A one-credit seminar course for junior-senior mathematics majors is described. The topic for the seminar is continued fractions, taught by a modified Moore Method, where the focus is on students creating their own mathematics. The students make conjectures after completing computational problems, then work on refining the needed hypotheses,…

This note provides a simple method to extend the usual Leibniz rule for higher derivatives of the product of two functions to several functions, which is within the reach of freshman calculus students.

This paper discusses a result of Li and Shen which proves the existence of a unique periodic solution for the differential equation x[dots above] + kx[dot above] + g(x,t) = [epsilon](t) where k is a constant; g is continuous, continuously differentiable with respect to x , and is periodic of period P in the variable t; [epsilon](t) is continuous…

The normal equations discussed in this paper for a least-squares parabolic fit have a unique solution if and only if there are at least three different x-values in the observations. This requirement is satisfied by most real sets of quantitative observations. For particular data sets, the appropriateness of parabolic fits should be assessed with…

In the seventh century, around 650 A.D., the Indian mathematician Brahmagupta came up with a remarkable formula expressing the area E of a cyclic quadrilateral in terms of the lengths a, b, c, d of its sides. In his formula E = [square root](s-a)(s-b)(s-c)(s-d), s stands for the semiperimeter 1/2(a+b+c+d). The fact that Brahmagupta's formula is…

Circular dichroism spectroscopy was used to measure the thermal unfolding of bovine pancreatic ribonuclease A (RNase A) with various concentrations of guanidine hydrochloride (GuHCl). A red shift in transition midpoint temperatures, T[subscript m], occurred with increasing concentration of the strong protein denaturant. van Hoff enthalpy changes,…

Meaningful visual experience requires computations that identify objects as the same persisting individuals over time, motion, occlusion, and featural change. This article explores these computations in the tunnel effect: When an object moves behind an occluder, and then an object later emerges following a consistent trajectory, observers…

The application range of Cohen's Kappa is extended to the field of sequential observation data, where omission mistakes of an observer may often occur. It is shown how the omission mistakes can be incorporated into the calculation of the Kappa coefficient without violating the statistic it is based on. The enhanced coefficient is termed Kappa…

This snapshot introduces a computer-based representation and activity that enables students to simultaneously "see" the combinatorial space of a stochastic device (e.g., dice, spinner, coins) and its outcome distribution. The author argues that the "ambiguous" representation fosters student insight into probability. [Snapshots are subject to peer…

When a simple random sample of size n is employed to establish a classification rule for prediction of a polytomous variable by an independent variable, the best achievable rate of misclassification is higher than the corresponding best achievable rate if the conditional probability distribution is known for the predicted variable given the…

This article discusses field tests that can be used in physical education programs. The most common field tests are anthropometric measurements, which include body mass index (BMI), girth measurements, and skinfold testing. Another field test that is gaining popularity is bioelectrical impedance analysis (BIA). Each method has particular strengths…

At the start of a freshman calculus course, many students conceive the classical definition of limit as the most problematic part of calculus. They not only find it difficult to understand, but also consider it of no use while solving most of the limit problems and therefore, skip it. This paper reformulates the rigorous definition of limit, which…

The modular exponentiation, y[equivalent to]x[superscript k](mod n) with x,y,k,n integers and n [greater than] 1; is the most fundamental operation in RSA and ElGamal public-key cryptographic systems. Thus the efficiency of RSA and ElGamal depends entirely on the efficiency of the modular exponentiation. The same situation arises also in elliptic…

This exploratory study was designed to compare several commonly used measures of alcohol use among college students in order to appreciate how estimations of college drinking may be affected by the type of assessment tool used. Consumption patterns of 42 college student drinkers were compared using a quantity-frequency measure, a graduated…

This investigation involves first assessing and then designing instruction to resolve student difficulties with addition facts. The ultimate goal was improving students' computational fluency.