Probably the one "new" mathematical topic that is most responsible for modernizing courses in college algebra and precalculus over the last few years is the idea of fitting a function to a set of data in the sense of a least squares fit. Whether it be simple linear regression or nonlinear regression, this topic opens the door to applying the…

Application of quadratic equations to standard problem in chemistry like finding equilibrium concentrations of ions in an acid solution is explained. This clearly shows that pure mathematical analysis has meaningful applications in other areas as well.

Teachers incorporate the chaos game and the concept of a fractal into various areas of the algebra and geometry curriculum. The chaos game approach to fractals provides teachers with an opportunity to help students comprehend the geometry of affine transformations.

This article presents a brief biography of Johann Carl Friedrich Gauss. Gauss was born on April 30, 1777, in the German city of Braunschweig (Brunswick). He was the only child of Gebhard Dietrich Gauss and Dorothea Benze. Neither of Gauss's parents had much education, his father could read and write, but earned his living doing menial jobs such as…

This study examined how 4 middle school textbook series (2 skills-based, 2 Standards-based) present equal signs. Equal signs were often presented in standard operations equals answer contexts (e.g., 3 + 4 = 7) and were rarely presented in nonstandard operations on both sides contexts (e.g., 3 + 4 = 5 + 2). They were, however, presented in other…

This paper analyses the answers of a group of first-year university Mathematics students to a questionnaire, with the aim of determining the difficulties they have when carrying out non-routine tasks related to improper integrals. The questionnaire consisted of nine questions including not only calculus tasks and determining the convergence of…

Despite the ready availability of computer algebra packages, from a pedagogical point of view, the authors still feel that integration should be taught extensively the classical way, by means of carefully selected examples which combine as many fundamental techniques as possible for their evaluation. Furthermore, whenever possible, these examples…

The ubiquity of calculators led to many "computational abuses", when numbers substitute for substance. On the other hand, it resulted in decrease in number oriented dexterity of students. The latter led to a disdain for even simple calculations to work about unfamiliar mathematical problems. As a reaction to the former, the reputation of…

A type of data layout that may be considered as an extension of the two-way random effects analysis of variance is characterized and modeled based on group invariance. The data layout seems to be suitable for several scenarios in psychometrics, including the one in which multiple measurements are taken on each of a set of variables, and the…

This note gives geometrical/graphical methods of finding solutions of the quadratic equation ax[squared] + bx + c = 0, a [not equal to] 0, with non-real roots. Three different cases which give rise to non-real roots of the quadratic equation have been discussed. In case I a geometrical construction and its proof for finding the solutions of the…

In this note several cubic polynomials and their roots are examined, in particular, how these roots move as some of the coefficients are modified. The results obtained are applied to eigenvalues of matrices. (Contains 8 figures and 1 footnote.)

A lively example to use in a first course in linear algebra to clarify vector space notions is the space of square matrices of fixed order with its subspaces of affine, coaffine, doubly affine, and magic squares. In this note, the projection theorem is illustrated by explicitly constructing the orthogonal projections (in closed forms) of any…

Excel assignments were used as extra credit in an intermediate algebra course. Ninety percent of the students had a home computer and seventy per cent were familiar with Excel. There was not a significant linear correlation between the amount of Excel that the students performed and their achievement in algebra. One-third of the students did less…

Three proofs are given for the fact that the derivative of an everywhere-positive non-constant real polynomial function must change sign. This self-contained note could find classroom use in courses on calculus or abstract algebra.

This article investigates a specific instance when the textbook answer for finding a root of a complex number differed with the answer given by the TI-83. After explaining the reason for the difference the article then expands the definition of the integral root of a complex number to an arbitrary complex power of a complex number.