Proving and refuting mathematical claims constitute a significant element in the development of deductive thinking. These issues are mainly studied during geometry lessons and very little (if at all) in lessons of other mathematical disciplines. This study deals with high school students' perceptions of proofs in the geometry. The study explores…

In this article, we consider the concept of rhotrices and present one-sided system of the form R[subscript n]x = b, where R[subscript n] is an n-dimensional rhotrix, x the unknown n-dimensional rhotrix vector and b the right-hand-side rhotrix vector.

A base for linear recursive sequences, such as the sequence of Fibonacci numbers, is defined within the framework of the sum of the digits of a number. Examples of bases of a number of such sequences are then outlined, and a Mobius strip is also used to illustrate the effects diagrammatically.

By using the Cauchy-Schwarz inequality a new proof of several standard inequalities is given. A new proof of Young's inequality is given by using Holder's inequality. A new application of the above inequalities is included.

The purpose of our article is to show two simpler and clearer methods of proving Stirling's formula than the traditional and conventional ones. The distinction of our method is to use the simple trapezoidal formula.

Evidence of deficiencies in basic mathematical skills of beginning undergraduates has been documented worldwide. Many different theories have been set out as to why these declines in mathematical competency levels have occurred over time. One such theory is the widening access to higher education which has resulted in a less mathematically…

We consider a problem appearing in an Australian Mathematics Challenge in 2003. This article considers whether a spreadsheet might be used to model this problem, thus allowing students to explore its structure within the spreadsheet environment. It then goes on to reflect on some general principles of problem decomposition when the final goal is a…

This article gives an elementary proof of the famous identity [image omitted]. Using nothing more than freshman calculus, the present proof is far simpler than many existing ones. This result also leads directly to Euler's and Neville's identities, as well as the identity [image omitted].

An outbox of a quadrilateral is a rectangle such that each vertex of the given quadrilateral lies on one side of the rectangle and different vertices lie on different sides. We first investigate those quadrilaterals whose every outbox is a square. Next, we consider the maximal outboxes of rectangles and those quadrilaterals with perpendicular…

Four different families of linear recurrences are derived for Catalan numbers. The derivations rest on John Riordan's 1973 generalization of Catalan numbers to a set of polynomials. Elementary differential and integral calculus techniques are used and the results should be of interest to teachers and students of introductory courses in calculus…

The fundamental theorems of the calculus describe the relationships between derivatives and integrals of functions. The value of any function at a particular location is the definite derivative of its integral and the definite integral of its derivative. Thus, any value is the magnitude of the slope of the tangent of its integral at that position,…

In this note, by using elementary calculus on time scales, we recall the direct proof of the equivalence between Rolle's and generalized (Cauchy's) mean value theorems on time scales.

A new proof for the monotonicity of the sequence [image omitted] is given as a special case of a large family of monotomic and bounded, hence convergent sequences. The new proof is based on basic calculus results rather than induction, which makes it accessible to a larger audience including business and life sciences students and faculty. The…

In this note, we present an interesting approach to sum subseries in closed form. This approach seems to be not widely known and remains under-appreciated. Our study will lead to the discovery of results some of which have been known for a long time, some which were found only recently, as well as those which appear to be new.

Effective assessment is a cornerstone in measuring student learning in higher education. For a course in Numerical Methods, a concept test was used as an assessment tool to measure student learning and its improvement during the course. The concept test comprised 16 multiple choice questions and was given in the beginning and end of the class for…