computing, in the Supporting Multiscale Architectural Design Processes " - from the section: Mathematics and Art This contribution aims at testing a parametric approach in the design process, oriented to a multi-scale hypothesis of transformation concerning Portovenere and its environment. Thanks to the mediation of the geometrical language, design objectives were translated into computational problems delivered to specifically created algorithms, whose solutions, while improving the final design, allowed also for the generation of a dynamic process able to propose strategies for other territories. |
| ČERETKOVÁ Soňa (SK), BULKOVÁ Kristína (SK) " Mathematics Trails in Initial Teachersʼ Education in Slovakia " - from the section: New Trends in Mathematical Education Mathematics trail is part of outdoor mathematics education which is going to be more popular. The extra point of the mathematics trails is connected with using mobile devices in mathematics education. The project dealing with the activity and topic is Erasmus+ project Mobile Mathematical Trails in Europe (MoMaTrE) and the project uses the mobile application called Math City Map (MCM). The trail tasks composition with MCM is available for wide public. Types of tasks created in Slovakia by students in initial teachers’ education is introduced in this contribution and compared with tasks created also in Slovakia but by educators, members of partners’ team of the project. |
| ČERŇANOVÁ Viera (SK) " On a Configuration Resulting from Circle Inversions " - from the section: Algebra and Geometry and Their Applications In this paper, we informally describe how to create a fabric, which is a configuration of circles consisting of two orthogonal frames and two orthogonal families of inscribed Pappus–like chains. The method consists in reusing circle inversions. We also present different types of fabrics in terms of symmetry. |
| CHEREVKO Yevhen (UA), BEREZOVSKII Vladimir (UA), NENKA Ruslana (UA),
LESHCHENKO Svitlana (UA) " Infinitesimal Conformal Transformations of Riemannian Manifolds which Preserve the Generalized Einstein Tensor " - from the section: Algebra and Geometry and Their Applications We study conformal transformations leaving the generalized Einstein tensor invariant. We have obtained the system of partial differential equations for the transformations, and explored its integrability conditions. Hence we have got the necessary and sufficient conditions in order that a manifold admit a group of conformal motions, preserving the generalized Einstein tensor. Also we have estimated the number of parameters which the group depends on. |
| CHVALINA Jan (CZ), SMETANA Bedřich (CZ) " Systems of Fragments of Artificial Neural Networks " - from the section: Algebra and Geometry and Their Applications When we study structure of the most used artificial neural network - a multilayer perceptron and functionality of an artificial neuron, there is possibility using certain analogy with relations between descriptions of differential equations of a certain quality, in this paper is developed new approach to these subjects. In deeper view of point there can be used some concepts of locale finite trees of fragments of artificial neural networks and further to research by usage of monounary algebras and their characteristics with description and modeling systems of investigated structures of time-varying artificial neurons. |
| CIABURRO Giuseppe (IT), IANNACE Gino (IT), TREMATERRA Amelia (IT) " The Acoustic Applications of The Complex Image Method " - from the section: Mathematics and Art The image source technique is used for determining the sound field in a closed environment. The sound field is determined by the sum of the reflections of the sound rays on the surfaces of the environment. In this paper the sound field is analysed in a closed environment with the technique of complex images. The sound field is given from the sum in amplitude and phase of the sound rays that are reflected from the surfaces of the room. The results of experimental measurements in a scale model are shown in comparison with the sound field models obtained by the energy method and by the complex images. The complex image method is a good tool for studying the propagation of the sound a closed environment. |
| CIABURRO Giuseppe (IT), IANNACE Gino (IT), TREMATERRA Amelia (IT) " Sound Attenuation with Metamaterials " - from the section: Mathematics and Art The study of metamaterials represents a new research field in the applied acoustics. This paper describes the state of art of the applications of the metamaterials in the acoustics field. The applications of metamaterials for the sound attenuation of an acoustic barrier are reported. The acoustic measurements were carried out with a scale model barrier. |
| ČIERNIKOVÁ Dominika (SK) " Application of the Frobishers´ Technique for Creating the Open Tasks " - from the section: New Trends in Mathematical Education Learning during mathematics lessons takes place largely thanks to the tasks learners have to solve. Some challenging tasks can be found in different textbooks, workbook or on the Internet pages, but they can also be created by the teachers themselves. The article shows different ways how to open a closed task, so it would have more solutions. Following the systematic way of modifying the tasks, students at the University propose some open tasks from the field Fractions. |
| CUMINO Caterina (IT), PAVIGNANO Martino (IT), ZICH Ursula (IT) " Geometry of a Barrel Vault with Lunettes Between Subjectivity and Objectivity of Its Representation: A Critical Approach " - from the section: Mathematics and Art Our contribution is part of a research project aimed at investigating Geometry as a cultural substrate and shared language between Architecture and Mathematics. We analyse the sequence of constructions for graphically representing a barrel vault with lunettes as outcome of a critical process of data discretization: we focus on the intersection curve between the surfaces underlying vault’s geometric structure and we reason about subjectivity and objectivity of its representation. |
| CUMINO Caterina (IT), PAVIGNANO Martino (IT), ZICH Ursula (IT) " Cloister Vaults Between Synthetic, Analytic and Built Geometry: Il Vólto Antonelliano in Torino. " - from the section: Mathematics and Art Our contribution is part of a research project aimed at investigating Geometry as a cultural substrate and shared language between Architecture and Mathematics. In this sense, spatial visualization plays a crucial role in architects’ educations and heavily draws on making use of mathematical instruments. In this intention the ‘nudo e schietto’ (naked and explicit) architectural model, as theorized by Leon Battista Alberti, turns out to be the most effective one: it favors the objectivity of the geometric description, having less details, even if final results are not necessarily rigorous. Analogously, from a mathematical point of view, the model is a description of a reality through its formalization in equations, while the physical model that materializes it is a mediation between descriptive rigor and practical feasibility and therefore forgets part of the generative geometric consistency while remaining adequate to purposes for which it was produced. |
| DE LAURO Enza (IT), DE MARTINO Salvatore (IT), FALANGA Mariarosaria (IT), TEDESCHINI LALLI Laura (IT) " Physical Mechanisms Associated with the Soundscape: The Trevi Fountain Case Study " - from the section: Mathematics and Art We investigate the soundscape around the Trevi fountain (Rome) acquired by means of several synchronized microphones with the aim to individuate the signature of the fountain from any other external disturbance. The present result is a complete separation of the sound emitted by the fountain from an external source associated with flying swallows. Thus, we introduce a methodology for the identification of medium and long-term changes in the soundscape, in order to promote suitable strategies for its conservation and protection. |
| DE LAURO Enza (IT), FALANGA Mariarosaria (IT) " Analysis of Acoustic Field Emitted by Organs: A Contribution for the Tuning of Ancient Instruments " - from the section: Mathematics and Art This work is devoted to the study of the acoustic field produced by flue organ pipes. Several experiments have been performed in order to investigate the characteristics of the acoustic wavefield with the aim to provide an objective method for the restoration and tuning of organs. We study the behaviour of the pipes when they are excited by different levels of blowing pressure and when a single pipe is played in presence of another even silent. Synchronization and shifts in frequency occur. |
