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Patterns and generalization are one of the most fundamental aspects of mathematics, which makes recent decades, mathematical tasks which include patterns, whether they are numerical or graphical, are mostly used, for example researching generalization. The aim of this paper is to investigate how a special kind of task concerning well-known palindromes can diversify the process of generalization in three different age groups of students. More precisely, the paper includes the analysis of solutions of one task concerning counting of numbers of palindromes by middle school, high school and university students with the special attention for finding similarities and differences among advance of process of generalization and using methods of solving in researched groups. The researched groups chosen randomly from two distant part of Poland, were consisted of 44 middle school students, 102 high school students and 51 university students (including 42 pre-service teachers). All students solved the same task in limited time without any assistance of teachers. The research was carried out between 2013 and 2015.

The paper is dedicated to analysing the role of "denominate numbers" in textbooks for Polish schools, whose author or co-author was Stefan Banach. Banach used the concepts of "number" and "denominate number" in his textbooks. The ways of introducing these concepts, as well as the associated manner of understanding numeration, are analysed in the paper. The methods of manipulating "denominate numbers" through various procedures are also discussed. The analysis is carried out in the context of the Polish ministerial ordinances related to teaching mathematics and the content of other textbooks, especially those used by Banach as a secondary school student. [ABSTRACT FROM AUTHOR]

In this paper we present a study of the most important Polish periodicals of the last 30 years that are related to mathematics education. Our research aim was to analyse how the changes in mathematics education that were caused by a new political situation in Poland were reflected in education journals. Journals that shaped Polish mathematics education varied significantly. We analysed both those journals that have a long history and those that arose spontaneously, thus reflecting the mood of this time of great change. Our analysis leads to the conclusion that journals, where the authors are mostly mathematics scientists or university lecturers, turned out to be in different to shifts in the educational system. A characteristic tendency reflecting the mood of times of change was the creation of new magazines, which were to be forums for sharing views on teaching mathematics. It turns out, however, that the journals created after 1990 had quite a short lifespan. Education journals that were directed to teachers for decades constituted a platform for discussion of new ideas and teaching styles, too. They offered a place to exchange opposing views. However, this situation slowly ceased to apply. [ABSTRACT FROM AUTHOR]

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It was proved in Forti and Schwaiger (C R Math Acad Sci Soc R Can 11(6):215–220, 1989), Schwaiger (Aequ Math 35:120–121, 1988) and with different methods in Schwaiger (Developments in functional equations and related topics. Selected papers based on the presentations at the 16th international conference on functional equations and inequalities, ICFEI, Bȩdlewo, Poland, May 17–23, 2015, Springer, Cham, pp 275–295, 2017) that under the assumption that every function defined on suitable abelian semigroups with values in a normed space such that the norm of its Cauchy difference is bounded by a constant (function) is close to some additive function, i.e., the norm of the difference between the given function and that additive function is also bounded by a constant, the normed space must necessarily be complete. By Schwaiger (Ann Math Sil 34:151–163, 2020) this is also true in the non-archimedean case. Here we discuss the situation when the bound is a suitable non-constant function. [ABSTRACT FROM AUTHOR]

In a deliberately provocative first part to this paper, I argue that nineteenth-century British mathematicians had an unduly high opinion of themselves and a striking lack of appreciation for contemporary continental developments. I argue that this failure was rooted in the institutions that supported mathematics, and was only remedied towards the end of the century. In the more sober second half of the paper I ask if historians of mathematics have subscribed to this overestimate, and explore some related questions, among them what are historians doing when they write history: telling it as it was, or righting or defending the record? Historians of mathematics also need to consider British priorities for research in the nineteenth century, and a comparison with other minor players (such as Japan, Portugal, or Poland) might be illuminating. [ABSTRACT FROM AUTHOR]

The paper contains a proposal for a simple way of measuring the morphological diversity of patterns on fingers. The mono/polymorphism index (Imp) is the sum of 45 mutual absolute differences between the numerical values of the patterns depending on their degree of morphological complexity. Wendt's 7-degree scale was used to quantify the patterns. The value Imp=0 denotes monomorphism, i.e., the presence of the same type of pattern on all the fingers of both hands, while high values denote a mosaic of patterns of diverse morphology (polymorphism). Elements of the individual values of the Imp index comprise mutual homolateral differences (10 differences for the fingers of the left hand and 10 differences for the right), on the basis of which an assessment was made between the sides of the body, and additionally 25 heterolateral differences. Generally, greater degree of morphological diversity in patterns is found in males, and on the fingers of the right hand in both sexes. The arithmetic mean of the Imp index differs significantly between males (55.17) and females (52.08). Its values are not directly related to the degree of morphological complexity of patterns included in the Wendt's index. There were found, however, intra-familial connections for this trait. In light of the values of the indices of correlation and association, it may be concluded that there are relatively weak but statistically significant parents-offspring relations, as well as between siblings. An objective way to determine the values of the Imp index would make it possible to use it both for the morphological characterization of dermatoglyphs in different populations and also in clinical, auxological and genetic research., (Copyright © 2014 Elsevier GmbH. All rights reserved.)

The author of this paper conducted research on the impact of the new curriculum of mathematics in secondary schools on the results achieved by students of the University of Economics in Katowice. She used marks in mathematics and mathematical analysis achieved by her students in the years 2001?2010. Moreover she conducted a survey about the level of difficulty of the tasks-leaving and the level of difficulty of the tasks, which students solved in class. She presented the test results that reached her students in mathematical analysis in 2010, too. [ABSTRACT FROM AUTHOR]

The article discusses the highlights of the Congress of Polish Statistics held to celebrate the 100th anniversary of the Polish Statistical Association in Poznan from April 18 to 20, 2011. Polish President Bronislaw Komorowski has assumed his honorary patronage over the conference. The event included plenary sessions on achievements of Polish statistics and the opening of an exhibition.

