History and Theory of Mathematics

We introduce a method for showing that there exist prime numbers which are very close together. The method depends on the level of distribution of primes in arithmetic progressions. Assuming the Elliott-Halberstam conjecture, we prove that there are infinitely often primes differing by 16 or less. Even a much weaker c…

• CEM YALÇIN YILDIRIM

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In the preprint [3], Goldston, Pintz, and Yıldırım established, among other things, \begin{equation} \liminf_{n\to\infty}{p_{n+1}-p_n\over\log p_n}=0, \end{equation} with $p_n$ the $n$th prime. In the present article, which is essentially self-contained, we shall develop a simplified account of the method used in [3].…

• CEM YALÇIN YILDIRIM

The purpose of this study was to investigate pre-service teachers’ views about the history of mathematics course in which GeoGebra was used. The qualitative research design was used in this study. The participants of the study consisted of 23 pre-service mathematics teachers studying at a state university in Turkey. A…

• YILMAZ ZENGİN

Let $p_n$ denote the $n^{\textrm {th}}$ prime. Goldston, Pintz, and Yıldırım recently proved that \begin{equation*} \liminf _{n\to \infty } \frac {(p_{n+1}-p_n)}{\log p_n} =0. \end{equation*} We give an alternative proof of this result. We also prove some corresponding results for numbers with two prime factors. Let $…

• CEM YALÇIN YILDIRIM

In this paper, we investigate special Smarandache curves according to Bishop frame in Euclidean 3-space and we give some differential geometric properties of Smarandache curves. Also we find the centers of the osculating spheres and curvature spheres of Smarandache curves.

A generalization of complex, dual, and hyperbolic numbers has recently been defined as hybrid numbers. In this study, using the Leonardo Pisano numbers and hybrid numbers we investigate Leonardo Pisano polynomials and hybrinomials. Furthermore, we also describe the basic algebraic properties and some identities of the…

• FERHAT KÜRÜZ

Poincaré has proved that there exist 3-dimensional manifolds with identical Betti numbers and coefficients of torsion but which are nevertheless distinguishable in the sense of Analysis Situs by the fact that they have different groups.fIt is proposed to set up an example of two 3-dimensional manifolds which are by no…

In this paper, we give the definitions of quaternionic Smarandache curves in 3-dimensional Euclidean space 3 E and we investigate some differential geometric properties of these curves. Mathematics Subject Classification : 11R52, 53A04

• MEHMET AKİF ÇETİN

In recent years, the topic of integrating history to mathematics lessons in teaching-learning processes has been frequently discussed among researchers. The main aim of this study is to present an example activity which enriched with history of mathematics and to take the views of students about teaching course in thi…

• SEVDA GÖKTEPE YILDIZ

This study analyzed the methods used to teach the multiplication of fractions in Turkish and American textbooks. Two Turkish textbooks and two American textbooks, Everyday Mathematics (EM) and Connected Mathematics 3 (CM), were analyzed. The analyses focused on the content and the nature of the mathematical problems p…

• ERCAN ÖZDEMİR
• TUĞRUL KAR