Undergraduate Course: Metric Spaces (MATH10101)
Course Outline
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 
SCQF Credits  10 
ECTS Credits  5 
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 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)
Prerequisites 

Corequisites  
Prohibited Combinations  
Other requirements  None 
Information for Visiting Students
Prerequisites  None 
Course Delivery Information
Not being delivered 
Learning Outcomes
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.

Reading List
1. Victor Bryant, Metric Spaces: Iteration and Application.
2. Wilson Sutherland, Introduction To Metric And Topological Spaces. 
Additional Information
Graduate Attributes and Skills 
Not entered 
Keywords  Not entered 
Contacts
Course organiser  
Course secretary  Miss Sarah McDonald
Tel: (0131 6)506336
Email: sarah.a.mcdonald@ed.ac.uk 

