Volume IV , issue 1 ( 2001 ) back
 Selected chapters from algebra, V. Real numbers and polynomials 1$-$34 I. R. Shafarevich

Abstract

This paper is the fifth part of the publication Selected chapters from algebra'', the first four having been published in previous issues of the Teaching of Mathematics, Vol\. I (1998), 1--22, Vol\. II, 1 (1999), 1--30, Vol\. II, 2 (1999), 65--80, Vol\. III, 1 (2000), 15--40, and Vol\. III, 2 (2000), 63--82.

Keywords: Real numbers, limits, infinite sums, decimal representations, real roots of polynomials, Sturm's theorem.

MSC Subject Classification: 00A35

 The first lecture on non-classical logics 35$-$40 Alexandros Pefku University of Belgrade, Faculty of Economics, Kamenička 6, 11000 Belgrade, Yugoslavia,

Abstract

The implication fragment of Heyting's logic is the minimal logical system for which deduction theorem holds. This is known, but not emphasized enough. In this note we present an elementary proof of this fact and propose how to use it in order to promote the concept of many-valued logics in a natural way, by giving a concept for the first lecture on this subject.

Keywords: Non-classical logics, deduction relation, deduction theorem, Heyting's logic.

MSC Subject Classification: 00A35

 Metric Euclidean projective and topological properties 41$-$70 Milosav M. Marjanović

Abstract

This paper is devoted to those readers who are professionally engaged in dealing with the questions of teaching and learning elementary school geometry. It consists of three lessons from a postgraduate course taught by this author at the Teacher's Training Faculty, University of Belgrade. Appearance of things in the surrounding world changes but some stable characteristic properties of their shapes stay unchanged. J. Piaget classifies these properties as topological projective and Euclidean and the spontaneous development of a child follows that order of ideas. It is a normal interest of a specialist in education to know how these ideas are mathematically established without wading through the books on these subjects which are often unapproachable to him or her. The aim of this paper is to make a direct approach to mathematical clarification of these ideas, based only on the reader's knowledge of the secondary school mathematics.

Keywords: Metric properties, Euclidean properties, projective properties, topological properties.

MSC Subject Classification: 00A35