In this paper the power of the [gamma] algorithm for obtaining the dual of a given cone and some of its multiple applications is discussed. The meaning of each sequential tableau appearing during the process is interpreted. It is shown that each tableau contains the generators of the dual cone of a given cone and that the algorithm updates the…

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…

Consider the family of monic polynomials of degree n having zeros at -1 and +1 and all their other real zeros in between these two values. This article explores the size of these polynomials using the supremum of the absolute value on [-1, 1], showing that scaled Chebyshev and Bernstein polynomials give the extremes.

In the last After the Bell column, the importance of algebraic thinking was discussed, with respect to a common practice used in scientific inquiry-the importance of rates. This column discusses the importance of functions in preparing students for empirical and experimental inquiry. Functions are not only a necessary mathematical tool for…

Several ways for solving inequalities have been suggested in the literature, among them graphical, verbal and algebraic solutions. A new look at solving inequalities via use of the intermediate value theorem is presented here, and this method may prove to be straightforward for many students.

Six proofs are given for the fact that for each integer n [greater than or equal to] 2, the nth root function, viewed as a function from the set of non-negative real numbers to itself, is not linear. If p is a prime number, then [Zeta]/p[Zeta] is characterized, up to isomorphism, as the only integral domain D of characteristic p such that D admits…

This article describes the connection between a novel puzzle and uses of algebra to generalize the fewest moves to solve it.

This article presents an alternative to the traditional method of multiplying polynomials, FOIL. The method can be used with any size of polynomial.

In this era of high-stakes testing and accountability, curricula are viewed as catalysts to improve high school students' mathematics performances and a critical question is whether single subject or integrated curricula produce stronger student outcomes. This study was designed to investigate the effects of an integrated reform-based curriculum,…

In this important resource, Dr. Fleming (a noted expert in the field of minority retention) draws on educational evaluations she has developed in the course of her distinguished career. This book analyzes the common factors and the role institutional characteristics play in minority student retention to show what really works in increasing…

The purpose of this quantitative quasi-experimental study was to analyze the effect of one type of professional development, Japanese lesson study, on student achievement at the high school level. The study examined the effect by comparing student achievement of students with non-lesson study teachers (control group) and those using the lesson…

Research investigating algebra students' abilities to generalize and justify suggests that they experience difficulty in creating and using appropriate generalizations and proofs. Although the field has documented students' errors, less is known about what students do understand to be general and convincing. This study examines the ways in which…

Newton's proof of the connection between elliptical orbits and inverse-square forces ranks among the "top ten" calculations in the history of science. This time-honored calculation is a highlight in an upper-level mechanics course. It would be worthwhile if students in introductory physics could prove the relation "elliptical orbit" [arrow right]…

In this paper, departments are urged to consider implementing the type of changes proposed in Beyond Crossroads in College Algebra. The author of this paper is chair of the Curriculum Renewal Across the First Two Years (CRAFTY) Committee of the Mathematical Association of America. The committee has members from two-year colleges, four-year…

PreCalculus students can use the Completing the Square Method to solve quadratic equations without the need to memorize the quadratic formula since this method naturally leads them to that formula. Calculus students, when studying integration, use various standard methods to compute integrals depending on the type of function to be integrated.…