MATHEMATICS AT BRISTOL - University of Bristol

Linear Algebra
In Level 1 students meet real vector spaces, matrices
with real entries, and techniques for their manipulation.
This unit is, by comparison, more general and
so more abstract, investigating vector spaces, linear
transformations and matrices over an arbitrary field,
and bilinear and quadratic "forms" over the real or
complex numbers. The unit is "pure" in the sense that
the emphasis is on insight rather than techniques, this
insight being attained through careful use of definitions
of the key concepts, and the formulation and proof
of the key results.
Applied Partial Differential Equations
The unit starts by extending elementary calculus to the
calculus of several variables. It develops the subject to
the point where the major theorems can be given: the
divergence theorem, and Green’s and Stokes’ theorems.
This material is fundamental to physical applied
mathematics, and it is also relevant to the second part
of the unit.
The second part of the unit studies some of the
classical equations of applied mathematics (Laplace’s
and Poisson’s equations and the diffusion equation).
Methods for the solution of these equations are
presented. The idea of conservation of a physical
quantity is explored and used to develop a model of
traffic flow. Solutions of the governing partial
differential equations illustrate the method of
characteristic curves and the formation of shocks.
Ordinary Differential Equations
Differential equations are a natural expression of the
laws governing a wide variety of systems that evolve
with time: systems of animal populations, of chemical
reactants, mechanical systems, and many others. This
unit gives a wide variety of analytical techniques for
understanding their behaviour and finding solutions
(numerical techniques are excluded – they are dealt
with in the unit Numerical Analysis). The unit contains
both theory and techniques, but the emphasis is on
theoretical developments which lead to useful methods
for solving the equations. Methods for both linear and
nonlinear ordinary differential equations are presented.
Numerical Analysis
This unit is intended to serve as a first course in
numerical analysis. As such, the fundamental concepts
of recursion, interpolation, projection, expansion and
discretisation are presented and explored. Some of the
applications considered are root finding, numerical
integration, parameter estimation and the numerical
solution of differential equations. The material is
organised in such a way as to expose key concepts.
At the same time, the presentational style is informal
and makes extensive use of illustrative examples.
Mathematics at Bristol
University mathematics is continually developing. It is a subject of
immense scope and application, and the language of science, engineering
and commerce. As a consequence, a mathematics degree opens up a wide
variety of career choices and exciting challenges.
A department passionate in terms of teaching
At Bristol you will be taught by world leaders in their fields of research.
Students receive the highest quality of mathematical education and
training for jobs in industry, commerce and education. Rated overall in the
top two or three in the country in the 2001 Research Assessment
Exercise, we are one of the very strongest Mathematics departments in
Europe in terms of research. Our graduates can look forward to a wide
range of excellent career prospects in research, the financial sector,
computing, industry, the professions and government.
Mathematics at university differs in a number of ways from the traditional
A-level syllabuses. First-year students are often surprised by the sheer
scope and opportunities that lie ahead. For this reason it is a good idea
to sample as wide a range of university mathematics as possible during
your first year. Only in this way will you be able to make informed and
sensible decisions about the subjects you would like to study in later
years. If you wish to study subjects other than mathematics (and there
is no compulsion for you to do so at Bristol) then the same applies.
A flexible course structure
We offer a wide range of three and four-year undergraduate programmes.
Students wanting to do a four-year degree have the choice of an M.Sci. or
a degree including study for one year in Continental Europe. These
programmes are designed to reflect the diverse roles degree study plays
in preparing graduates for careers in fields where specific and/or broadly
based advanced mathematical knowledge and techniques are essential.
Our programme structure enables free movement at the end of the first
year between most Single Honours programmes, and from most Joint
Honours to Single Honours.
26
3