| DE MARCHIS Martina (IT), MENGHINI Marta (IT), ROGORA Enrico (IT) " The Importance of “Extensive Teaching” in the Education of Prospective Teachers of Mathematics " - from the section: New Trends in Mathematical Education In recent discussions on university curricula we fostered the idea that an extensive teaching of mathematics is needed in the education of prospective teachers. Most universities only provide courses on methodological didactical issues - if any - or intensive teaching, more suitable for prospective researchers. The goal of this paper is to clarify the meaning of extensive teaching, in the sense already considered in the work of Guido Castelnuovo, and to discuss its relevance today. |
| DEMLOVÁ Marie (CZ) " Increasing Students´ Motivation - Example form Discrete Mathematics " - from the section: New Trends in Mathematical Education In mathematics education, especially for engineering students, two main problems occur, the first one being unfamiliarity with the language of mathematics, the second one being students’ motivation. Very often students, especially engineering ones, perceive mathematics as an obstacle to their engineering degree, which results in surface learning. The contribution deals with one example of a part of a discrete mathematics course that can serve well to increase motivation of students to work with mathematical notions and develop some mathematical competencies. Experience from teaching discrete mathematics course for 1st and 2nd year students is given. |
DILLINGEROVÁ Monika (SK), VANKÚŠ Peter (SK) |
| DOTLAČILOVÁ Petra (CZ) " Modal Length of Life - Calculation Using Kannisto and Weibull Models " - from the section: Financial and Actuary Mathematics The aging population has been increasingly discussed in last days. Therefore, the attention is increasingly focused on mortality analysis. For this, the life expectancy is most often used. The other one is modal length of life. It can be also used for describing mortality. In this article, modal length of life will be used for mortality analysis. The Kannisto and Weibull models will be used for its calculation. The aim is to show the possibility of calculating modal length of life using these models. |
| ĎURIŠ Viliam (SK) " Solving Some Special Tasks for Arithmetic Functions and Perfect Numbers " - from the section: Modeling and Simulation in Engineering and Scientific Computations Arithmetic functions help us determine which of the three sets (abundant, deficient, perfect) a given number belongs to. Arithmetic functions can also be used to identify various other properties of numbers and they have a special position in the number theory. This paper points to the fact that arithmetic functions can be used to solve various special practical tasks and determine the properties of numbers. The paper also highlights the relationship between Mersenne numbers and perfect numbers, as well as the issues connected with the search for the highest primes. |
| DZENITE Ilona (LV), CERNAJEVA Sarmite (LV), MATVEJEVS Aleksandrs (LV) " Attractiveness of Engineering Higher Education Study at RTU for Foreign Students " - from the section: New Trends in Mathematical Education Due to a successful commitment to developing an international education offer, the number of foreign students enrolled in studies at Riga Technical University (RTU) is increasing significantly every year. In this paper, the authors describe the reasons why engineering studies at RTU are becoming so attractive to foreign students. The conclusions are made on the basis of student surveys and the long teaching experience of the Professors of the Engineering Mathematics Department. |
| ETTLER Tomáš (CZ), NOVÝ Pavel (CZ) " Diagnostic Meaning of Correlation Relationship " - from the section: Statistical Methods in Technical and Economic Sciences and in Practise Brief description of a method based on computing correlation between parameters for vocal cords recorded by high speed video camera. This method gives us possibility to analyze vocal cords kinematics and tries to evaluate specific vocal cords based on statistical data. |
| FALCOLINI Corrado (IT) " How Gold is the Golden Ratio? " - from the section: Mathematics and Art We discuss the well-known importance of the golden ratio in Science and Art with few examples: its theoretical value is often taken as a good model in many applications. How good is this model in practice? We agree with many authors that more precision is needed giving, when possible, a measure of the best possible approximation. We deal with several definitions and representations, also comparing this irrational number and its rational approximations to other similar constants. |
| FERDIÁNOVÁ Vˇera (CZ), PORUBA Jakub (CZ) " Augmented Reality in Lecture on Constructional Geometry " - from the section: New Trends in Mathematical Education Augmented reality is very popular among children and students, because it is almost a sci-fi element. It is an integral part of everyday life of young generation, as it is part of Instagram and Facebook. The popularity of augmented reality is currently rising and therefore we decided to use it in a lecture on Constructional Geometry, especially in the area of stereometry, which is difficult for students without spatial imagination. The aim of the article is to present an experiment, which we realized during the lecture and in which we used a device supporting 3D graphic preview, anaglyph and augmented reality. |
| FERREIRA Manuel Alberto M. (PT) " A Look on Mathematical Fundamentals for Minimax Theorem and Nash Equilibrium Existence " - from the section: Statistical Methods in Technical and Economic Sciences and in Practise We present two results of Game Theory, very important in Economics: minimax theorem and Nash equilibrium existence, together with their mathematical fundamentals. For minimax theorem, the mathematical structure considered is real Hilbert spaces. Moreover, the convex sets strict separation plays here an important role. For Nash equilibrium existence, Kakutani’s theorem is the key result to consider. Then follows a presentation of some propositions that identify matches between those outcomes. |
| FESZTEROVÁ Melánia (SK), PORUBCOVÁ Lýdia (SK), TIRPÁKOVÁ Anna (SK) " The Usage of Statistical Methods for Evaluation of Inorganic Nitrogen Content in Soil " - from the section: New Trends in Mathematical Education This paper shows the impacts of ago-technical arrangements oriented on thedynamics of inorganic nitrogen content. From the tilt practices, this effect described two methods of cultivation (medium depth ploughing-B1, shallow ploughing-B2) with tree variants of fertilization in two depths. The results of the analyzes confirmed that the average inorganic nitrogen content decreased as the depth increased and the date of soil sampling as a function of the growing season. |
| FRANK Jan (CZ), HONZÍK Lukáš (CZ) " Positivity of Polynomial in the Context of Czech Education " - from the section: Algebra and Geometry and Their Applications Decomposition of a polynomial as a Sum of squares of polynomials (SOS) is one of the classical methods how to prove that certain polynomial f is a positive semidefinite polynomial. At present, this is a technique that is not usually taught at Czech high schools or in (Computer) Algebra courses in the preparation of mathematics and/or computer science teachers at the faculties of education. In the case of polynomials of one variable, sum of squares decomposition could be a simple problem and this technique could be used by mathematical olympics solvers. The opposite case represents higher degree polynomials in multiple variables. Here we cannot solve the problem without computer technology and mathematical software. Thanks to this software, it is possible to look at the classical problems in an innovative way through the optics of computer technologies, and it is possible to solve problems which were almost impossible to solve in the past. Through the cognitive technologies, we can also bring near the more difficult parts of this issue and more abstract concepts to high school students and teachers at elementary and high schools. |
| FREIXAS Josep (ES), PONS Montserrat (ES) " A Mathematical Perspective on How Test-Type Exams Are Evaluated " - from the section: New Trends in Mathematical Education Typically, the test type exams with binary answers (true / false) are corrected by adding a +1 to the correct answers, a -1 to the incorrect ones and 0 to non-answered questions. This mainly obeys to a purely statistic criterion which incentives answering questions randomly when the student has the impression that she will not pass the exam with what she knows. From our point of view this method of qualification is not suitable and therefore should be amended as soon as possible. Unfortunately, it is still now massively used in many Faculties worldwide. The objective of the work is to provide an alternative method to accurately qualify such exams. |
