Most any students can explain the meaning of "a[superscript b]", for "a" [element-of] [set of real numbers] and for "b" [element-of] [set of integers]. And some students may be able to explain the meaning of "(a + bi)[superscript c]," for "a, b" [element-of] [set of real numbers] and for…

The use of smartphones is increasingly gaining popularity in education. Students and teachers can determine scientific concepts using smartphones equipped with sensors such as Global Positioning System (GPS -- a navigation system that provides location information) and orientation (a device to measure coordinates according to a reference frame).…

Following a line of inquiry regarding the exact number of real roots of a real polynomial, this investigation considers: Descartes' Rule of Signs, the Budan-Fourier Theorem, and versions of Sturm's Method in contrast with the approximate root count gleaned from graphing utilities. Online applets are provided to allow the reader to freely…

This article draws on extensive experience working with secondary and tertiary teachers and educators using an applet to display rational polynomials (up to degree 7 in numerator and denominator), as support for the challenge to deduce as much as possible about the graph from the graphs of the numerator and the denominator. Pedagogical and design…

In this column, the authors discuss apps useful in developing mathematical reasoning. They place these into a theoretical framework, suggesting how they could be used in an instructional model such as the Algorithmic Instructional Technique (AIT) developed by Vasquez (2003). This model includes four stages: modeling, practice, transition, and…

Descriptions of a program called muMATH and a computer language called muSIMP are given to show what the state of the art is in mathematical programing material for personal computers. The intent is to get college mathematics instructors thinking about what the future portends for their field. (MP)

Until recently the testing of a 100-digit number to determine whether it is prime or composite could have taken a century. However, in the past two years a method has been developed enabling a computer to determine the primality of an arbitrary number in about 40 seconds of running time. (Author/JN)

The development of a computer-based, university-wide testing system at Brigham Young University is discussed, as is its application to two large-enrollment math classes. The hardware configuration, software applications, general philosophy, budget, and personnel requirements of the system are also explained. Development of the system over time is…

Describes experiences at Duke University in teaching mathematics using computer graphics. Includes comments on the software library, slide shows, assessment of activities, teaching of calculus and differential equations, and various graphics devices for instructional purposes. (JN)

When problems defy solution, mathematicians can settle for "almost." This branch of mathematics (called computational complexity) encompasses both the number of parts involved in a problem and the intricacy of their interrelatedness. Current research in this area is discussed, considering various computer applications involved. (JN)

Describes a number sequence made by counting the occurrence of each digit from 9 to 0, catenating this count with the digit, and joining these numeric strings to form a new term. Presents a computer-aided proof and an analytic proof of the sequence; compares these two methods of proof. (YP)

The rule of 78 is used by banks and loan companies to compute the amounts due when installment loans are paid early. Describes an unexpected case of negative amortization when the rule is applied. Presents an actual problem and discusses the case. (YP)

Describes two methods to resolve common difficulties in solving problems. The first is used when the solver becomes stuck with a problem and no idea seems to come to mind. The second is suitable when the solver is trapped in a loop and goes in circles around the problem. (JN)

Presents computer programs (Applesoft Basic) for: (1) 2-D rotation about any point through any angle; (2) matrix transformation for 2-D rotation; (3) 3-D translation; (4) 3-D rotation; and (5) hyperboloid rotated in 2-D space. Includes background information and sample output for the matrix transformation subroutines. (JN)

Sophomore and junior students in the College of Engineering at Cornell University have been taught engineering mathematics using new computer software that performs exact symbolic algebraic and calculus operations. Describes this software, the computer-based mathematics laboratory, changes in the teaching/learning environment, and short- and…