Aims

To introduce the programming language Python and its application to mathematical problems. To promote familiarity with the environment for standard mathematical operations, and to work towards the ideas of coding user-defined functions and scripts, and further towards programming aimed at solving more substantial problems.

To promote independent thinking and critical appraisal by linking the computational experience to the tackling of unfamiliar problems that have not been directly demonstrated to them and which can be formulated mathematically.

Module summary

Computing methods are of great use in a wide range of applications of pure and applied mathematics, as well as statistics. This module will introduce and develop familiarity with mathematical computing, relate this to problem solving techniques based on independent thinking, and develop the ability to apply such methods independently, towards specific goals in mathematical study and applications.

Outline Of Syllabus

Use of Python for mathematical computing. Getting started, input and output, data types, plotting and simple calculations, control statements, functions, classes. An introduction to numerical methods.

Individual problems based on existing mathematical knowledge (such as calculus, sequences and series, single value functions, curve sketching and simple numerical analysis, linear algebra, matrix manipulations, permutations and combinations).

Mathematical problems and puzzles from logic, number theory, geometry, algebra, strategy.

Teaching Rationale And Relationship

Lectures are used for the delivery of theory and explanation of methods, illustrated with examples, and for giving general feedback on marked work. Material will be available to tackle asynchronously following each lecture, with a practical which gives a chance for individual support.

Assessment Rationale And Relationship

The course assessments allow the students to develop their problem solving techniques, to practise the methods learnt in the module, to assess their progress and to receive feedback; these assessments have a secondary formative purpose as well as their primary summative purpose.