Wyniki wyszukiwania - BazTech

1

Some remarks on strong sequences

Jureczko J.

Scientific Issues of Jan Długosz University in Częstochowa. Mathematics

|

2018

|

Vol. 23

25--34

EN

Strong sequences were introduced by Efimov in the 60s’ of the last century as a useful method for proving well known theorems on dyadic spaces i.e. continuous images of the Cantor cube. The aim of this paper is to show relations between the cardinal invariant associated with strong sequences and well known invariants of the continuum.

2

Strong sequences and their consequences in social choice

Jureczko J.

Silesian Journal of Pure and Applied Mathematics

|

2016

|

Vol. 6, iss. 1

49--58

EN

One of the most famous theorems in social choice theory – Arrow impossibility theorem – was published in 1951. Since Arrowian paper most researchers tried to ﬁnd diﬀerent versions of this theorem not only for ﬁnite but also for inﬁnite sets of alternative and individuals, where one can treat this situation as anticipation for future social behaviour. The aim of this paper is to ﬁnd some results concerning social voting for inﬁnite sets using one of the combinatorial methods of set theory – strong sequences method. This method was introduced by Eﬁmov in 1965 for proving wellknown theorems in dyadic spaces, (i.e. continuous images of the Cantor cube).

3

Using graphic display calculator in solving some problems with polynomials

Jureczko J.

Scientific Issues of Jan Długosz University in Częstochowa. Mathematics

|

2014

|

Vol. 19

83--93

EN

A graphic display calculator (GDC) is becoming more and more popular in teaching mathematics as it is used to examine some mathematical activities of students of almost all ages. Various modes of GDC are considered to be a useful tool in understanding of particular parts of mathematics. In most cases the properties of functions are examined by observation of their graphs. However, there are some properties of the functions which one cannot see during the graphs analysis (for example properties concerning complex roots of polynomials). The aim of this paper is to analyse how 17-and-18-year-old students for whom GDC is an obligatory device can generalize some relations between polynomials and so called “shadows” of these functions. The whole paper is concerned with in investigation of properties of quadratic, cubic and quartic functions with both real and complex roots.