MTH6126,
Metric Spaces, 2013-2014
Welcome
to MTH6126 Metric Spaces! I will
be giving the Metric Spaces module in its current format for the second time this year. Metric spaces generalizes the idea of distance in Euclidean spaces - the
line R, the
plane R2,
and the n-dimensional
real space Rn -
to more general sets including sets of functions. We call these structures metric spaces, and their properties, when further
generalized, give rise to the
elements of topological spaces and the discipline of Topology. This is a major area of pure
mathematics, of which geometry is
a part.
I
will be making typeset notes available every 2 weeks. The typeset notes will
contain no diagrams.
T: 0207
5442 5464
W: www.maths.qmul.ac.uk/~arrow
LECTURE/TUTORIAL
TIMES and LOCATIONS, OFFICE HOURS
are avialble on the UG
website.
·
MTH6126 Course
Description
·
MTH6126 (TeX
background lecture notes by Mark Jerrum in 2010)
·
A good text which covers the course material - W.A. Sutherland
Introduction
to Metric and Topological Spaces, Oxford Science Publications (1975).
At the end of this
module, students should be able to:
·
define
metric space and associated properties, and recognise
these properties in specific examples;
·
interpret
concepts from analysis of a single real variable (convergence, uniform
continuity) in the context of metric spaces;
·
define open
and closed sets, and know how they relate to continuity, etc.;
·
define
important concepts such as compactness and completeness, recognise
them in concrete examples, and use them to derive conclusions.
Final
exams and solutions to them for the period 2009-2012 have links below.
Assuming no change from previous years, the rubric of the final examination is that there are two parts.
In the first part of the examination, there are four questions, each worth 10 marks, and you must answer all of them.
In the second part of the examination, there are three questions,
each worth 30 marks, and you should answer at least two of them. The best two
of your answers to this part will count towards your final mark, except in case
that you need the answers to all three questions to get a bare pass.
· Introduction
to Metric and Topological Spaces, W.A. Sutherland, Oxford Science Publications.