Discusses synchronous impact factors and theoretical models derived from observations based on "Science Citation Index", and presents an exception to the general rules based on data from the "Chinese Science Citation Database". Considers that the observed discrepancies could be statistical fluctuations of the basic…

Discussion of word frequency and keywords in text focuses on a method to estimate automatically the stability classes that indicate a word's popularity with time-series variations based on the frequency change in past electronic text data. Compares the evaluation of decision tree stability class results with manual classification results.…

In this article the author presents readers with some very useful activities, ideas and problems. He has used these at various times over the years and together they make a very interesting collection. These pieces have come together from different sources, but like a jigsaw, they complete the picture of understanding of the numbers inside the…

This article examines an innovative question taken from the 1988 Extension 1 (3 unit) Mathematics New South Wales Higher School Certificate examination. Similar questions have made regular subsequent appearances in trial examinations around NSW and many texts now devote whole chapters to the subtle and somewhat laborious process of establishing…

This study proposed practical ways to display mathematical formula on the Web and input mathematical formulae onto the Web according to the authors' successful experience of implementing mathematical forum which allowed displaying and inputting mathematical notations and equations. Authors believe that this study will pose more questions and…

A method for generating sums of series based on simple differential operators is presented, together with a number of worked examples with interesting properties.

A novel and simple formula for computing the matrix exponential function is presented. Specifically, it can be used to derive explicit formulas for the matrix exponential of a general matrix A satisfying p(A) = 0 for a polynomial p(s). It is ready for use in a classroom and suitable for both hand as well as symbolic computation.

The analysis of tautochrone problems involves the solution of integral equations. The paper shows how a reasonable assumption, based on experience with simple harmonic motion, allows one to greatly simplify such problems. Proposed solutions involve only mathematics available to students from first year calculus.

This paper focuses on the representation of a proper fraction "a"/"b" by a decimal number base "n" where "n" is any integer greater than 1. The scope is narrowed to look at only fractions where "a","b" are positive integers with "a" less than "b" and "b" not equal to 0 nor equal to 1. Some relationships were found between "b" and "n", which…

In this note, using the method of undetermined coefficients, we obtain the power series for exp ( f ( x )) and ln ( f ( x )) by means of a simple recursion. As applications, we show how those power series can be used to reproduce and improve some well-known results in analysis. These results may be used as enrichment material in an advanced…

This note provides a scheme that can overcome difficulties in calculating statistical quantities using certain formulae because of errors in the means. Specifically the diversions and discrepancies arising from the results obtained from three groups of widely used formulae for computing the estimated regression coefficients, the gradient b and the…

The goals of this note are to derive formulas for the coefficients a and b in the least-squares regression plane y = at + bx + c for observations (t[subscript]i,x[subscript]i,y[subscript]i), i = 1, 2, ..., n, and to present meanings for the coefficients a and b. In this note, formulas for the coefficients a and b in the least-squares fit are…

This article describes a way to use color to help students develop formulas for functions that describe growing patterns. (Contains 4 figures.)

Full account of the latent regression model for the National Assessment of Educational Progress is given. The treatment includes derivation of the EM algorithm, Newton-Raphson method, and the asymptotic standard errors. The paper also features the use of the adaptive Gauss-Hermite numerical integration method as a basic tool to evaluate…

This article proposes an instructional idea where students can figure out an individual's secret personal information using the power of mathematics, particularly the power of algebraic thinking. The proposed examples in this article start with a personalized context that other people do not know and end up with generalized patterns of solutions.…