The demand for higher education keeps on increasing. The invention of information technology and e-learning have, to a large extent, solved the problem of shortage of skilled and qualified teachers. But there is no guarantee that this will ensure the high quality of learning. In spite of large number of students, though the delivery of learning…

Entropy analyses as a function of the extent of reaction are presented for a number of physicochemical processes, including vaporization of a liquid, dimerization of nitrogen dioxide, and the autoionization of water. Graphs of the total entropy change versus the extent of reaction give a visual representation of chemical equilibrium and the second…

Students' collaboration while learning could provide better learning environments. Collaboration assumes social interactions which occur in student groups. Social theories emphasize positive influence of such interactions on learning. In order to create an appropriate learning environment that enables social interactions, it is important to…

Standard distributions are ubiquitous but not unique. With suitable scaling, the graph of a standard distribution serves as the graph for every distribution in the family. The standard exponential can easily be taught in elementary statistics courses.

An interesting graphical interpretation of complex roots is presented, since it is probably unfamiliar to many mathematics teachers. (MNS)

Two problems related to the mean-value theorem lead into a problem requiring the use of the universal chord theorem. This latter theorem is discussed and a proof given. (MP)

Two mathematical brainteasers, with solutions depending on involved trial-and-error processes, are shown to have ingenious solutions. (MP)

An example is given of a problem-solving approach by outlining the development of a generalization of the Pythagorean Theorem as applied to points on a unit circle. (MP)

Nine examples of this principle show what a powerful tool it is. Several map coloring theorems are proven and some exercises are listed. (MP)

The goal of this pamphlet is to provide instructors of various scientific disciplines with mathematically accurate graphs of elementary polynomial functions. The figures in this pamphlet are intended to provide suitable material for the preparation of classroom handouts and overhead transparencies. In addition, sample sets of exercises are…

How tedious algebraic manipulations for simplifying general quadratic equations can be supplemented with simple geometric procedures is discussed. These procedures help students determine the type of conic and its axes and allow a graph to be sketched quickly. (MNS)

Four different types of problems from graph theory are presented and discussed. (MK)

A diagrammatic approach to invariants of knots is the focus. Connections with graph theory, physics, and other topics are included, along with an explanation of how proofs of some old conjectures about alternating knots emerge from this work. (MNS)

Curve stitching activities can be used to motivate calculus students. The problem described here involves showing that a given envelope of a curve is parabolic. (SD)

An examination of a student question concerning a calculus problem leads to a discussion of some of the symmetric properties of a specific set of polynomials. (MP)