| FULIER Jozef (SK), VALLO Dušan (SK) " Some Aspects of Visualisation and Visual Thinking in Mathematics and Mathematics Teacher Education " - from the section: New Trends in Mathematical Education In our contribution we discuss the importance of the visual thinking development and the visual competence of students in mathematics education. The bearing of use of the visual representations in mathematics teacher education is also discussed with an emphasis on the education in the elementary mathematical analysis. We present how to create modifications of the Dirichlet function with interesting properties, too. |
| GABKOVÁ Jana (SK) " EduScrum – the Innovative Active Learning and Teaching Method into Basic Mathematics II Course " - from the section: EduScrum method has been implemented to teaching at the Faculty of Mechanical Engineering, Slovak University of Technology in Bratislava – FME STU for the first time in subject Mathematics I, scheduled in the first year at the bachelor study programmes in academic year 2018/2019. On the base of responses (questionnaire and personal interviews) from students participating in the experiment, this method has been implemented also in subject Mathematics II. Individual work of students was applied again as an alternative method of the eduScrum method. The paper brings not only the way of implementation of both methods but also a qualitative and quantitative analysis of the experiment´s results. |
| GABKOVÁ Jana (SK), OMACHELOVÁ Milada (SK) " Eduscrum in Basic of Statistical Analysis Course at Fme STU in Bratislava " - from the section: The contribution provides information about experience with an innovative method eduScrum focused on active learning and teaching. Based on a positive feedback and good experience with this method in courses Mathematics I and Mathematics II and following the requirement of our students, the method was implemented also in the course Basics of Statistical Analysis. Apart from describing the implementation of this method in the teaching process and statistical evaluation of its effectivity, the paper also includes the opinions of students themselves on the selected method. |
| GABKOVÁ Jana (SK), RICHTÁRIKOVÁ Daniela (SK), LETAVAJ Peter (SK) " Assessment of Mathematical Competence via Contents Models " - from the section: Competency based education has taken on increased importance, and today it seems to be the answer on how to prepare students for their future occupations when very quickly changing technology considerably influences the character of all human activities. But how to learn teach and assess competences? The paper presents the partial outputs of the Rules_Math Project co-funded by the Erasmus+ Programme of the European Union designing the standards for assessment of mathematical competence at technical bachelor studies via contents models. In addition, we introduce a particular model designed at FME STU for assessing mathematical competencies on differentiation. |
| GAYOSO MARTÍNEZ Víctor (ES), HERNÁNDEZ ENCINAS Ascensión (ES),
HERNÁNDEZ ENCINAS Luis (ES), MARTÍN MUÑOZ Agustín (ES)
" Mathematics and Physics in Side-Channel and Fault Attacks to Cryptosystems " - from the section: Mathematical Aspects of Network Science and Applications In this work we show how by measuring certain physical magnitudes (known as side channels) and using simple mathematical operations after inducing a fault it is possible to break the security of cryptosystems embedded in physical devices. Mathematical formulations are also used as countermeasures to thwart both side-channel and fault attacks. |
| GAYOSO MARTÍNEZ Víctor (ES), HERNÁNDEZ ENCINAS Luis (ES),
MARTÍN MUÑOZ Agustín (ES), QUEIRUGA DIOS Araceli (ES)
" Elliptic Curves as a Basic Tool for the Securityewline of Blockchain " - from the section: Mathematical Aspects of Network Science and Applications Blockchain is one of the most important technologies that have been developed in the last years. Even though Bitcoin is its best-known success case, blockchain has also been implemented in smart contracts and logistic applications, to name a few examples. This paper presents a review of the elliptic curves and digital signatures used as part of the mathematical tools implemented in blockchain. |
| GERGELITSOVÁ Šárka (CZ), HOLAN Tomáš (CZ) " SAVE – Saving Student’s Responses " - from the section: New Trends in Mathematical Education Getting feedback on the use of the materials they create for students is important for teachers. In case of teacher-created GeoGebra applets the teacher does not even know whether students use them. We created system SAVE to store universal data coming from students to give feedback to the teacher on how the students deal with the homework. This paper illustrates using SAVE for saving from simple HTML pages and from embedded GeoGebra applet and it explains getting the applet data. |
| GLOVŇOVÁ Veronika (SK) " Teachers’ Beliefs About Learning from Errors Occurring in the Learning Process " - from the section: New Trends in Mathematical Education Errors are in our society often seen as an undesirable phenomenon which teacher tries to avoid and also leads students to avoid them. Generally, little is said about errors as an educational tool that can provide good learning opportunities. This paper shows the results of the interviews, where twelve teachers of mathematics were confronted about their ways of using errors as a learning tool. The paper also stresses the importance of dealing with errors in a preparation of teachers of mathematics. |
| GOCHEVA-ILIEVA Snezhana (BG), IVANOV Atanas (BG),
STOIMENOVA-MINOVA Maya (BG) " Prediction of PM10 Air Pollution Using Random Forests and ARIMA Error Correction Models " - from the section: New Trends in Mathematical Education A hybrid method has been proposed for analysis and prediction of atmospheric air pollution with particulate matter PM10 depending on meteorological conditions. The approach is based on random forests and correction of errors using ARIMA transfer function Box-Jenkins methodology. Both methods are applied for modelling data collected during five years for the town of Haskovo, Bulgaria. Model fit of over 85% is achieved as well as a very good prediction of high values of PM10. |
| GOCHEVA-ILIEVA Snezhana (BG), KULINA Hristina (BG), ILIEV Anton (BG), IVANOV Atanas (BG), ILIEV Iliycho (BG) " A Model for Assessment of Mathematical Competencies in Engineering Education " - from the section: New Trends in Mathematical Education This paper discusses issues related to the competence-oriented education and assessment of the knowledge of mathematics of university students. A specific model is presented for the assessment of mathematical competencies in vector algebra for engineering degrees. |
| GÖNCIOVÁ Zuzana (SK), HUBEŇÁKOVÁ Veronika (SK), SEMANIŠINOVÁ Ingrid (SK) " Mathematics Teachers Reflecting on Student´s Non-Standard Reasoning About Dividing the Fractions " - from the section: New Trends in Mathematical Education The national curriculum of the Slovak republic in mathematics suggests teaching in an inquiry way, which is the mathematically demanding way of teaching. Therefore, we ask whether Slovak mathematics teachers are ready to teach in this way. Our research question concerns teachers' knowledge of practices in mathematics (KPM) and focuses on fraction division. Data from 46 middle school mathematics teachers were analysed. Different levels of KPM were revealed, from simple inductive reasoning to regular correct proof. Our research revealed that among Slovak teachers, there is a group that uses inductive reasoning in order to verify the general applicability of the non-standard algorithm. Moreover, part of the teachers showed up problems with the conceptual understanding of the fractions division. This result indicated the need to strengthen further teacher education with an emphasis on mathematical knowledge. |
| GROSINGER Patrik (SK), ŠOLEK Peter (SK), RYBÁŘ Jan (SK) " Comparison of Planar Crane Models " - from the section: Differential Equations, Dynamic Systems and Their Applications This article focuses on analyzing various controlled planar dynamic crane models and provides simulations of multiple used approaches. A number of publications are devoted to the control of a plane crane model. This simplifying circumstance is justified, and most bridge cranes allow only one direction to shift the payload. It is therefore acceptable to replace this spatial system with a planar one. And the simplest controlled linearized model without friction and damping, non-linear model without friction and damping, and both mentioned models considering rolling friction between trolley and its rails. Models with viscous damping will not be considered because this damping is small for cranes. This article provides a comparison of individual computational approaches as well as comparisons with real-world crane response. Finally, there is a suitable and simple method of linearized system control with respect to rolling friction, which consists of a combination of feedback linearization method and PPM method. |
