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• Combinatorics – competition – Excel

  427-435

  László Zsakó

  Views:

  31

  In 2001 the Informatics Points Competition of the Mathematics Journal for Secondary School Students (KÖMAL) was restarted [1]. The editors set themselves an aim to make the formerly mere programming competition a bit more varied. Therefore, every month there has been published a spreadsheet problem, a part of which was related to combinatorics. This article is intended to discuss the above mentioned problems and the solutions given to them at competitions. We will prove that traditional mathematical and programming tasks can be solved with a system developed for application purposes when applying a different way of thinking.

• Combinatorics teaching experiment

  27-44

  Károly Csabay

  József Daragó

  Views:

  36

  Teaching combinatorics has got its conventional method. One has to see: the combinatorical formations won't be follow each other by a heuristic way. The formulas kept by pupils seem to come from "deus ex machina". We try to offer now an alternative way to approach combinatorical concepts from a nontraditional direction and point of view.

• Learning and teaching combinatorics with Sage

  389-398

  István Vajda

  Views:

  44

  Learning Mathematics is not an easy task, since this subject works with especially abstract concepts and sophisticated deductions. Many students lose their interest in the subject due to lack of success. Computer algebra systems (CAS) provide new ways of learning and teaching Mathematics. Numerous teachers use them to demonstrate concepts, deductions and algorithms and to make learning process more interesting especially in higher education. It is an even more efficient way to improve the learning process, if students can use the system themselves, which helps them to practice the curriculum.
  Sage is a free, open-source math software system that supports research and teaching algebra, analysis, geometry, number theory, cryptography, numerical computation, and related areas. I have been using it for several years to aid the instruction of Discrete Mathematics at Óbuda University. In this article I show some examples how representations provided by this system can help in teaching combinatorics.

• Teaching sorting in ICT

  101-117

  Péter Szlávi

  Gábor Törley

  Views:

  30

  This article is aimed at considering how an algorithmic problem – more precisely a sorting problem – can be used in an informatics class in primary and secondary education to make students mobilize the largest possible amount of their intellectual skills in the problem solving process. We will be outlining a method which essentially forces students to utilize their mathematical knowledge besides algorithmization in order to provide an efficient solution. What is more, they are expected to use efficiently a tool that has so far not been associated with creative thinking. Sorting is meant to be just an example, through which our thoughts can easily be demonstrated, but – of course the method of education outlined can be linked to several other algorithmic problems, as well.

• Examining relation between talent and competence through an experiment among 11th grade students

  17-34

  Veronika Árendás

  Views:

  31

  The areas of competencies that are formable, that are to be formed and developed by teaching mathematics are well-usable in recognizing talent. We can examine the competencies of a student, we can examine the competencies required to solve a certain exercise, or what competencies an exercise improves.
  I studied two exercises of a test taken by students of the IT specialty segment of class 11.d of Jedlik Ányos High School, a class that I teach. These exercises were parts of the thematic unit of Combinatorics and Graph Theory. I analysed what competencies a gifted student has, and what competencies I need to improve while teaching mathematics. I summarized my experience about the solutions of the students, the ways I can take care of the gifted students, and what to do to the less gifted ones.

• Thoughts on Pólya’s legacy

  157-160

  Alan Schoenfeld

  Views:

  132

  There is a saying, "the older I get, the smarter my parents become." What it means, of course, is that the more we learn, the more we appreciate the wisdom of our forebears. For me, that is certainly the case with regard to George Pólya.

  There is no need to elaborate on Pólya's contributions to mathematics – he was one of the greats. See, for example, Gerald Alexanderson's (2000) edited volume The Random Walks of George Pólya, or Pólya's extended obituary (really, a
  53-page homage) in the November 1987 Bulletin of the London Mathematical Society (Chung et al., 1987). Pólya was one of the most important classical analysts of the 20th century, with his influence extending into number theory, geometry, probability and combinatorics.

• Comparing various functions of the divisors of an integer in different residue classes

  247-258

  Ildikó Kézér

  Views:

  29

  The main goal of this paper is to investigate some problems related to the distribution of the divisors of a number in different residue classes. We study these questions modulo 3, and use mostly just elementary number theory. In some special cases, we demonstrate how this problem is related to other fields of maths, especially to combinatorics. Since the author is also a secondary school teacher, we use elementary methods that can be discussed in secondary school, mainly within the framework of group study sessions or in special maths classes. We do think that the investigation of these types of questions can motivate children to find their own way to create their own questions, and to get a deeper insight into problem solving by these experimentations.

• Trigonometric identities via combinatorics

  73-91

  Beáta Bényi

  Views:

  71

  In this paper we consider the combinatorial approach of the multi-angle formulas sin nΘ and cos nΘ. We describe a simple "drawing rule" for deriving the formulas immediately. We recall some theoretical background, historical remarks, and show some topics that is connected to this problem, as Chebyshev polynomials, matching polynomials, Lucas polynomial sequences.

  Subject Classification: 05A19

• A didactic analysis of merge sort

  195-210

  Christian Rinderknecht

  Views:

  22

  Due to technical difficulties, educators teaching merge sort often avoid the analysis of the cost in the general and average cases. Using basic discrete mathematics, elementary real analysis and mathematical induction, we propose a self-contained derivation of bounds αn log_2 n + βn + γ in all cases. Independent of any programming language or pseudo-code, supported by intuitive figures, it is suitable for informatics students interested in the analysis of algorithms. It is also a good exercise in showing that induction allows us to actually discover constants, instead of simply checking them a posteriori.