This paper outlines the history of logic in Poland in the years 1918–1939 (with some additions concerning the periods before 1918 and after 1945). The disciplinary and social history of logical investigations in Poland is widely described. The author stresses topics characteristic for Polish logic, namely prepositional calculus, many-valued logic, Lezśniewski's systems, Chwistek's systems and the works in the history of logic. [ABSTRACT FROM PUBLISHER]

In the paper the views and tendencies in the philosophical reflection on mathematics in Poland between the wars are analyzed. Views of most outstanding representatives of Lvov–Warsaw Philosophical School and of Polish Mathematical School are presented. Their influence on logical and mathematical researches is considered. [Copyright &y& Elsevier]

Fernández (2020) has found a number of serious typos in Kaur et al (2019) that must be corrected. A list of corrections is enumerated below. All of these are typographical mistakes in the transcription of the equations and have no bearing on the results or conclusions of the work. Once the typos are corrected the only point remaining to address in the comment by Fernández (2020) is the connection between the homotopy perturbation method (HPM) and the Taylor series approach. Indeed we have acknowledged this relationship in Kaur et al (2019) (see discussion, section 5) and have cited several references to that effect, including Melzak (1957a,1957b), Lushnikov (1973) and Song and Poland (1992). In Kaur et al (2019) we offer HPM as an alternative to the series expansion method, apply it to initial conditions other than monodisperse, and present a number of new solutions that have not been reported in the previously literature. [ABSTRACT FROM AUTHOR]

Background: Predicted maturity offset and age at peak height velocity are increasingly used with youth athletes, although validation studies of the equations indicated major limitations. The equations have since been modified and simplified. Objective: The objective of this study was to validate the new maturity offset prediction equations in independent longitudinal samples of boys and girls. Methods: Two new equations for boys with chronological age and sitting height and chronological age and stature as predictors, and one equation for girls with chronological age and stature as predictors were evaluated in serial data from the Wrocław Growth Study, 193 boys (aged 8-18 years) and 198 girls (aged 8-16 years). Observed age at peak height velocity for each youth was estimated with the Preece-Baines Model 1. The original prediction equations were included for comparison. Predicted age at peak height velocity was the difference between chronological age at prediction and maturity offset. Results: Predicted ages at peak height velocity with the new equations approximated observed ages at peak height velocity in average maturing boys near the time of peak height velocity; a corresponding window for average maturing girls was not apparent. Compared with observed age at peak height velocity, predicted ages at peak height velocity with the new and original equations were consistently later in early maturing youth and earlier in late maturing youth of both sexes. Predicted ages at peak height velocity with the new equations had reduced variation compared with the original equations and especially observed ages at peak height velocity. Intra-individual variation in predicted ages at peak height velocity with all equations was considerable. Conclusion: The new equations are useful for average maturing boys close to the time of peak height velocity; there does not appear to be a clear window for average maturing girls. The new and original equations have major limitations with early and late maturing boys and girls. [ABSTRACT FROM AUTHOR]

We present results of an abstract, agent based model of opinion dynamics simulations based on the emotion/information/opinion (E/I/O) approach, applied to a strongly polarized society, corresponding to the Polish political scene between 2005 and 2015. Under certain conditions the model leads to metastable coexistence of two subcommunities of comparable size (supporting the corresponding opinions)—which corresponds to the bipartisan split found in Poland. Spurred by the recent breakdown of this political duopoly, which occurred in 2015, we present a model extension that describes both the long term coexistence of the two opposing opinions and a rapid, transitory change due to the appearance of a third party alternative. We provide quantitative comparison of the model with the results of polls and elections in Poland, testing the assumptions related to the modeled processes and the parameters used in the simulations. It is shown, that when the propaganda messages of the two incumbent parties differ in emotional tone, the political status quo may be unstable. The asymmetry of the emotions within the support bases of the two parties allows one of them to be ‘invaded’ by a newcomer third party very quickly, while the second remains immune to such invasion. [ABSTRACT FROM AUTHOR]

This study attempted to validate an anthropometric equation for predicting age at peak height velocity (APHV) in 193 Polish boys followed longitudinally 8–18 years (1961–1972). Actual APHV was derived with Preece–Baines Model 1. Predicted APHV was estimated at each observation using chronological age (CA), stature, mass, sitting height and estimated leg length. Mean predicted APHV increased from 8 to 18 years. Actual APHV was underestimated at younger ages and overestimated at older ages. Mean differences between predicted and actual APHV were reasonably stable between 13 and 15 years. Predicted APHV underestimated actual APHV 3 years before, was almost identical with actual age 2 years before, and then overestimated actual age through 3 years after PHV. Predicted APHV did not differ among boys of contrasting maturity status 8–11 years, but diverged among groups 12–15 years. In conclusion, predicted APHV is influenced by CA and by early and late timing of actual PHV. Predicted APHV has applicability among average maturing boys 12–16 years in contrast to late and early maturing boys. Dependence upon age and individual differences in actual APHV limits utility of predicted APHV in research with male youth athletes and in talent programmes. [ABSTRACT FROM AUTHOR]

Deals with the mathematical significance of the city of Vilnius in early twentieth-century Poland. Description of a scenic route; Archives of Polish mathematicians; List of professors that took part in the Second Congress of Polish Mathematicians; Role of Antoni Zygmund in strengthening the mathematical circle.