| HABALA Petr (CZ) " A New Numerical Methods Library for Maple " - from the section: Modeling and Simulation in Engineering and Scientific Computations We introduce a new numerical methods library for Maple. We compare its commands with their standard Maple counterparts, based on features that could be found desirable when we want our students to experiment and explore. |
HAVENS Christopher (US), TEDESCHINI LALLI Laura (IT) |
| HECKENBERGEROVÁ Jana (CZ), KRÖMER Pavel (CZ), HASAL Martin (CZ) " Modelling Daily Traffic Flow Distributions by Finite Mixtures of Simple von Mises Distributions " - from the section: Statistical Methods in Technical and Economic Sciences and in Practise Graphical representation of traffic flows and their accurate modelling is an important topic in intelligent transportation systems, urban planning, and smart environments in general. In this contribution, location–specific daily traffic flows are represented by finite mixtures of Von Mises distributions. The distribution parameters are found by an evolutionary algorithm (differential evolution) that is able to fit data with a high level of accuracy. Statistical models augmented with frequency data are represented by circular plots that can be used as a form of visually appealing and easily understandable fingerprints of the daily traffic flow patterns. |
| HENCL Martin (CZ), MAREK Jaroslav (CZ) " Macrostructures of Zdeněk Sýkora " - from the section: Mathematics and Art In Czechoslovakia, Zdeněk Sýkora became the first artist to use the computer in the process of artistic creation. The computer was used to generate random numbers, which became the input parameters of the painter's algorithms. Zdeněk Sýkora began to consider randomness, geometry, and the computer as instruments of his work. His artworks were physically painted using the computer results as source. In the relatively short period of 1972-1973, the painter created so-called Macrostructures, which he obtained by oblique cut-outs from structural paintings. The subject of this paper will be the generation of Macrostructures using a programmed application based on Sýkora's system. |
| HROMADOVÁ Jana (CZ), MORAVCOVÁ Vlasta (CZ), ROBOVÁ Jarmila (CZ), HALAS Zdeněk (CZ) " Problems of Pre-Service Mathematics Teachers’ Education in Geometry " - from the section: New Trends in Mathematical Education The paper deals with problems of pre-service mathematics teachers’ education in geometry at Faculty of Mathematics and Physics, Charles University. It turns out that students come to the faculty with insufficient knowledge of planimetry and stereometry, and thus it is necessary to develop their pedagogical content knowledge based on the Shulman concept. We illustrate students’ problems with particular examples from credit tests, and we also present how the situation has been improved under the new accreditation. |
| HRUBÝ Petr (CZ), NÁHLÍK Tomáš (CZ), SMETANOVÁ Dana (CZ) " Transversal Vibrations of Rods With an Asymmetrically Located Burden " - from the section: Modeling and Simulation in Engineering and Scientific Computations In this paper the vibrations of the rod with an asymmetrically located burden are studied. The following cases are analysed: rod weight is negligible; rod weight is significant; rod with joints and rod with one free and one fixed end. The case of a single-burden rod is studied in detail. An approximate solution of the problem is found.. |
| IŽOLD Roman (SK), JANČO Roland (SK) " Propagation of Negative Pressure Wave Inwater-Filled Steel Pipe " - from the section: Modeling and Simulation in Engineering and Scientific Computations The aim of this paper is to examine measurement possibilities of the hydrophones used as sensors in leak detection system. The paper presents a proposal and a subsequent realization of the experimental setup used to investigate negative pressure wave actuation caused by ball valve opening in a water-filled pipe. Results presented in this work clarify leak detection possibilities actuated by ball valve opening. |
| JANČAŘÍK Antonín (CZ) " Designing Geometry Construction Problems in the Techambition System " - from the section: New Trends in Mathematical Education This paper contributes to the discussion on design and development of teaching materials and e-learning environments for solid geometry construction problems. The author describes his own experience with developing the Techambition system, presents questions arisen while creating the system and explains the reasons for selecting specific solutions to the questions. |
| JÁNSKÝ Jiří (CZ) " Teaching of Mathematics in Maple Program " - from the section: New Trends in Mathematical Education This article deals with the use of computer technology in teaching mathematics at the University of Defence. Specifically, it discusses the experience of using the Maple program in courses Mathematics I, Mathematics II, and Mathematics III. The article explains reasons for choosing this program for teaching. The main aim is, however, to show specific examples and describe in detail the problems that occur when teaching mathematics on a computer, and to present possible actions steps to minimize these difficulties. |
| KASPŘÍKOVÁ Nikola (CZ) " EWMA-Based LTPD Acceptance Sampling Plans and Cost Savings " - from the section: Statistical Methods in Technical and Economic Sciences and in Practise The paper addresses LTPD sampling plans minimizing the mean inspection cost per lot of process average quality for inspection by variables based on EWMA statistic. The situation of known standard deviation of selected quality characteristic is considered. The savings which may be obtained using this plan in comparison with the benchmark attribute sampling plan is shown. |
| KLŮFA Jindřich (CZ) " Analysis of the Results of Examinations at University " - from the section: New Trends in Mathematical Education The problem of objectivity of examinations in mathematics at the University of Economics in Prague is studied in this paper. Examinations in mathematics include mid-term test, final test and oral examination. These tests are standard tests, the multiple choice question tests are not used (the objectivity of the multiple choice question tests is evident). This problem was studied using some methods of mathematical statistics. |
| KOHOUT Václav (CZ), PĚCHOUČKOVÁ Šárka (CZ) " Bootstrap and Moment Estimator of the Tail Index γ " - from the section: Statistical Methods in Technical and Economic Sciences and in Practise One of the major interests in extreme-value statistics is to infer the tail properties of the distribution functions in the domains of attraction of an extreme-value distribution and predict rare events. There is the primary problem to find the estimation of the tail index usually performed on the basis of the largest k order statistics in the sample. The question that has been often solved in applications of extreme value theory is the choice of k or an estimation of . We shall be here mainly interested in the use of the bootstrap methodology to estimate Extreme Value Index (EVI) . We study and compute general case of this tail index . We shall also compare, through Monte Carlo simulation, these bootstrap methodologies with other data - driven choices of the optimal sample fraction. |
| KONEČNÁ Petra (CZ), PTÁČEK Jiří (CZ) " Level of Mathematical Knowledge and Skills of 1ST Year Students of Informatics and Mathematical Study Programmes " - from the section: New Trends in Mathematical Education The contribution introduces results of a survey of level of mathematical knowledge and skills of 1st year students of selected Bachelor study programmes, which was provided by two phase testing of students at the beginning of their university study. It also focuses on more detailed analysis of types of errors, which students made in selected tasks. |
| KONTRIKOVÁ Lenka (CZ), TEICHMANN Dušan (CZ), HOŘINKA Jiří (CZ), OLIVKOVÁ Ivana (CZ) " Using Mathematical Methods for Planning the Establishment of a New Flight Connection " - from the section: Statistical Methods in Technical and Economic Sciences and in Practise At present, air transportation is a very dynamically developing industry. The high dynamicity level can be seen not only in the technical aspect of aircraft and airport infrastructure and in the scope of air traffic, but also in airline management. The reason for this momentum is the continuing efforts of air carriers to seek out new business opportunities and the ever-increasing demand of a large number of regional airports for new flight connections. Airports are therefore in the role of demander and air carriers are in the role of supplier. As the preparation of the operation of a new flight connection is a long-term and very unstable process in which any complication may cause the air carrier to lose interest in operating the new connection to the airport, due attention should be paid to minimize these complications. Careful planning of the process by airports is one way to minimize complications. In this paper we will deal with the planning of one phase of the flight connection implementation process using mathematical methods. |
