Mathematics is one of the oldest and most universal means of creating, communicating, connecting and applying structural and quantitative ideas. The discipline of Mathematics allows the formulation and solution of real-world problems as well as the creation of new mathematical ideas, both as an intellectual end in itself, but also as a means to increase the success and generality of mathematical applications. This success can be measured by the quantum leap that occurs in the progress made in other traditional disciplines, once mathematics is introduced to describe and analyses the problems studied.
It is therefore essential that as many persons as possible be taught not only to be able to use mathematics, but also to understand it.
Students doing this syllabus will have been already exposed to Mathematics in some form mainly through courses that emphasise skills in using mathematics as a tool, rather than giving insight into the underlying concepts. To enable students to gain access to mathematics training at the tertiary level, to equip them with the ability to expand their mathematical knowledge and to make proper use of it, it is, therefore, necessary that a mathematics course at this level should not only provide them with more advanced mathematical ideas, skills and techniques, but encourage them to understand the concepts involved, why and how they “work” and how they are interconnected. It is also to be hoped that, in this way, students will lose the fear associated with having to learn a multiplicity of seemingly unconnected facts, procedures and formulae. In addition, the course should show that that mathematical concepts lend themselves to generalisations, and that there is enormous scope for applications to the solving of real problems.
Mathematics covers extremely wide areas. However, students can gain more from a study of carefully selected, representative areas of Mathematics, for a “mathematical” understanding of these areas, rather than to provide them with only a superficial overview of a much wider field. While proper exposure to a mathematical topic does not immediately make students into experts in it, that proper exposure will certainly give the students the kind of attitude which will allow them to become experts in other mathematical areas to which they have not been previously exposed. The course is, therefore, intended to provide quality in selected areas, rather than a large area of topics.
To optimise the competing claims of spread of syllabus and the depth of treatment intended, all items in the proposed syllabus are required to achieve the aims of the course. None of the Modules of the two Units making up the whole course will, therefore, be optimal. However, Unit 1, representing the basics of the syllabus, is assessed separately, can stand on its own, can be combined with other Units, such as Statistical Analysis, and can be separately certified. Unit 2, which will also be separately assessed and certified, will also be accessible on its own by students who have already adequately covered the material contained in Unit 1.
While there will be a great deal of attention to the application of mathematics to solving problems arising in other areas, including mechanics and statistics, it is not the intention to develop a general account of these subjects; there is, therefore, no section on statistics or mechanics; these are expected to be specifically addressed in other courses.
Through a development of understanding of these areas, it is expected that the course will enable students to:
- Develop mathematical thinking, understanding and creativity;
- Develop skills in using mathematics as a tool for other disciplines;
- Develop the ability to communicate through the use of mathematics;
- Develop the ability to use mathematics to model and solve real world problems;
- Gain access to mathematics programmes at tertiary institutions.