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Semester 2

Metric Spaces (MATH10101)

Subject

Mathematics

College

SCE

Credits

10

Normal Year Taken

3

Delivery Session Year

2023/2024

Pre-requisites

Course Summary

This course covers the basics of convergence and point set topology in the context of metric spaces.

Course Description

This course follows on from the Analysis part of FPM and Honours Analysis. In FPM we studied limits of sequences and limits of functions on the real line. We also learned about continuous functions and some of their properties such as the intermediate value property and having a maximum and a minimum on closed and bounded intervals. In Honours Analysis we extended the theory of limits to sequences of real functions and studied uniform convergence. In this course we extend these notions to the more general setting of metric spaces, i.e., sets equipped with a distance (metric). Many important spaces in Analysis have metrics. For example, the space of square integrable functions which is used in the study of Fourier series is equipped with the L² metric,and the Sobolev spaces that are used in PDEs are equipped with metrics that measure the size of derivatives. A very important class of metric spaces, namely Hilbert and Banach spaces, will be studied in Linear Analysis.

Assessment Information

Written Exam 80%, Coursework 20%, Practical Exam 0%

Additional Assessment Information

Exam: 80%, Coursework: 20%

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