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In this paper, a new test of normality and independence is proposed. This test is designed through a multivariate empirical characteristic by considering a result form [Ejsmont 2016]. [ABSTRACT FROM AUTHOR]

Using approximate, rounded values implies, in a sense, that an exact numerical value may be ignored. In many cases the difference between the exact and approximate values is not important, and replacing exact numbers by their approximate values does not result in undesired consequences. Yet in certain circumstances, rounding significantly influences the solutions of given problems. This is the case, among others, when we allocate indivisible goods. It may happen that the rounding mode affects the result of allocation so much that the rounding differences cannot be neglected by the agents participating in distribution. This paper presents the classic problem of distributing mandates in representative bodies along with different rounding modes in respective solution procedures. [ABSTRACT FROM AUTHOR]

The problem of tiling by squares was formulated more than one hundred years ago and has been mostly regarded as an interesting mathematical issue in geometry, yet without any special practical associations. In addition to a historical outline of the problem, this paper demonstrates how Smith's 1940 method using digraphs helps associate an issue linked to two-dimensional dissection or packaging with such economic problems as transportation network planning, researching linkages between suppliers and the like. We also discuss simple perfect squared rectangles whose relevant laws of nature are as yet unknown, according to the principle that elegant scientific structures sooner or later find their equivalents in the real world. [ABSTRACT FROM AUTHOR]

In this paper the most important distributions in free probability (and maybe in the universe) will be presented. It is worth emphasizing that these distributions are not known among economists. [ABSTRACT FROM AUTHOR]

The paper includes an inductive proof of the four-color theorem. The notions of producing maps and minimum local colorings are applied. [ABSTRACT FROM AUTHOR]

First-year students usually ask whether they really need mathematics. This paper presents several simple examples applying differential calculus in microeconomics, which allow students to perceive that learning mathematics during their studies of economics does "pay off". [ABSTRACT FROM AUTHOR]

The formal description of economic phenomena requires the application of mathematical notions and mathematical techniques. When making formal description of economic phenomena we have to formulate all accepted assumptions in an open way. This prevents us from all errors and misunderstandings that can be created while formulating conclusions, results and forecasts. In this paper we present the advantages resulting from the application of formal description of economic phenomena. We also discuss approaches to the mathematical model link and we present some observations about the teaching of mathematics on economic studies. [ABSTRACT FROM AUTHOR]

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]