Jacek Stańdo

Nonstandard Nonobtuse Refinements of Planar Triangulations

Throughout the paper, we consider conforming planar triangulations of a given polygon into triangles, i.e., the union of all triangles of any particular triangulation is always equal to the polygon, and any two different triangles in any particular triangulation may only have a common edge, or a common vertex, or no common point (cf. [12]). In most of cases namely such conforming triangulations are used in the finite element modelling and analysis.

The Use of Quasi-Red and Quasi-Yellow Nonobtuse Refinements in the Solution of 2-D Electromagnetic PDE’s

In the paper, new refinement techniques called “quasi-red” and “quasi-yellow” are applied for the solution of a non-linear Poisson’s equation describing magnetic flux density in 2-D. The equation is solved using the finite element method with non-obtuse triangulation. The goal is to modify initial mesh in some non-standard way to have solely non-obtuse triangles. Usefulness of the method is demonstrated on the problem of optimal shape design of an electromagnet.

First Electronic Examination for Mathematics and Sciences Held in Poland - Exercises and Evaluation System

The development of new information technology poses a question about the future shape of education. You can now ask: Will not traditional course books, the traditional school, a traditional teacher, the traditional examination process change rapidly? The work will be described first as an electronic mock exam in mathematics and then as a natural exam carried out on the Internet in Poland. The aim of this paper is to present the typology of the tasks and the electronic system of evaluation. The E-examination was conducted for the first time in Europe on such a large scale in the real-time (320 Polish schools from all over Poland took part in it, including 3000 students). The conducted trial is the first step towards changing external examinations in Poland.

How Can ICT Effectively Support Educational Processes? Mathematical Emergency E-Services - Case Study

Rapid development of Information and Communication Technologies poses many questions about the future of education. Experts have been analyzing the role of traditional course books, examinations, schools and traditional teachers in educational processes and they are wondering about their roles on the threshold of these significant changes in education. Nowadays, the way that young people share the knowledge which they have been provided with has considerably changed. It has already been confirmed by the results and findings of the Mathematical Emergency E-Services project which has been realized for over a year now by the Technical University of Lodz. The article presents, discusses and analyzes e-learning consultations between Mathematics teachers and students in real time carried out within the project’s activities.

Construction of New Cubature Formula of Degree Eight in the Triangle Using Genetic Algorithm

In the following paper we present new cubature formulas in the triangle for polynomial of degree eight. They have positive weights, containing no points outside the domain. With the use of genetic algorithm we have created a special algorithm effectively searching for cubatures.

Using Neural Networks to Detect Errors in Coding Exams

The system of external evaluation has been in use in Poland for over 10 years now. The paper presents and thoroughly describes the algorithm used and discusses the efficiently of the applied method. Chapter 1 of the paper introduces the details of the system of external examinations in Poland and presents the basic concepts of RBF networks. Chapter 2 describes the structure of the examination and Chapter 3 deals with the problem and its solution.

E-mature – Report of an Electronic Mathematics Exam

Internet applications have been revolutionary in our daily life since the moment that they were first implemented several years ago. An increasing number of institutions is changing traditional methods for the ‘e’ ones. It also affects the educational field. The beginnings were mainly about the external teaching. For a few years now extensive research, regarding the e-exams has been done [6],[7],[8], that is the system which enables checking pupils’ knowledge and skills in the real time instead of doing written exams. This paper shows the report based on the first mock e-mature in mathematics in Poland.