Aims: The first aim is to show how the computer may be used, throughout all of mathematics, to enhance understanding. This will be achieved primarily through seven hours of computer-based contact sessions. Introductory examples of the use of computers in mathematics will be based on the familiar A-level maths. The second aim, approached through practical experience in the contact sessions, and through nine supporting lectures, is to introduce mathematical issues arising in the design and analysis of computational algorithms.
Objectives: The module will be taught using the Matlab-Maple software package. This choice will provide you with a uniform computing environment in which numeric and symbolic calculation can be performed. Through using this software tool you will be introduced to the rudiments of computer programming.
You will learn how to graph functions, study vectors and matrices graphically and numerically, how to iterate and use iteration to study sequences and series, how to solve algebraic and differential equations symbolically and numerically and how to study statistical properties of sets of numbers. In the lectures you will learn about various algorithmic paradigms and the study of computational cost.
DJ & NJ Higham, MATLAB guide, SIAM Publications, Philadelphia, September 2000.