Tychonov's 1935 solution of the heat equation, exhibiting nontrivial heat fluxes spontaneously appearing along an isolated conducting rod initially held at zero degrees, has intrigued some specialists for almost a century. No doubt those practicing heat engineers who took mathematics seriously were initially relieved to learn that the construction…

Peer-mediation in a school environment, when carried out correctly, can benefit not only the parties of the conflict, but also their environment, including the school, the team, the family and the mediator. A serious same has been designed and a prototype developed for the training of minors and young adults as mediators. The core of the game is a…

A simulation study is a useful tool in examining how validly item response theory (IRT) models can be applied in various settings. Typically, a large number of replications are required to obtain the desired precision. However, many standard software packages in IRT, such as MULTILOG and BILOG, are not well suited for a simulation study requiring…

The Central Limit Theorem is one of the most important concepts taught in an introductory statistics course, however, it may be the least understood by students. Sure, students can plug numbers into a formula and solve problems, but conceptually, do they really understand what the Central Limit Theorem is saying? This paper describes a simulation…

Modeling using mathematics and making inferences about mathematical situations are becoming more prevalent in most fields of study. Descriptive statistics cannot be used to generalize about a population or make predictions of what can occur. Instead, inference must be used. Simulation and sampling are essential in building a foundation for…

Engineers often need to predict how a part, mechanism or machine will perform in service, and this insight is typically achieved thorough computer simulations. Therefore, instruction in the creation and application of simulation models is essential for aspiring engineers. The purpose of this project was to develop a unified approach to teaching…

If the prospective students of probability lack a background in mathematical proofs, hands-on classroom activities may work well to help them to learn to analyze problems correctly. For example, students may physically roll a die twice to count and compare the frequency of the sequences. Tools such as graphing calculators or Microsoft Excel®…

This article is concerned with the question of whether the missing data mechanism routinely referred to as missing completely at random (MCAR) is statistically examinable via a test for lack of distributional differences between groups with observed and missing data, and related consequences. A discussion is initially provided, from a formal logic…

Many past educational validity studies of business gaming simulation, and more specifically total enterprise simulation, have been inconclusive. Studies have focused on the weaknesses of business gaming simulation; which is often regarded as an educational medium that has limitations regarding learning effectiveness. However, no attempts have been…

The use of Miller's Theorem in the determination of the high-frequency cutoff frequency of transistor amplifiers was recently challenged by a paper published in this TRANSACTIONS. Unfortunately, that paper provided no simulation or experimental results to bring credence to the challenge or to validate the alternate method of determination…

The authors describe a collection of dynamic interactive simulations for teaching and learning most of the important ideas and techniques of introductory statistics and probability. The modules cover such topics as randomness, simulations of probability experiments such as coin flipping, dice rolling and general binomial experiments, a simulation…

The present article deals with the problem of combined harvesting of a Michaelis-Menten-type ratio-dependent predator-prey system. The problem of determining the optimal harvest policy is solved by invoking Pontryagin's Maximum Principle. Dynamic optimization of the harvest policy is studied by taking the combined harvest effort as a dynamic…

While the potentials of virtual worlds to support experiential learning in medical education are well documented, assessment of student learning within these environments is relatively scarce and often incongruent. In this article, a conceptual framework is proposed for formatively assessing dispositional behaviours in scenario-based learning…

The interactive nature of computer simulation allows students to develop a deeper understanding of the laws of charged particle optics. Here, the use of commercially available optical design programs is described as a tool to aid in solving charged particle optics problems. We describe simple and practical demonstrations of basic electrostatic…

A k-dimensional integer point is called visible if the line segment joining the point and the origin contains no proper integer points. This note proposes an explicit formula that represents the number of visible points on the two-dimensional [1,N]x[1,N] integer domain. Simulations and theoretical work are presented. (Contains 5 figures and 2…