| KOVÁŘ Radoslav (CZ), HABARTA Filip (CZ),
MALÁ Ivana (CZ), ŠTĚPÁNEK Lubomír (CZ), ČABLA Adam (CZ) " Survival Regression Model with Lagged Covariates " - from the section: Statistical Methods in Technical and Economic Sciences and in Practise This paper extends the survival regression model with time-changing covariates to the case when the hazard rate is affected with a lag. Firstly, we illustrate the importance of modelling the lagged effect correctly both in the classical and in the landmarking framework. Secondly, we propose a method of estimating the lag and we validate our approach in a simulation study. Finally, we apply the methodology on a credit scoring dataset. |
| KRÁČALÍK Michal (AT) " Mathematical modelling of Continuum Mechanics in Context of Industry 4.0 with Emphasis on Mathematical Education " - from the section: New Trends in Mathematical Education This article discusses modelling and simulation of the product in the context of the industry 4.0. It briefly describes second order partial differential equations and their solution in general form with respect to continuum mechanics that is useful in modelling of physical phenomena’s of seemingly different fields as solid mechanics, fluid mechanics or acoustic. The demand on increased multi-physical simulations is discussed together with the mathematical education at the technical university. |
| KULINA Hristina (BG), IVANOV Atanas (BG), GOCHEVA-ILIEVA Snezhana (BG) " Modelling of Beer Industry Data Using Principal Components and Time Series Arima Methods " - from the section: Statistical Methods in Technical and Economic Sciences and in Practise This study explores the interaction between the main market factors - digital and non-digital advertising, atmospheric temperature, price, distribution and others on the sales volume growth. Monthly observations for almost five years have been used for a big brewery brand in Bulgaria. Multivariate and stochastic ARIMA time series models with 82% and over 95% of coefficient of determination are constructed. The models are applied for a one-month ahead forecast of the beer sales volume. |
| KUZMIN Alexander (RU) " Non-Uniqueness of Inviscid Transonic Flow over Symmetric Double Wedges " - from the section: Modeling and Simulation in Engineering and Scientific Computations The 2D airflow over 8%-thick double wedges is studied numerically. Solutions of an initial-boundary value problem for the system of Euler equations are obtained with a finite-volume solver. The solutions demonstrate non-unique flow regimes in significant bands of the given inflow Mach number M∞. The realization of a certain regime depends on the time history of M∞ and angle of attack. At the endpoints of the bifurcation bands, there are abrupt changes of the flow structure. |
LEJA Jozef (SK), GMUCA Štefan (SK) |
| LORENZI Marcella Giulia (IT) " Art and Artificial Intelligence " - from the section: Mathematics and Art Artificial intelligence is part of everyday life, in many applications that improve our lives, following computer science advances. With AI, computers can learn from artistic experiences, being programmed to make choices and adjust to feedback from the environment. Can a computer be considered an artist? Is creativity programmable? Looking at examples, from the past to cutting edge, the paper deals with some applications of mathematics/computer science/AI in visual and performance art. |
| MAGNAGHI-DELFINO Paola (IT), MELE Giampiero (IT), NORANDO Tullia (IT) " Fortress Plans According to Euclid " - from the section: Mathematics and Art Deep reasons link shape and geometry to the planning and the layout of Renaissance’s fortresses. In the 15th century, the diagram of many of them has a pentagonal shape. The pentagon is tied to the golden section and one can construct it starting from the golden triangle and its gnomon. To draw the approximated golden triangle, one establishes the relationship between the sides by means Fibonacci’s numbers, for example 5 and 8. The authors verify this relationship between numbers, shape and size in the layout of Castel Sant’Angelo (Rome). |
| MAGRONE Paola (IT) " Sierpinski´s Curve: a (Beautiful) Paradigm of Recursion " - from the section: Mathematics and Art This paper focuses on the original articles written by Waclaw Sierpinski in 1915, where he introduced the recursive structure that bears his name, the Sierpinski’s triangle. His first aim was to exhibit an example of a new set, a curve, traced starting from the geometry of the well-known triangle. The triangle, which embodies geometric recursion, was rigorously defined in 1915, but appeared also before Sierpinski, and is still a reference point for scientists. |
| MAREK Patrice (CZ), ČADKOVÁ Věra (CZ) " Optimization and Testing of Money Flow Index " - from the section: Financial and Actuary Mathematics The paper deals with whether the Money Flow Index (MFI) can still be used successfully for trading, and whether the parameters recommended in the literature are the best that an investor can use. Simulations in randomized time interval for the largest companies in the S&P 500 Index show that trading strategy based on MFI may be more profitable than a simple buy-and-hold strategy; however, parameters of MFI need to be optimized because those recommended in the literature do not produce the best results. |
| MATULOVÁ Markéta (CZ), DEMCHENKO Hanna (CZ) " Inquiry-Based Mathematics Education: Literature Database and Bibliographic Analysis " - from the section: New Trends in Mathematical Education This paper presents a bibliographic database gathering 437 scientific papers related to Inquiry-Based Education in Mathematics covering the period of 1980-2018. Based on the data-set, we conducted a bibliographic analysis to determine the distribution of publications in several categories according to their classification. We also identified the most high-impact papers and journals, most frequent keywords, and most productive countries as well as their trends. |
| MATVEJEVS Andrejs (LV), ĻOHINA Ksenija (LV) " A Stochastic Model of the Logistic System Dynamics " - from the section: Differential Equations, Dynamic Systems and Their Applications The stochastic vehicle allocation problem addresses the movement of vehicles between locations over a given planning horizon. The demand for vehicles to carry loads between locations is uncertain, and vehicles are assumed able to handle several loads over the course of the planning horizon. Assuming random and coming at random time moments demands, we construct a stochastic model for this transport logistic scheme and derive Gaussian approximation for transport and stock level of goods dynamics. The proposed stochastic model in tandem with stochastic approximation procedure permits to take into account random character of demand for freight services and to supplement the classical deterministic analysis with Gaussian approximation for possible random deviations. |
| MENDONÇA Jorge (PT), BABO Lurdes (PT), PINTO Carla (PT) " Skills of Bachelor Engineering Students Attending Active-Learning Math Courses " - from the section: New Trends in Mathematical Education We focus on Bachelor Engineering degrees students’ skills while taking actively taught Math courses. The applied active-learning techniques were Jigsaw, eduScrum, Think-Pair-Share, and Challenge-based-learning. Students were asked to fulfil a questionnaire at the end of the semester, to provide their perceptions of the learning environment and of their own competences. Their responses were analysed using statistical techniques, namely Principal Component Analysis. Results revealed three major sets of skills, which may be identified as interpersonal, personal and cognitive skills. Additionally, ranking scores was computed for each set of skills and the obtained values indicate that AL is considered a valuable teaching tool. |
| MENDONÇA Jorge (PT), BABO Lurdes (PT), PINTO Carla (PT) " Skills of Bachelor Engineering Students Attending Active-Learning Math Courses " - from the section: New Trends in Mathematical Education We focus on Bachelor Engineering degrees students’ skills while taking actively taught Math courses. The applied active-learning techniques were Jigsaw, eduScrum, Think-Pair-Share, and Challenge-based-learning. Students were asked to fulfil a questionnaire at the end of the semester, to provide their perceptions of the learning environment and of their own competences. Their responses were analysed using statistical techniques, namely Principal Component Analysis. Results revealed three major sets of skills, which may be identified as interpersonal, personal and cognitive skills. Additionally, ranking scores was computed for each set of skills and the obtained values indicate that AL is considered a valuable teaching tool. |
| MIERLUS MAZILU Ion (RO), YILMAZ Fatih (TR) " Some Practical Applications of Matrices and Determinants in Real Life " - from the section: New Trends in Mathematical Education In this paper, we present some applications of math in other domains also in real life problems. In this sense, we have some illustrative practical applications related to matrices and determinants. |
| NÁHLÍK Tomáš (CZ) " Fishsperm Analysis " - from the section: New Trends in Mathematical Education Modern fishery and aquaculture need the support of image processing for analysis of the health status of fish sperms to produce high-quality population. This manuscript describes some problems during imaging of the sperm cells and presents methods of image processing for automatic detection of the cell. The article also describes which features of the sperm should be measured. |
| NOVOTNÁ Jarmila (CZ), ULOVEC Andreas (AT), MORAOVÁ Hana (CZ) " Teaching Mathematics to Migrant or Minority Students: Concepts for Creating Materials " - from the section: New Trends in Mathematical Education Literature confirms that pupils with migrant backgrounds encounter more difficulties when learning (not only) mathematics than their majority classmates. One of the things their teachers complain about is the lack of suitable materials. The aim of the presented study is to point out the major principles for creation of suitable materials for teaching in multilingual and multicultural environments. The reported research was conducted within the frame of the Austrian-Czech project Aktion 84p12. |
| ORSZÁGHOVÁ Dana (SK), FĽAK Pavel (SK) " Mathematics Competences and Skill of Students in Bachelor Economics Study Program: Case Study " - from the section: New Trends in Mathematical Education Quality of education is the important factor for university evaluation. In academic years 2015/2016 and 2016/2017 it was performed pedagogic survey at the Slovak University of Agriculture in Nitra to determine the level of competences and skills of students in solving mathematical tasks. In the analysis we applied basic statistical characteristics of studied traits and testing significance of relations by Student t-test. Obtained results confirmed several statistically significant differences. |
| OTAVOVÁ Miroslava (CZ), SÝKOROVÁ Irena (CZ) " Analysis of Students Who Failed Mathematics Course " - from the section: The paper presents the analysis of probability of failing the basic course in mathematics at the University of Economics, Prague. The evaluation of the course is continuous and students acquire points that sum up to overall evaluation not only during the exam period, but also from a mid-term test. From the analysis it turns out that students who score better in the mid-term test have higher chance to pass the course at first attempt, especially when they obtain more than 60% of points in their mid-term test. |
| PACURAR Cristina Maria (RO) " Kazimir Malevich and Symmetries " - from the section: Mathematics and Art The present paper analyses the mathematical concept of symmetry in the artwork of the Russian artist Kazimir Malevich. Symmetries are a perpetual presence in his entire artistic work, from the early stages, where Impressionism had the first place, to the later paintings, which belong to Suprematism. The first part of the paper investigates the symmetry of the painting The athlete of the future, from 1913. The second part deals with the evolution of symmetry in three different paintings focusing on the same subject, which is three female figures. The paintings considered in this part can be reduced to a zero of forms - which is the essence of Suprematism - that possesses symmetry, and the paintings are analysed from this point of view. |
| PASÁČKOVÁ Jana (CZ) " Nonoscillation Theorems for a Four-Dimensional Neutral Difference System " - from the section: Differential Equations, Dynamic Systems and Their Applications We investigate a four-dimensional nonlinear neutral difference system. We define t he possible t ypes of nonoscillatory s olutions and we present r esults about boundedness or unboundedness of these solutions. |
| PAVLENKO Oksana (LV) " Lower Weight For Exam Grades – Better Academic Performance? " - from the section: New Trends in Mathematical Education The aim of this paper is to analyze the changes in students’ academic performance in mathematical subjects like Probability Theory and Mathematical Statistics at Riga Technical University after the evaluation system reform in 2017. Students’ grades in Probability Theory and Mathematical Statistics for the period of four academic years between 2015 and 2019 have been analyzed using statistical methods. The findings show that reducing the share of the exam in the final grade has motivated students to study harder during the semester but has not had a significant impact on their performance on the exam. |
| POLÁK Mikuláš (SK), PECKO Marcel (SK), BOHDAL Robert (SK), FERKO Andrej (SK) " Experimental 3D Shape Reconstruction From High-Precision 2D Cruse Scans Using Shadows and Focusing " - from the section: Modeling and Simulation in Engineering and Scientific Computations We describe two experiments with the hi-tech CRUSE CS 220ST1100 contactless scanner. The 2D scans guarantee high precision both in geometry and radiometry. The experiments verify the precision of non-standard scanning and two standard object reconstructions. We tested the reconstruction of 3D shape from shadows and from experimental focusing. We discuss educational aspects of given approach within the innovative course on Visual Data of Cultural Heritage. |
| POTŮČEK Radovan (CZ) " The Sum of the Series of Reciprocals of the Cubic Polynomials with Three Different Negative Integer Roots " - from the section: Modeling and Simulation in Engineering and Scientific Computations This contribution is a follow-up to four author’s previous papers and deals with the sum of the series of reciprocals of the cubic polynomials with three different negative integer roots. We derive the formula for the sum of these series, state two special cases of this formula and verify it by some examples using the basic programming language of the computer algebra system Maple 19. |
| POZDÍLKOVÁ Alena (CZ), MAREK Jaroslav (CZ), OBOLECKÝ Jan (CZ) " Profitability Analysis of Artificial Intelligence Methods and Technical Indicators in the Forex Exchange " - from the section: Statistical Methods in Technical and Economic Sciences and in Practise For algorithmic trading many methods have been suggested. This article will be devoted to predicting the behavior of currency pairs on the Forex exchange. Several methods of artificial intelligence and statistical analysis will be used to predict the future of forex currency pairs. We adopt the idea of transforming the window of time series into the spectral plane, and then analyzing the clusters using hierarchical clustering, Kohonen maps and evolutionary algorithms. Next, we will use a radically different approach to time series analysis in the time domain: fuzzy time series and genetic algorithm. In the numerical study we will compare the success of artificial intelligence algorithms and multivariate statistical analysis with the success of technical indicators MACD and ROC. |
| RASTEIRO Deolinda M. L. D. (PT), CARIDADE Cristina M.R. (PT) " Probability and Statistical Methods: Assessing Knowledge and Competencies " - from the section: New Trends in Mathematical Education This paper is one of the results of RULES_MATH project which aims to develop tools to assess mathematical competencies. Eight mathematical competencies identified are recognized in the assessment made to students in what concerns learning probability theory concepts. Since 2017 a study was carried out with Mechanical Engineering students at Coimbra Institute of Engineering. The results obtained cover the test as a tool to assess competencies and also its fitness to our students. |
| RŮŽIČKA Vojtěch (CZ) " Examples of Simplified Notations Used in Calculus and Their Influence on Teaching at Undergraduate Level " - from the section: New Trends in Mathematical Education The paper is devoted to simplified notations used in calculus, especially in differential calculus. We focus on notations that are widely used in teaching at undergraduate level, but often they are explained either just briefly or not at all. We explain them in more detail, but without additional definitions - we are not trying to show formal corrections of these simplified notations. The aim of this paper is to demonstrate how to effectively explain these simplified notations. |
