Undergraduate Course: Metric Spaces (MATH10101)
|School||School of Mathematics
||College||College of Science and Engineering
|Credit level (Normal year taken)||SCQF Level 10 (Year 3 Undergraduate)
||Availability||Available to all students
|Summary||This course covers the basics of convergence and point set topology in the context of metric spaces.
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 Lē 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.
Entry Requirements (not applicable to Visiting Students)
||Other requirements|| None
Information for Visiting Students
Course Delivery Information
|Not being delivered|
On completion of this course, the student will be able to:
- Demonstrate an understanding of metric spaces by proving unseen results using the methods of the course.
- Correctly state the main definitions and theorems in the course.
- Produce examples and counterexamples illustrating the mathematical concepts presented in the course.
- Explain their reasoning about rigorous Analysis clearly and precisely, using appropriate technical language.
|1. Victor Bryant, Metric Spaces: Iteration and Application.|
2. Wilson Sutherland, Introduction To Metric And Topological Spaces.
|Graduate Attributes and Skills
||Course secretary||Miss Sarah McDonald
Tel: (0131 6)506336