Foundations - 2019 entry

University level mathematics differs from that taught in schools not only in the difficulty of the topics and higher abstraction, but also in the style of teaching. This modules aims to ease the transition to university level mathematics by bridging the gap between mathematics taught prior to university level, and the material covered in the first year of our mathematics degree. While being in a university teaching and learning environment, you will revisit essential skills such as those in algebra, coordinate geometry, vectors, series and sequences, as well as some topics which are covered in Further Mathematics A-level such as complex numbers, matrix algebra, differential equations, and Maclaurin series. In this module, you will go over the theory and see many solved examples, as well as practice many examples to master these essential topics. Attending the lectures of this module is highly recommended to those students who do not have an A-level in Further Mathematics or equivalent, but those who do can also utilise these sessions to review the material and gain more practise experience.

This module aims to support the transition to year 1 undergraduate mathematics with elements of revision and self-study.

On successful completion of this module, you should be able to:

Module Specific Skills and Knowledge:
1 manipulate algebraic and numerical expressions accurately and with confidence;
2 compute with vectors, matrices and complex numbers;
3 perform accurate calculus manipulations using a variety of standard techniques;
4 sketch the graphs of a variety of functions of one variable;
5 recognise and solve equations involving logarithmic, exponential, trigonometric and hyperbolic functions;
6 find the general term of a sequence or series.
Discipline Specific Skills and Knowledge:
7 manipulate basic mathematical objects necessary in order to progress to successful studies in the mathematical sciences;
Personal and Key Transferable/ Employment Skills and  Knowledge:
8 formulate and solve problems and communicate reasoning and solutions effectively in writing;
9 use learning resources appropriately;
10 exhibit self management and time management skills.

Functions: logarithmic; exponential; trigonometric; hyperbolic.
Partial fractions; binomial theorem.
Basic vector arithmetic; coordinates in plane; basic matrix arithmetic.
Complex numbers: definitions & arithmetic; representations.
Differentiation & integration.
Graph sketching.
Sequences and series: sigma notation; recursion formula.
Polar coordinates.

This module is not formally assessed and is to support the transition to year 1 only.

Basic reading: Any A-level texts on mathematics and further mathematics

ELE: http://vle.exeter.ac.uk

Reading list for this module: