Keele University Mathematics Undergraduate Programmes 2020 2020 Entry | Page 11

Undergraduate Programmes 2020 | 11
Degree Content
This section gives a brief indication of the content of each of the modules listed earlier.
Year 1 Modules
Calculus Algebra
The first half of this module forms a
bridge between A-level and degree level
mathematics. Many of the topics covered
will be familiar, but the emphasis will
be different, focusing on understanding
and tackling some of the more technical
issues necessarily left unresolved at
A-level. Starting with a brief look at the
real number system, the module then
examines real-valued functions and, in
particular, the trigonometric, exponential
and logarithmic functions. Moving on to
the notion of a ‘limit’, the module then
discusses infinite series, differentiation
and integration in a rather more careful
and precise way than at A-level. The aim of the first part of this module is
to introduce students to the fundamental
mathematical concepts of logic, numbers,
and sets in a setting that will be unfamiliar
in its level of abstraction, but that will
provide an essential grounding for later
modules. Progressing to functions,
complex numbers, and divisibility in
the set of integers, this module also
introduces students to the Fundamental
Theorem of Arithmetic.
The second half builds on these
foundations, and is largely technique
based, with much of the material being
essential for second and third year
applied and methods modules. Topics
studied will include ordinary differential
equations, the theory and application
of Taylor series, and functions of two
variables, including partial differentiation
and double integration techniques.
The second part of the module
concentrates on an introduction to linear
algebra. Topics studied are systems
of linear equations, matrices and their
algebra, determinants, vectors in 2-, 3-,
and n- dimensional Euclidean space and
a brief introduction to some of the basic
concepts of general vector spaces.
The emphasis throughout is on rigorous
proof, precise derivation of results, and
drawing together apparently disparate
areas of mathematics.
Investigations and
Problem Solving
This module is designed to aid the
transition from A-level Mathematics to
degree-level mathematics. At A-level,
students are presented with highly
structured questions, having been
taught the specific processes required
to solve them. In this module students
will be presented with unfamiliar and
less structured problems which may be
open to several different approaches.
The module enhances students’
employability skills through teamwork on
extended projects, presentations, and the
opportunity to reflect and articulate their
strengths and weaknesses.
Applied Mathematics
This module is designed to help students
appreciate mathematics as a method
for describing and solving real-world
problems. We introduce the mathematical
modelling cycle that provides a
conceptual model to study real-world
problems. Students will develop
mathematical and problem solving
ideas through a number of short
exercises and a project.
Mathematical Methods
This module extends a range of
mathematical skills and techniques from
A-Level and applies them in more difficult,
unstructured problems. Students develop
skills in reading and comprehending
mathematical arguments and develop
an awareness of the relevance of
Mathematics to other fields of study.
keele.ac.uk/scm