MST121 Using Mathematics

(from October 2006)

I started this course (or, the pre-course bumph) in October 2005. I managed to do the prep material with not too much bother, but I decided that I was not quite comfortable enough with it all and plumped for doing MU120 instead. I now intend to study MST121 in October 2006, hopefully then fully comfy with it all - and (big bonus!) fully conversant with my calculator!

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This broad introduction to the nature of mathematics and its uses in the modern world shows how mathematics can be used to investigate and answer questions from science, technology and everyday life. It uses a range of fundamental techniques, in particular recurrence relations, matrices and vectors, calculus and statistics. Use of computer software (Mathcad) is part of the course. The skills of communicating results and defining problems are also developed. This course and Exploring mathematics (MS221) will together give you a good foundation for higher-level mathematics and physics courses.

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This course offers an enjoyable way in to university-level mathematics – whether you intend to concentrate mainly on mathematics courses or to study other subject areas – provided that you are already familiar with some mathematical topics (see Entry below). It gives a broad introduction to the nature of mathematics and its uses in the modern world, showing how mathematics can be used to investigate and answer questions from science, technology and everyday life. To do this the course introduces a range of mathematical techniques, including: recurrence relations, matrices and vectors, calculus and statistics. It will equip you with the mathematical skills required for most science and technology courses.

The course introduces the use of computer software to help you in doing mathematics. This is an integral part of its approach, so you will need regular and convenient access to a suitable personal computer. The software greatly increases the speed and accuracy with which mathematical manipulations can be performed, and so enhances your ability to apply mathematical techniques to the investigation and solution of practical problems.

The course begins with Starting points, which features a first exploration of the main software package applied to some basic mathematical material. The rest of the course is in four sections.

Mathematics and modelling starts from situations in the World that can be modelled by mathematical techniques. The models use such mathematics as the properties and representations of arithmetic and geometric sequences, lines and circles, and functions such as x2, sin x, cos x and ex.

Discrete modelling deals with population models and their long-term behaviour, and introduces the arithmetic of matrices and vectors in order to examine the interdependence of different subpopulations. Vectors are also used to model problems involving various physical quantities, such as forces.

Continuous models covers calculus and introduces the process of differentiation. Derivatives are obtained for many functions, and these are used to model motion and to solve optimisation problems. Next we look at integration, first as the reverse of differentiation and then as the limit of an infinite sum. A list of standard integrals is obtained, and these are applied to solve simple differential equations, to find areas, and in other modelling contexts.

Modelling uncertainty is about probability and statistics. A chapter on chance invokes intuitive ideas of randomness and adds to your experience of thinking about probability through the use of purpose-designed software. This is followed by computer-aided exploration of sampling and sampling distributions and by an examination of regression.

The course also develops skills beyond mathematical technique, such as identifying and defining problems and communicating the results of your mathematical work – these are required for the effective application of mathematics to solve problems.

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