| ŠEBA František (CZ), KRBÁLEK Milan (CZ) " Super-Poissonian Statistics in Traffic Flow " - from the section: Statistical Methods in Technical and Economic Sciences and in Practise We utilize number variance, a statistical tool originating from Random Matrix Theory, to investigate the nature and level of correlation among vehicles in real road two-lane traffic data. We show that while for both fast and slow lane the number variance is non-Poissonian, indicating a strong correlation between vehicles, the nature of the correlation itself differs lane by lane considerably. For the slow lane, the number variance exhibits a sub-Poissonian behaviour, similar to a short-ranged Dyson gas, and follows the predictions of Random Matrix Theory. For the fast lane, however, the number variance enters for certain densities a super-Poissonian regime, indicating that the system can’t be described by a short-ranged repulsive interaction only. We further show that the systems behaviour can be explained by a so called “vehicle bunching” effect, which is a result of lane-change behaviour originating in the slow lane, and which has remarkable similarities to an effect observed in thermal light photon counting experiments in quantum optics. |
| ŠEDIVÁ Blanka (CZ), ˇTOUPAL Tomáš (CZ) " Outlier Detection Techniques in Multidimensional Datasets " - from the section: Statistical Methods in Technical and Economic Sciences and in Practise Outliers can significantly impact data summarization results and data analysis across all types of data analysis. Identifying outliers in multidimensional data is, therefore, one of the key approaches in data preprocessing. across all types of data analysis. In this article, we present several univariate and multivariate methods for the identification of outliers in multidimensional data. |
| SEIBERT Jaroslav (CZ), KOUDELA Libor (CZ) " The Merrifield-Simmons Index for Two Types of Phenylenes " - from the section: Mathematics and Physics in Contemporary Science and Technique The Merrifield-Simmons index i (G) of a simple undirected graph G = (V;E) is the number of all independent sets of vertices in G. This number is one of the most popular topological indices in chemistry. In this contribution we obtain exact formulas for the Merrifield-Simmons index of two types of the branched phenylenes whose molecular graph consists of two linear chains of alternating hexagons and quadrangles, together forming a bent chain. |
| ŠIMANDL Václav (CZ) " Exploitation of Geometry in Programming Classes " - from the section: New Trends in Mathematical Education The article examines the use of geometry in programming classes in the Python language. The programming coursebook written by us for high schools provides a collection of tasks based on constructivism and geometry. A number of tasks involve rectangles, ellipses and texts being drawn on canvas. Classroom piloting revealed that the tasks are sufficiently motivating for pupils but they have difficulty with activities requiring them to determine the correct coordinates of drawn figures. |
| ŠIMPACH Ondřej (CZ), ŠIMPACHOVÁ PECHROVÁ Marie (CZ) " Does the Technical Efficiency Calculated by SFA Statistically Significantly Varies in Different Samples? " - from the section: Statistical Methods in Technical and Economic Sciences and in Practise The aim of the paper is to analyse whether and how the results of Stochastic Frontier Analysis (SFA) changes if we use different samples of firms. We do not question the size of the sample, but the composition of it. SFA is frequently used method to calculate the technical efficiency of agricultural holdings and authors come often to different results. The results of SFA are sometimes used for policy-making and decision-making in agriculture and the results must be reliable. Agricultural holdings differ, and those differences can influence the results of SFA, i.e. the value of technical efficiency. We examined this issue empirically on a sample of 548 farms with 2268 observations for years 2013 to 2017. Accounting data were taken from Albertina database, data about acreage form LPIS. We chose randomly 5 samples per 500 observations (the number of farms differed as the panel was unbalanced). Technical efficiency for each sample was calculated by the same technique. Particularly True Fixed Effects model was used to model the Cobb-Douglas production function. Technical efficiency was calculated by Jondrow et al. (1982) method. Differences in medians of technical efficiency were tested by non-parametric Kruskal-Wallis test and Mood’s median test. H0: there are no statistically significant differences in medians of technical efficiency was rejected in the first test but was not rejected in the other. We came to ambiguous results but nevertheless we can warn that the selection of the sample for calculation of technical efficiency might influence the results. |
| ŠLESAR Peter (SK), JANČO Roland (SK) " Analysis of Welding Aluminium Plates by Friction Stir Welding " - from the section: Friction stir welding is a solid-state welding technique that utilizes thermo-mechanical influence of the rotating welding tool on parent material resulting with monolith joint - weld. In particular, FSW can be used to join high-strength aerospace aluminium alloys and other high temperature metallic alloys that are hard to weld by conventional fusion welding. This work deals with the assessment of two aluminium plates using friction welding. |
| STAŠ Michal (SK) " On the Crossing Numbers of Join K2,3 + Pn " - from the section: Algebra and Geometry and Their Applications The main aim of the paper is to give the crossing number of join product G* +Pn for the connected graph G* of order five isomorphic with the complete bipartite graph K2,3, and Pn is the path on n vertices. In the proofs, it will be extend the idea of the minimum numbers of crossings between two different subgraphs from the family of subgraphs which do not cross the edges of the graph G* onto the family of subgraphs which cross the edges of G* exactly once. Due to the mentioned algebraic topological approach, we are able to extend known results concerning crossing numbers for join products of new graphs. |
| STRÁNSKÁ Jana (CZ) " Otakar Borůvka and his Successors in the Field of Differential Equations " - from the section: Differential Equations, Dynamic Systems and Their Applications Otakar Bor°uvka (1899 – 1995) was an important Czechoslovak mathematician that worked at the Masaryk University in Brno for five decades, next two decades in the Mathematical Institute of the Czechoslovak Academy of Science in Brno. He focused on many mathematical branches: mathematical analysis, differential geometry, graph theory and algebra. This paper focuses on his research in the field of differential equations and his influence to the next generations of mathematicians in the Czech and Slovak Republic. The paper is completed by the notes on Equadiff series in Czechoslovakia and on mathematical trips. |
| ŠTUBŇOVÁ Michaela (SK) " Prediction of Financial Time Series Using Artificial Neural Networks " - from the section: Financial and Actuary Mathematics With the development of information technology, modern methods of soft computing for analysing financial time series are at the forefront. The aim of the paper is to analyse the predictive ability of artificial neural networks in predicting the stock indices. The performance of dynamic nonlinear autoregressive networks with a different number of time delays were analysed. It can be stated that this type of neural network should be incorporated into the technical analysis of stock markets. |
| SURYNKOVÁ Petra (CZ) " On the Synthetic Constructions of Specific Planar Curves of Kinematic Geometry " - from the section: Algebra and Geometry and Their Applications The paper addresses the synthetic constructions of selected planar curves determined as trajectories of moving points or as envelopes of moving curves in the plane. We will show the synthetic constructions of centers of curvature and osculating circles of those curves. For better understanding, we will newly support these synthetic constructions by dynamic applets created in GeoGebra software. |
| TOMICZEK Petr (CZ) " Second order problem with ALP condition and unbounded nonlinearities " - from the section: Differential Equations, Dynamic Systems and Their Applications The nonlinear second order ordinary differential equation u´´(x) + m2 u(x) + g(x,u(x)) = f(x), x in [0,pi ], u(0) = u(pi) = 0 is investigated in this article. We suppose that the nonlinearity g is unbounded and satisfies an ALP type condition. We prove the existence result to this problem using a saddle point theorem. |
