Introduction: We present some aspects of a wider investigation (Canadas, 2007), whose main objective is to describe and characterize inductive reasoning used by Spanish students in years 9 and 10 when they work on problems that involved linear and quadratic sequences. Method: We produced a test composed of six problems with different…

The U.S. Constitution requires a national census once every 10 years. The census is a count of everyone (all ages, races, ethnic groups, both citizens and non-citizens) residing in the United States: in all 50 states, Washington D.C., Puerto Rico, U.S. Virgin Islands, Guam, the Commonwealth of the Northern Mariana Islands, and American Samoa.…

A cyclical conditional maximum likelihood estimation procedure is developed for the multidimensional unfolding of two- or three-way dominance data (e.g., preference, choice, consideration) measured on ordered successive category rating scales. The technical description of the proposed model and estimation procedure are discussed, as well as the…

We discuss a class of trigonometric functions whose corresponding Fourier series, on a conveniently chosen interval, can be used to calculate several numerical series. Particular cases are presented and two recent results involving numerical series are recovered. (Contains 1 note.)

Defined mathematically, the internal rate of return (IRR) of a cash-flow stream is the discount rate at which its net present value is 0. What is the significance or meaning of such a measure? Using simple example problems and illustrative calculations, the author explains a technically correct but, at the same time, intuitively meaningful…

Reports an error in "Confidence intervals for gamma-family measures of ordinal association" by Carol M. Woods (Psychological Methods, 2007[Jun], Vol 12[2], 185-204). The note corrects simulation results presented in the article concerning the performance of confidence intervals (CIs) for Spearman's r-sub(s). An error in the author's C++ code…

Motivated by centaurs jumping around a circular stadium, we derive Kronecker's Approximation Theorem, which in turn provides elementary solutions to difficult problems in the theory of Diophantine approximations.

The recognition that human minds/brains are finite systems with limited resources for computation has led some researchers to advance the "Tractable Cognition thesis": Human cognitive capacities are constrained by computational tractability. This thesis, if true, serves cognitive psychology by constraining the space of computational-level theories…

We discuss a general class of trigonometric functions whose corresponding Fourier series can be used to calculate several interesting numerical series. Particular cases are presented. (Contains 4 notes.)

Using only fairly simple and elementary considerations--essentially from first year undergraduate mathematics--we show how the classical Stokes' theorem for any given surface and vector field in R[superscript 3] follows from an application of Gauss' divergence theorem to a suitable modification of the vector field in a tubular shell around the…

The Hill cipher is the simplest example of a "block cipher," which takes a block of plaintext as input, and returns a block of ciphertext as output. Although it is insecure by modern standards, its simplicity means that it is well suited for the teaching of such concepts as encryption modes, and properties of cryptographic hash functions. Although…

Professional astronomers use specialized software not normally available to students to determine the rotation periods of asteroids from fragmented light curve data. This paper describes a simple yet accurate method based on Microsoft Excel[R] that enables students to find periods in asteroid light curve and other discontinuous time series data of…

This article studies various holiday distributions, the most interesting one being Easter. Gauss' Easter algorithm and Microsoft Excel are used to determine that the Easter distribution can be closely approximated by the convolution of two well-known uniform distributions. (Contains 8 figures.)

A new class of Euler's method for the numerical solution of ordinary differential equations is presented in this article. The methods are iterative in nature and admit their geometric derivation from an exponentially fitted osculating straight line. They are single-step methods and do not require evaluation of any derivatives. The accuracy and…

Development of adaptive tests used in K-12 settings requires the creation of stable measurement scales to measure the growth of individual students from one grade to the next, and to measure change in groups from one year to the next. Accountability systems like No Child Left Behind require stable measurement scales so that accountability has…