Use of online video in a first year tertiary mathematics unit

The exploratory case study reported here used an action learning approach to examine the impact of online video on students studying a first year mathematics unit aimed at non-mathematics majors. After this intervention, the students completed a written questionnaire to determine their views on the impact of online video material on their understanding. Although most students were frequent users of online video only a proportion viewed the online video material. Two thirds of students who viewed the online video found it useful for visualising and understanding the practical applications of exponential function. The findings of this pilot study are encouraging and provide impetus to repeat the intervention, and develop online video material in other difficult areas of mathematics

Computational aspects of the optimal transit path problem

In this paper we present a novel method for short term forecast of time series based on Knot-Optimizing Spline Networks (KOSNETS). The time series is first approximated by a nonlinear recurrent system. The resulting recurrent system is then approximated by feedforward B-spline networks, yielding a nonlinear optimization problem. In this optimization problem, both the knot points and the coefficients of the B-splines are decision variables so that the solution to the problem has both optimal coefficients and partition points. To demonstrate the usefulness and accuracy of the method, numerical simulations and tests using various model and real time series are performed. The numerical simulation results are compared with those from a well-known regression method, MARS. The comparison shows that our method outperforms MARS for nonlinear problems

Use of online video in the teaching of exponential functions

Graduates with high level mathematical skills are a commodity that Australia needs more of. However the number of high school students taking a level of mathematics sufficient for their university studies is on the decline. This lack of relevant mathematical preparation makes the teaching of these students in their first year mathematics units challenging. Visualisation is an important tool in mathematical problem solving. The use of online videos (eg, YouTube) to illustrate applications of mathematical concepts can help to enhance a student’s engagement and ultimately their conceptual understanding. Conducted at a large Australian university with students enrolled in a first year service teaching mathematics unit taught in a traditional lecture and tutorial format, online videos were introduced to enhance students’ understanding of exponential function. The videos present the concepts in real world contexts in a visual way that is relevant and thus provides a starting point for engaging students in mathematical thinking. Online video was augmented with specific exercises in the same context as the videos. The outcomes of this intervention will be discussed

Minimum Risk Path Planning for Submarines through a Sensor Field

One of the basic necessities in combat operations is the planning of paths for the traversal ofmilitary hardware and vehicles through adversarial environments. Typically, while still meetingmission objectives, the vehicle is required to arrive at a pre-described target while minimizingits risk exposure to enemy defence systems. As well as the technological constraints of thevehicle, such as fuel capacity, additional restrictions that can be imposed on the path includelimits on travelling time and route length. We specifically look at the problem of determining anoptimal submarine transit path for a submarine through a field of sonar sensors, subject to a totaltime and final position constraint. The path should be designed so as to minimize the overallprobability of detection. The strategy we propose involves a two stage approach. The first stageinvolves a discretized approximation of the problem by first constructing a grid like networkover the region. Possible paths are then restricted to the movement between the knots points (i.e.nodes) of this grid. In other words, the approximate problems involve finding the most costeffective paths through a network, subject to a total time constraint. What we have therefore is aConstrained Shortest Path Problem (CSPP). To solve the resulting CSPP we develop anefficient network heuristic method that uses a parameterization of the edge weights of thenetwork and the application of Dijkstra’s Algorithm. The second stage involves thedevelopment of an optimal control model, by introducing a very simple dynamical model for thevessel’s movements, and a solution procedure that utilizes the solution obtained in the first stageas a starting point. The optimal control model for our submarine transit path problem is in fact adiscrete valued control problem where the precise times between speed and heading switchesneed to be determined. We show that this optimal control problem can be readily solved withthe use of a technique known as the Control Parameterization Enhancing Transform (CPET),which, via a simple transformation, puts the problem into readily solvable standard canonicalform by standard optimal control software. Various aspects of our proposed method arediscussed. These include, among other things, the effects of different degrees of coarseness ofdiscretization used in the problem. A solution of the CSPP will only provide a good initial pointfor the optimal control problem if a sufficiently refined network grid model is used. We alsoshow how the subsequent number of switching points used within the optimal control phase canmake a significant difference on the final solution obtained. Computational results are presented supporting the use of our methodology

Modification of pentobarbital effects by natural and synthetic polypeptides: Dissociation of brain and pituirary effects

Thyrotropin releasing hormone (TRH) antagonizes pentobarbital sedation and hypothermia; somatotropin release inhibiting factor amplifies them. Other hypothalamic polypeptide releasing factors, Substance P and a variety of amino acids are ineffective. Three congeners of TRH antagonize pentobarbital; one amplifies it. The potencies of congeners as pentobarbital antagonists are unrelated to their potencies as pituitary thyrotropin releasers