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Mathematica Applicanda > 2019 > 47 > 2

Mathematica Applicanda > 2019 > 47 > 2

Mathematica Applicanda > 2019 > 47 > 2

Mathematica Applicanda > 2019 > 47 > 1

Mathematica Applicanda > 2019 > 47 > 2

The 47th National Conference on Mathematics Applications was held on September 4-11, 2018 in Zakopane Kościelisko. Together with the conference, the XXIV National Conference on Mathematics Applications in Biology and Medicine (4-7 September 2018) was held simultaneously with two common first days of the meeting. The plenary lecture was delivered by Urszula Ledzewicz (Southern Illinois University Edwardsville,...

Mathematica Applicanda > 2019 > 47 > 2

In this paper we present a version of a simple mathematical model of acquiring drug resistance which was proposed in Bodnar and Foryś (2017). We based the original model on the idea coming from Pérez-García et al. (2015). Now, we include the explicit death term into the system and show that the dynamics of the new version of the model is the same as the dynamics of the second model considered by us...

Mathematica Applicanda > 2019 > 47 > 2

In Robbins' problem of minimizing the expected rank, a finite sequence of independent, identically distributed random variables are observed sequentially and the objective is to stop at such a time that the expected rank of the selected variable (among the sequence of all variables) is as small as possible. In this paper we consider an analogous problem in which the observed random variables are...

Mathematica Applicanda > 2019 > 47 > 1

In this article we introduce a De Vylder type of approximation of the ruin probability for a two-dimensional risk process, where claims and premiums are shared with a predetermined proportion. Such a process is usually associated with the insurer-reinsurer model. Applying De Vylder's idea to the risk process we obtain an approximation of the ruin probability for an arbitrary claim amount distribution...

My commentary to the article Utopian Mathematics by prof. Michał Szurek presents a teacher's point of view.

One of the main views which appears throughout prof. Pawlak's paper is one initially expressed by Anna Zofia Krygowska, the most influential researcher of mathematics education in Poland. According to this view - the teacher and his preparation, and thus the problems of teaching mathematics, are never "ahistorical" (Krygowska, 1981, as quoted by Pawlak, 2019). In other words, the problems...

The book "A Beautiful Soul: Mathematician of the God" allows us to look at the past for a moment and, at least, brings us closer to the relationship between science and faith. The book describes the figure of Maria Gaetana Agnesi. She is commonly known as the author of one of the first integral calculus textbooks."Analytical Institutions for the Use of Italian Youth". Her name...

The article discusses circumstances under which arithmetic and algebra textbooks were written by A. Smetona, future president of Lithuania and a member of the Textbook Publishing Commission under the Lithuanian Scholarly Assembly. The main features of publications for developing Lithuanian gymnasiums of that time and their importance in the history of Lithuanian education.

This article presents the subject of the Applied Mathematics Seminar, conducted in 1948-1960 by Professor Hugon Steinhaus in Wrocław and is an important supplement to the analysis presented in the work of Szczotka (2018). This topic is illustrated by a more detailed discussion of some of the works on this subject and some of the results obtained by the participants of the Seminar. The results are...

In the years 1933--2013 at the University of Poznań was awarded nine honorary doctorates for mathematicians, while two other candidates did not obtain the approval of a higher authority. Mathematicians from Poland and abroad received them. The purpose of this work is to provide information on nine mathematicians who were given the title and two persons who were refused. An important part of this description...

Tadeusz Posament was born in 1905 in Lvov. After graduating from high school, he studied at the Faculty of Mechanical Engineering and graduated from the General Faculty of the Lvov Polytechnic in 1931 with a master's degree in mathematics. Mathe-matical supervisor of his diploma work was Kazimierz Kuratowski, who highly appreciated his mathematical skills. Soon, two publications appeared, discussing...

This work is a continuation of the author's presentation of the history of mathematics in Russia as a research area within the history of science (v. Lokot (2018)). The elements of the history of mathematics began to intensively emerge in the epoch of Peter the Great and have undergone several stages of development. There are five stages that Russian scientists have gone through, shaping the elements...

The article introduces the figure of Jerzy Jan Battek (January 14, 1927 - August 12, 1991), who belonged to this generation of youth who managed to survive the period of World War II, without interrupting school education altogether. During the occupation, he studied in secret sets of the Second Science Center and obtained a small high school diploma in 1945. He graduated in 1947 at the State Secondary...

When projecting the globe on a plane surface it is not possible to satisfy more than one of the following three criteria: conformity of angles, equidistance and equivalence of areas. Mercator's solution for the use in navigation was to use a cylindrical projection with increasing distances between parallels so that the rhumb lines became straight lines. We present the derivation of the meridional...

This note reviews how the contemporary concept of the Poisson process (sometimes called the Poisson random measure or Poisson point process) evolved through out the time up to recent times. That is from F. Lundberg and W. Feller up to A. Renyi (1967) paper and finally, a construction of Poisson processes by binomial (or Bernoulli) processes, which can be found in J.E. Moyal (1962), J. Mecke (1967)...

In the years 1869--1937, there were 15 Conventions of Polish Naturalists and Physicians. Since 1875, naturalists who have discussed in their several sections participated in the conventions. Mathematical conventions started in 1881 and finished in 1933. Three pre-war conventions: 1,900 in Krakow, 1907 in Lviv and 1911 in Krakow, gathered for over 1000 participants. At eight Congresses, starting from...

In this article we present results of research aiming at describing the strategies used by 10-year-old children while solving one geometric task. The research was lead through three different stages. In May 2015 the Educational Research Institute in Poland carried out a survey titled Competences Of Third Grades. One task, related to the domain "the geometric imagination", solved by 199 361...

The article presents the results of research on milestones (significant events, critical points, and crystallizing experiments) in the course of life of outstanding mathematicians and mathematically talented adolescents. The work covers the period of approximately the last 80 years. Four distinct group of mathematicians had received their education and pursued their scientific careers at that time:...

Professor Z. Krygowska in her article, opening the frst issue of the PTM (Polish Mathematical Society) journal Didactics of mathematics (Dydaktyka Matematyki), (Krygowska, 1981) noted that the teacher and his preparation, and thus the problems of teaching mathematics, are never ahistorical. We live here and now, our pupils (students, doctoral students) are immersed in the contemporary time and in...

On September 3-7, 2019, in Krakow, the Jubilee Congress of Polish Mathematicians took place, organized to celebrate the 100th anniversary of the Polish Mathematical Society. The congress became an opportunity to meet mathematicians who are active in the country. Additionally, mathematicians who, for various reasons, went abroad and conduct their activities there, were also present. Finally, the congress...