| TOMICZKOVÁ Světlana (CZ) " Geometric Software in Courses of Differential Geometry " - from the section: New Trends in Mathematical Education Today systems of dynamic and interactive geometry represent a powerful tool for making teaching and learning processes more effective and more efficient. In Geometry courses, especially Differential Geometry, we use software to visualize basic concepts of differential geometry, such as equidistant, curvature of curves, Gaussian and mean curvature or special types of surfaces. However, some tools in this software do not always work correctly. We discuss how to correct the mistakes and how software can help visualize geometric properties and also the questions and problems which we can encounter during display. We use these issues to show students theoretical and practical (computer) problems of differential geometry. |
| ŤOUPAL Tomáš (CZ), ŠEDIVÁ Blanka (CZ) " Multivariate Nonparametric Kernel Estimation " - from the section: Statistical Methods in Technical and Economic Sciences and in Practise This paper is focused on multivariate estimation of density and distribution function by nonparametric kernel approach. The main goal is to describe univariate and multivariate nonparametric kernel estimation using selected kernel functions and smoothing parameters including a real application. The influence of basic parameters on the resulting models and proposed optimization methods are also analysed for further models of use (e.g. in reliability theory). |
| VÁCLAVÍKOVÁ Zuzana (CZ) " Science Students´ Perception of Functional Dependencies and Their Interpretation with Real Phenomena " - from the section: New Trends in Mathematical Education Although the concept of a function is being taught in mathematics since the elementary school, its understanding is still problematic for university students. The Department of Mathematics at the Faculty of Science in the University of Ostrava provides a course of mathematics focused on the concept of a function and we are dealing with two questions – how to teach it effectively with the expected outcomes and what is incomprehensible for students. We used the eye-tracker technology to better understand students' thinking to find points that are crucial to the correct or wrong solution of the examples. |
| VÁGOVÁ Renáta (SK), KMETOVÁ Mária (SK), LIEBAN Diego (BR) " The Interplay of Physical and Digital Resources to Explore Cube Cross-Sections " - from the section: New Trends in Mathematical Education This paper draws on a design-based research project aimed at integrating the combined use of physical and digital resources. In particular, it focuses on the project design and detailed description of the first worksheet used in the project. The combined use of multiple images strives to support the development of students’ mental images, visual abilities and processes. The material was designed under the lens of the instrumental genesis approach, regarding the visualisation model elements. |
| VALLO Dusan (SK) " Modeling of Catacaustic Curve in GeoGebra Environment " - from the section: New Trends in Mathematical Education This paper is focused on some inspiration on how to use dynamical geometry software Geogebra in teaching Mathematics and in teachers training education at the university level. For this purpose, we concerned with an example of the catacaustic curve. We demonstrate the problem in the combination of the interactive graphics environment and algorithmic approach based on using the command Sequence. Some didactical remarks are included in the discussion of the paper, too. |
| VARGOVÁ Michaela (SK), SLAVÍČKOVÁ Mária (SK) " Students’ Misconceptions in Definition of a Limit of Sequence " - from the section: Algebra and Geometry and Their Applications Students used to formulate their definitions by simplifying the language. Not all of these simplifications are correct or describe the same object. We will present students' interpretations of the limit of sequence to demonstrate how their definitions change the meaning of it comparing to the original one. |
| VELICHOVÁ Daniela (SK) " Visualization in Teaching = Activation of Students " - from the section: Algebra and Geometry and Their Applications In the paper we discuss some of the new challenges of teaching by introducing active learning methods. Implementation of ICT into teaching scenarios enables to visualize abstract mathematical concepts and makes students think about these more deeply, in connection to their geometric interpretations and applications. We present some examples of interactive applets in dynamic mathematical software and educational videos used in teaching basic courses of university mathematics and geometry at technical university. |
| VELICHOVÁ Daniela (SK) " Maryam Mirzakhani and the Heritage She Left " - from the section: Algebra and Geometry and Their Applications Paper brings a brief life story of Maryam Mirzakhani, the first female Field medallist, and an overview of the great mathematical heritage she has left for us. This legacy comprises not only rich and potential mathematical ideas and strategies to solve difficult problems primarily rooted in the field of hyperbolic surfaces but spanning throughout the large scope of mathematical domains. Message left by her great achievements is an important motivational impulse to all women who dare to work in the still male dominated world of mathematics. |
| VINTERE Anna (LV), MACAITIENE Renata (LT) " Mathematics Education Development in Line With the Trends of Sustainable Development: Experience Within the Network "MATNET" " - from the section: New Trends in Mathematical Education This article describes 10 years' cooperation experience of Latvia University of Life Sciences and Technologies and Siauliai University (Lithuania) in development of mathematics education in line with the trends of sustainable development in three strands: determining the relevance of mathematical competences to the labour market, evaluation of the experience and attainments by UNESE indicators and the analysis of the mathematics study course for economists. |
| YILMAZ Fatih (TR), MIERLUS MAZILU Ion (RO), RASTEIRO Deolinda (PT) " Solving Real Life Problems Using Matrices and Determinants " - from the section: Modeling and Simulation in Engineering and Scientific Computations In this paper we provide several real-world motivated examples illustrating the power of the linear algebra tools as the product of matrices. In this sense, we present some illustrative practical applications related to matrices and determinants. |
| ZAMBOJ Michal (CZ) " Visualizing Objects of Four-Dimensional Space: From Flatland to the Hopf Fibration " - from the section: Algebra and Geometry and Their Applications One of the fundamental questions of a three-dimensional geometer is how to imagine a four-dimensional object. And yet, he draws pictures of three-dimensional objects in the two-dimensional paper. Moreover, would a two-dimensional geometer understand our sketches? Based on analogies, we give an overview of methods of examination of four-dimensional objects. We emphasize visualization as the main element of perception of four-dimensional space. For this purpose, we describe the double orthogonal projection of the four-dimensional space onto two mutually perpendicular three-dimensional spaces as a generalization of the classical Monge’s projection. In such a projection, we construct a four-dimensional playground for convenient synthetic creation of four-dimensional objects. All our constructions are easily accessible with the interactive 3D modeling software GeoGebra. Furthermore, we apply the method of projection to an intuitive investigation of various four-dimensional mathematical phenomena – polytopes, four-dimensional quadrics, three-sphere and its stereographic projection, complex plane, and the Hopf fibration. |
| ŽDÍMALOVÁ Mária (SK) " Aggregation, Architecture, Design, Art " - from the section: Mathematics and Art In this contribution the paper discuss aggregation, types of aggregations, aggregation Architecture, aggregation in Urbanism and finally its application into design, fashion, mathematics and mathematical modelling. |
| ZEITHAMER Tomáš (CZ), POSPÍŠIL Jiří (CZ) " Generalized Law of Retail Gravitation " - from the section: Nothing This paper is one of the outcomes of the preparatory work on a research project exploring the effects of solar activity on Earth´s economy and extraterrestrial economy from a global perspective. The equation of the field of retail gravitation is derived by the Einstein´s methodology modified for the description of the field of terrestrial as well as extraterrestrial retail gravitation. |
| First Edition Bratislava 2020 ISBN 978-80-227-4983-1 |
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