Volume XI , issue 2 ( 2008 ) back
 The chemical formula $C_{n}H_{2n+2}$ and its mathematical background 53$-$61 Ivan Gutman Faculty of Sciences, Kragujevac University, Radoja Domanovića 12, 34000 Kragujevac, Serbia

Abstract

Already in the elementary school, on the chemistry classes, students are told that the general formula of alkanes is $C_nH_{2n+2}$. No proof of this claim is offered, either then or at any higher level. We now show how this formula can be proven in a mathematically satisfactory manner. To do this we have to establish a number of elementary properties of the mathematical objects called trees.

Keywords: Graph Theory; Trees; Chemistry; Alkanes.

 The role of programming paradigms in teaching and learning programming 63$-$83 Milena Vujošević-Janičić and Dušan Tošić Faculty of Mathematics, University of Belgrade, Studentski trg 16, 11000 Belgrade, Serbia

Abstract

The choice of the first programming language and the corresponding programming paradigm is critical for later development of a programmer. Despite the huge number of programming languages introduced over the last fifty years, the key issues in programming education remain the same and choosing appropriate first programming language is still challenging. In this paper we overview some of the most important issues relevant for programming education, especially for introductory courses, and we discuss the problem of choosing the first programming language. Some statistical data about first programming language are presented.

Keywords: Programming paradigms; Programming education; First programming language.

 The Fibonacci sequence and the golden quadratic 85$-$91 José C. \'I\~niguez and B. Argentina \'I\~niguez José C. \'I\~niguez, Cochise College, Douglas Campus, 4190 W Highway 80, Douglas, Arizona 85607

Abstract

The fact that the golden mean ($\Phi=1.61803\dots$) appears both as the limit of the ratio of consecutive Fibonacci numbers, as well as one of the solutions of the golden quadratic, prompted us to conduct a graphical analysis of this equation in order to ascertain what kind of connection its geometry has with the Fibonacci sequence. Our results indicate that the following are all subsumed by the geometry of this equation: the Fibonacci sequence, a sequence of powers of $\Phi$, Division in Extreme and Mean Ratio, $\Phi$, as well as the golden rectangle.

Keywords: Fibonacci sequence, $\Phi$, Division in extreme and Mean Ratio, Golden rectangle.

 Solving sextics by division method 93$-$96 Raghavendra G. Kulkarni HMC division, Bharat Electronics Ltd., Jalahalli Post, Bangalore - 560013, INDIA.

Abstract

A polynomial is said to be reducible over a given field if it can be factored into polynomials of lower degree with coefficients in that field; otherwise it is termed as an irreducible polynomial~[1]. This paper describes a simple division method to decompose a reducible sextic over the real field into a product of two polynomial factors, one quadratic and one quartic. The conditions on the coefficients of such reducible sextic are derived.

Keywords: Sextics; reducible polynomials; reducible sextic.

 Fourier series and Laplace transform through tabular integration 97$-$103 Sanjay K. Khattri Stord Haugesund Engineering College, Norway

Abstract