An Important Historical Milestone: The Classification of the Cubic Equations

This article investigates the use of the history of mathematics as a pedagogical tool for the teaching and learning of mathematics, using the history of the cubic equation as a specific example.Cubic equations arise intrinsically in many applications in natural sciences and mathematics. For example, in physics, the solutions of the equations of state in thermodynamics, or the computation of the speed of seismic Rayleigh waves require the solutions of cubic equations. In mathematics, they are instrumental in solving the quartic equations, for in the process, these are reduced to cubic equations. The impossibility of trisecting an angle or doubling a cube using only a straightedge and compass is equivalent to solving some cubic equations. As the name implies, the cubic spline approximation, an important tool in numerical analysis, also entails working with cubic functions. Although cubic equations were explored by the ancient Babylonian, Greek, Chinese, Indian, and Egyptian scholars, it took the collective work of many well-known mathematicians such as Diophantus, Archimedes, Fibonacci, del Ferro, Khayyam, Tartaglia, Cardano, Viète, Descartes, and Lagrange to finally obtain a full solution. Our goal in this paper is to investigate one of the most formidable steps in this extensive and prolific history, namely the complete classification of the cubic equations by Omar Khayyam in eleventh century, who was the first scholar to classify cubic equation and hence facilitate a methodical and logical approach to obtaining a general solution

Pedagogy on the Ethnomathematics--Epistemology Nexus: A Manifesto

In this paper, we will elaborate on a pronouncement that should be at the onset of any study in epistemology and ethnomathematics, namely, we will argue that learners do think mathematically and it is our responsibility as educators to recognize and appreciate their modes of mathematical reasoning. We will conduct our study in five parts. Following a brief introduction, in the second part, we will briefly discuss some of the critical tenets of epistemology especially as it applies to mathematics. The third part will be devoted to elucidating the basic nomenclature and hypotheses associated with ethnomathematics. In the fourth part we will expound on the organic and intrinsic relationship between these two fields. Lastly, we will propose some changes in the way academic mathematicians regard philosophy and pedagogy of mathematics that, in our opinion, will facilitate students’ understanding of the cultural aspects of mathematics

POLYMORPHISMS OF HPC2/ELAC2 AND SRD5A2 (5α-Reductase Type II) GENES IN PROSTATE CANCER

ABSTRACT Prostate cancer is the proliferation of malignant cells in the prostate gland. The HPC2/ELAC2 gene on chromosome 17p11.2 and SRD5A2 gene on chromosome 2p22-23 are predisposing genetic factors. We examined the relationship between Ser217Leu and Ala541Thr polymorphisms of the former gene, and Ala49Thr and Val89Leu polymorphisms of the latter gene to prostate cancer in Turkish men, using the polymerase chain reaction (PCR) method and appropriate restriction enzymes. The HPC2/ ELAC2 gene Ser217-Leu and SRD5A2 gene Ala49Thr polymorphisms were associated with an increased risk of prostate cancer in Turkish men [for the HPC2/ELAC2 gene Ser217Leu polymorphism: odds ratio (OR) 2.7; confidence interval 95% (CI 95%) 1.6-4.8; p 0.000<0.05, and for the SRD5A2 gene Ala49Thr polymorphism: OR 2.4; CI 95% 1.2-4.9; p 0.004<0.05]

The Role Of Diffusion-Weighted Mr Imaging And Adc Values In The Diagnosis Of Gastric Tumors

Background: The aim of this study was to investigate the role of diffusion-weighted MR imaging (DWI) in the diagnosis of gastric tumors by means of measuring the apparent diffusion coefficient (ADC) values of these lesions, and making a comparison with the endoscopic biopsy results. Subjects and Methods: Seventy patients having gastric tumor constituted the case group. For the control group 30 healthy individuals were included. Abdominal MRI examinations were performed with a 1,5 Tesla unit. DWI examinations were obtained by single shot spin echoplanar imaging. The ADC was measured based on the tissue of the gastric tumoral entities and normal gastric mucosa in the control group. Results: Mean ADC values were 0,84 ± 0,17 × 10-3 mm2/s and 1,79 ± 0,08 × 10-3 mm2/s in gastric tumor group and in control group, respectively, being statistically significant (p < 0.05). There was no significance among ADC values of adenocarcinoma subgroups. The comparison of the ADC values in the adenocarcinoma and lymphoma cases were also found to be statistically significant. Conclusions: DWI is beneficial in the diagnosis of malignant gastric lesions by the aid of ADC measurements. Although ADC quantification seems to be invaluable in the evaluation of histopathologic subgroups of adeno - carcinoma, it can help in the diagnosis of gastric lymphoma

A tonal context model for musical sound processing

Ph.D. - Doctoral Progra