Problems originating from different sources often take on a similar mathematical form. So, for example, the map-colouring problem and the problem of drawing up a lecture time-table that minimizes the number of classrooms needed have similarities that suggest their solution might be found using methods from the same branch of mathematics viz Combinatorics. Similarly, the Meat Board problem and the design of a stable steering mechanism in a car both involve the use of Control Theory for their solution. It is the task of the Applied Mathematician, in this second stage of problem solving to identify the branch of mathematics in which this problem falls and then to select and use the appropriate techniques from this branch for the solution of the mathematical problem.
In the third stage the results from solving the mathematical problem must be interpreted in terms of the original real-world problem. Often the interpretation is unsatisfactory and it is necessary to reconsider the model. Eventually valid conclusions may be drawn regarding solutions of the original problem.
Historically, Mathematics arises out of a human need to develop general techniques for solving practical problems. For this reason, high-school pupils are exposed largely to the kind of mathematics that lends itself to application in physics, elementary statistics, biology, engineering, computer science and other disciplines
Over the last 300 years, however, it has become clear that mathematics is an important subject in its own right, and not just a slave to other disciplines. Scientists have become aware that in order to develop powerful problem-solving tools, one needs quite abstract mathematics; a body of pure mathematics is required which can be studied independently of physics, biology and other user-disciplines.
Pure and Applied Mathematics are therefore offered as different subjects, although there is much interdependence between them and each serves as an inspiration to the other.
Our first year Mathematics modules (Math 110/120) attempt to bridge the gap between maths for use in other subjects and maths as a discipline in its own right. Applicable topics such as calculus, linear algebra and introductory combinatorics are taught, but as the course progresses, there is a gradual increase in the rigour with which these topics are treated, thereby ensuring that the students have exposure both to the activities of the pure mathematician and to the techniques required by the applied mathematician and other scientists.
second year level, the student is in a reasonable position to select
either pure or applied mathematical courses for specialization or as
a background to other major subjects.