Mathematical Modeling Course Research Articles

An examination for mathematical modelling

First year mathematics degree students at Leicester Polytechnic attend a course in mathematical modelling. The aim is to introduce the students to mathematical modelling concepts and to model development. Work is set and marked during the course and this forms a vital part of the students' assessment. In addition to this, however, the students are assessed by means of a three hour examination at the end of the year. This examination is significantly different from the normal ‘five out of eight’ type. The philosophy and organization of the examination are discussed in this paper. An example of a particular examination, that for June 1986, is included as an appendix to illustrate the points made in the discussion.

Variations of Trypia's model for production planning

In a recent issue of this journal, Trypia presented a mixed‐integer programming model to plan production of a line of products in several departments of a firm. Strict capacity restrictions were imposed on each production facility. This paper presents three variations of Trypia's model suitable for discussion in production management and mathematical modelling courses. First, it presents the uncapacitated version of Trypia's problem, mainly to highlight an interesting and useful structural property in the model. Next, a more realistic version of Trypia's problem, in which alternative short‐term capacity expansion strategies, such as overtime, extra shifts and sub‐contracting are available to management, is presented. Finally, the multi‐period version of Trypia's problem is discussed.

Book Reviews

Giordano, Frank R. and Weir, Maurice D. 1985, A First Course in Mathematical Modeling, Brooks-Cole Publishing Division of Wadsworth, Belmont, California, 382 pp., $35.25—reviewed by Nancy V. Phillips McLeod, Raymond, Jr. 1985, Decision Support Software for the IBM Personal Computer, Science Research Associates, Chicago, Illinois, 60680, 224 pp., $16.00—reviewed by Paul Gray

The role of a ‘micro’ in a mathematical modelling course

The authors have been involved in teaching a course in mathematical modelling for a number of years. With the growth of readily available microcomputers with improving graphic facilities, the potential for use within the modelling process is increasing enormously. The paper will comment on the developing role of the micro within a modelling course, specifically its use in the areas of demonstration, realization and investigation of performance.

A role for mathematical modelling†

† This paper was based primarily on the material contained in two previous papers by the author, details of which are: (a) James, D. J. G., How should the mathematical training of an engineering undergraduate be conducted?‐‐presented at the European Seminar on the Mathematical Education of Engineers‐‐Developments and Innovation; University of Kassel, March 1984, published in the seminar proceedings contained in this journal issue; and (b) James, D. J. G., and Wilson, M. A., The Role of a ‘Micro’ in a Mathematical Modelling Course, Presented at Conference on Micros in Education, Loughborough University of Technology, April 1984, to be published in a later issue of this journal.

Applying Mathematics: A Course in Mathematical Modelling (D. N. Burghes, I. Huntley and J. McDonald)

Applying Mathematics: A Course in Mathematical Modelling (D. N. Burghes, I. Huntley and J. McDonald)

How Should Mathematical Modelling and Computer Technology Influence Mathematics Degree Courses?

How Should Mathematical Modelling and Computer Technology Influence Mathematics Degree Courses?

Developing an undergraduate mathematical modelling course

The development of an undergraduate mathematical modelling course currently in its fifth iteration at the United States Military Academy is described. The principal purpose of the course designed for sophomores is to provide students the opportunity to practice model construction in an artistic fashion while demonstrating the utility and universality of elementary mathematics. The resolution of issues such as the determination of course prerequisites, choice of model construction or model selection, number and type of student projects, choice of disciplines in which to model, instructor preparation, text selection and development of supporting textual materials is discussed. After a detailed description of the course, the authors discuss lessons learned and evaluate the course.

Student problems with a modelling exercise

In this paper an attempt is made to outline some of the problems facing the student who undertakes a course in mathematical modelling. A case study, considered by several cohorts of students, is used as a medium for introducing the various types of obstacles the students encounter. This approach also results in a demonstration of some of the errors that can be made in operating a modelling course and the paper concludes by offering suggestions on how to overcome certain difficulties that are exposed.

Teaching mathematical modeling— reflections and advice

In this article the authors describe their course in mathematical modelling, and give a list of major do's and don'ts. They stress the difference between models and modelling and show how modelling examples can be introduced into existing undergraduate courses.

Introducing mathematical modelling to undergraduates

Some motivation for, and thoughts behind, the development of a course in mathematical modelling are described. The structure of the course and some of the problems of teaching and assessment are reviewed. The course has the characteristics that it is introductory and discipline‐independent.