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Knight, D. G. – International Journal of Mathematical Education in Science and Technology, 2004
If the point of suspension of a multiple pendulum is suitably oscillated then the pendulum can remain in motion in an upside-down position. Since such pendulums can model flexible materials, this inverted motion is sometimes referred to as an 'Indian rope trick'. Despite the complexity of the governing differential equations, this rope trick can…
Descriptors: Motion, Algebra, Mathematical Formulas, Computation
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Chen, Hongwei – International Journal of Mathematical Education in Science and Technology, 2004
The telescoping sum constitutes a powerful technique for summing series. In this note, this technique is illustrated by a series of problems starting off with some simple ones in arithmetic, then some in trigonometry, famous families of numbers, Apery-like formulas, and finally ending with a class of problems that are solved by computer.
Descriptors: Arithmetic, Trigonometry, Mathematics Education, Mathematical Formulas
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Ching, Wai-Ki; Ng, Michael K. – International Journal of Mathematical Education in Science and Technology, 2004
Hidden Markov models (HMMs) are widely used in bioinformatics, speech recognition and many other areas. This note presents HMMs via the framework of classical Markov chain models. A simple example is given to illustrate the model. An estimation method for the transition probabilities of the hidden states is also discussed.
Descriptors: Markov Processes, Probability, Mathematical Models, Computation
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Hombas, Vassilios – International Journal of Mathematical Education in Science and Technology, 2004
The mean and variance of the number of turning points in random permutations of two kinds of distinct elements are evaluated. These results are applied to a Wald-Wolfowitz run test.
Descriptors: Statistics, Mathematics, Mathematical Formulas, Computation
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Sani, B. – International Journal of Mathematical Education in Science and Technology, 2004
In this article, an alternative multiplication method for rhotrices is proposed. The method establishes some relationships between rhotrices and matrices. This article has discussed a modified multiplication method for rhotrices. The method has a direct relationship with matrix multiplication, and so rhotrices under this multiplication procedure…
Descriptors: Mathematical Formulas, Higher Education, College Mathematics, Algebra
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Wu, Dane W. Wu; Bangerter, Laura M. – International Journal of Mathematical Education in Science and Technology, 2004
Given a set of urns, each filled with a mix of black chips and white chips, what is the probability of drawing a black chip from the last urn after some sequential random shifts of chips among the urns? The Total Probability Formula (TPF) is the common tool to solve such a problem. However, when the number of urns is more than two and the number…
Descriptors: Probability, Biology, Mathematical Formulas, Computation
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Guasti, M. Fernandez – International Journal of Mathematical Education in Science and Technology, 2005
Three major techniques are employed to calculate [pi]. Namely, (i) the perimeter of polygons inscribed or circumscribed in a circle, (ii) calculus based methods using integral representations of inverse trigonometric functions, and (iii) modular identities derived from the transformation theory of elliptic integrals. This note presents a…
Descriptors: Trigonometry, Calculus, Computation, Geometric Concepts
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Zhang, Chunming; Lu, Yuefeng – International Journal of Mathematical Education in Science and Technology, 2004
A family of integrals over infinite intervals appears frequently in the statistical literature on non-parametric regression. This note presents two simple transform methods, based on beta function and Parseval identity, to explicitly evaluate these integrals. These methods will benefit researchers and practitioners working in non-parametric…
Descriptors: College Mathematics, Intervals, Computation, Mathematics Instruction
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Mamon, Rogemar S. – International Journal of Mathematical Education in Science and Technology, 2004
Within the general framework of a multifactor term structure model, the fundamental partial differential equation (PDE) satisfied by a default-free zero-coupon bond price is derived via a martingale-oriented approach. Using this PDE, a result characterizing a model belonging to an exponential affine class is established using only a system of…
Descriptors: Factor Analysis, Structural Equation Models, Bond Issues, Computation
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Amit, Miriam; Fried, Michael N.; Satianov, Pavel – International Journal of Mathematical Education in Science and Technology, 2004
Teachers of first-year college mathematics and engineering courses must often spend considerable time reviewing material originally taught in high school. Instead of this being a mere exercise in repetition, this article suggests that such a review can enrich and revitalize by unifying some of the subjects that need to be re-taught. In the example…
Descriptors: College Mathematics, Graphs, Mathematics Instruction, Geometric Concepts