Keele University Mathematics Undergraduate Programmes 2020 2020 Entry | Page 16

16 | Mathematics
Year 4 Modules (MMath)
The availability of modules, and their content, may change from time to time subject
to student uptake, staff availability and timetabling restrictions.
Masters Project
This module gives MMath students
the opportunity to develop research
skills for studying and researching
mathematics. Students will develop
skills such as working in depth on a
problem over an extended period of
time, writing reports, and communicating
mathematical results to a range of
academic audiences. Students will also
produce a dissertation. The module will
provide employability skills targeted at
future academic work, but also relevant
for general graduate employment.
Algebraic Number Theory
Algebraic number theory can be
viewed as the application of the
techniques of abstract algebra to solve
problems in number theory, or as the
study of a special class of numbers
called algebraic numbers. The module
defines and studies certain groups, rings
and fields arising from number-theoretic
problems, and uses properties of these
objects to solve concrete problems
concerning Diophantine equations
such as Fermat’s Equation.
Combinatorial Designs
This module will show how traditional
areas of pure mathematics, such as
group theory, number theory, projective
geometry, and rings and fields, have
been applied to construct a variety
of combinatorial designs. It will also
look at applications of these designs
to the construction of error-correcting
codes, secret-sharing schemes, and
experimental designs.
keele.ac.uk/scm
Symmetric Differential
Equations
This module will show how dynamical
systems, in particular differential
equations, can benefit from the
mathematical clarity of abstract algebra.
This is an expanding field that helps to
explain how many disparate systems,
related only by their symmetry, can exhibit
strikingly similar behaviour. The module
also discusses the application of this field
to pattern-formation in physical systems.
Continuum Mechanics
Although every type of solid material
or fluid has a discrete structure at a
small enough length scale, many of
them can be idealised as a continuum
in certain circumstances. The discipline
of continuum mechanics arose from the
desire to treat such continua, not in an
ad hoc manner, but within the framework
of a unified set of principles. Continuum
mechanics is an expanding field, finding
applications wherever soft materials are
involved, for example in relation to bones,
arteries and electroelastic media.
Hydrodynamic
Stability Theory
A fluid is anything that flows,
like liquids and gasses, and this
module is concerned with the
stability of fluid flows. The module
will focus on understanding the basic
mechanisms that create instability in
flows (leading, for example, to turbulence
or aerodynamic drag), and on the
methods used to calculate the growth
rates and length scales of unstable
disturbances to flow. Applications
include climate and weather models,
fuel mixing in engines, and air-flow
around aircraft wings.
Linear Elasticity
This module covers topics such as
linear elasticity, strain, stress, and
wave propagation in elastic media.
The module derives the mathematical
theory of linear elasticity by development
of the governing equations of elastic
solid media, including the equilibrium
equations, geometrical relations between
strain and displacements, together with
the stress-strain constitutive relations.
The module will investigate some of
the applications of this theory.
Perturbation Methods
This module introduces students to
the asymptotic techniques which are
indispensable tools in dealing with
mathematical problems arising in the
real-world. These ‘raw’ problems very
rarely resemble simple models which
can be solved exactly. Fortunately, very
often the ‘raw’ problems have either large
or small parameters, or there is a way to
determine an approximate solution which
is sufficient for most practical purposes. 
The module will present an overview
of the main analytical perturbation
techniques based upon use of a small/
large parameter or small/large values
of a coordinate.