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University of Wales, Bangor - Department of Mathematics
Mathematics Year 2 Modules |
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Lecturer Prof Tim Porter
Recommended book:
Pre-requisites IAN1012, IMM2001,
Syllabus
Convergence
Revision of material from Mathematical Analysis 1.
Convergence of sequences and series. Contiuity of functions.
Uniform continuity introduced. Continuity of functions of 2 variables.
Sequences and series of functions
Uniform convergence.
Linear spaces of sequences
Linear spaces of functions. Norms, completeness and convergence.
Brief discussion of applications.
(Lebesgue integration would be mentioned here but not treated in any detail.)
Metric spaces
Introduction to metric spaces.
Examples - normed linear spaces, subsets of R^n,
introduction to convergence and continuity in metric spaces.
Brief excursion into topology.
Open and closed sets, introduction to the notion of compactness,
link with uniform continuity. Spaces of subsets.
Examples leading to Hausdorff metric and discussion of fractals.
Assessment
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