We give closed forms, recursion formulas and experimental results for the series ∑ nk/ ( 2n n ) and ∑ 2−nnk/ ( 3n n ) with k ∈ Z. Mathematics Subject Classification (2000). Primary 05A10, 11B65; Secondary 11Y16, 11Y65.

One of the most important applications of grounded cognition theories is to science and mathematics education, where the primary goal is to foster knowledge and skills that are widely transportable to new situations. This presents a challenge to those grounded cognition theories that tightly tie knowledge to the specifics of a single situation. In this chapter, we develop a theory learning that...

The behavior of generalized Cesàro (C, αn)-means (αn ∈ (−1, 0), n = 1, 2, . . . ) of conjugate trigonometric Fourier series of H classes in the space of continuous functions is studied. 2000 Mathematics Subject Classification: 42A50.

For the purpose of constructive reverse mathematics, we show the equivalence of the uniform continuity theorem to a series of propositions; this illuminates the relationship between Brouwer’s fan theorem and the uniform continuity theorem.

Two questions are on the mind of many mathematics educators; namely: What is the mathematics that we should teach in school? and how should we teach it? This is the second in a series of two papers addressing these fundamental questions. The first paper (Harel, 2008a) focuses on the first question and this paper on the second. Collectively, the two papers articulate a pedagogical stance oriente...

This column will publish short (ranging from just a few paragraphs to ten or so pages), lively and intriguing computer-related mathematics vignettes. These vignettes or snapshots should illustrate ways in which computer environments have transformed the practice of mathematics or mathematics pedagogy. They could also include puzzles or brain teasers involving the use of computers or computation...

This paper is the second part of a case study concerning shape classification and shape recognition for automatic diagnosis of hepatitis. Two new methods are proposed and tested here. The first method is a classification schema based on ISODATA algorithm. This approach requires corpuscle segmentation to be performed on each input image in order to extract area, perimeter and circularity coeffic...

Recently Zagier proved a remarkable q-series identity. We show that this identity can also be proved by modifying Franklin’s classical proof of Euler’s pentagonal number theorem. Mathematics Subject Classification (2000): 05A17 11P81