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

This article presents the results of a 7th-grade classroom teaching experiment that supported students' understanding of integer addition and subtraction. The experiment was conducted to test and revise a hypothetical learning trajectory so as to propose a potential instructional theory for integer addition and subtra…

• DİDEM AKYÜZ

No abstract yet.

• MEHMET FATİH ÖZMANTAR

No abstract yet.

No abstract yet.

• MEHMET FATİH ÖZMANTAR

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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

No abstract yet.

• HÜSEYİN BAHADIR YANIK

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• HÜSEYİN BAHADIR YANIK

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.