| The chemical formula $C_{n}H_{2n+2}$ and its mathematical background | 53$-$61 |
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$-$83 |
Abstract
The choice of the first programming language and the corresponding programming paradigm is critical for later development of a programmer. Despite the huge number of programming languages introduced over the last fifty years, the key issues in programming education remain the same and choosing appropriate first programming language is still challenging. In this paper we overview some of the most important issues relevant for programming education, especially for introductory courses, and we discuss the problem of choosing the first programming language. Some statistical data about first programming language are presented.
Keywords: Programming paradigms; Programming education; First programming language.
| The Fibonacci sequence and the golden quadratic | 85$-$91 |
Abstract
The fact that the golden mean ($\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$-$96 |
Abstract
A polynomial is said to be reducible over a given field if it can be factored into polynomials of lower degree with coefficients in that field; otherwise it is termed as an irreducible polynomial~[1]. This paper describes a simple division method to decompose a reducible sextic over the real field into a product of two polynomial factors, one quadratic and one quartic. The conditions on the coefficients of such reducible sextic are derived.
Keywords: Sextics; reducible polynomials; reducible sextic.
| Fourier series and Laplace transform through tabular integration | 97$-$103 |
Abstract
This article is intended for first year undergraduate students. In this work, we explore the technique of tabular integration, and apply it for evaluating Fourier series and Laplace transform.
Keywords: Fourier series; Laplace transform; tabular integration.