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DRPS : Course Catalogue : School of Mathematics : Mathematics

Undergraduate Course: Metric Spaces (MATH10101)

Course Outline
SchoolSchool of Mathematics CollegeCollege of Science and Engineering
Credit level (Normal year taken)SCQF Level 10 (Year 3 Undergraduate) AvailabilityAvailable to all students
SCQF Credits10 ECTS Credits5
SummaryThis 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.

**Please note that this course will be a required pre-requisite from 2022/23 for the following courses: MATH10051 Fourier Analysis, MATH10076 General Topology, MATH10024 Probability, Measure & Finance, MATH11135 Functional Analysis and MATH11136 Real Analysis**

**Please note that this course will be recommended from 2022/23 for the following courses: MATH10100 Introduction to Partial Differential Equations, MATH10082 Linear Analysis and MATH11137 Nonlinear Schrodinger Equations**
Entry Requirements (not applicable to Visiting Students)
Pre-requisites Students MUST have passed: Honours Analysis (MATH10068)
Prohibited Combinations Other requirements None
Information for Visiting Students
High Demand Course? Yes
Course Delivery Information
Academic year 2021/22, Available to all students (SV1) Quota:  None
Course Start Semester 2
Timetable Timetable
Learning and Teaching activities (Further Info) Total Hours: 100 ( Lecture Hours 22, Seminar/Tutorial Hours 5, Summative Assessment Hours 2, Programme Level Learning and Teaching Hours 2, Directed Learning and Independent Learning Hours 69 )
Assessment (Further Info) Written Exam 70 %, Coursework 30 %, Practical Exam 0 %
Additional Information (Assessment) Exam: 70%, Coursework: 30%
Feedback Not entered
Exam Information
Exam Diet Paper Name Hours & Minutes
Main Exam Diet S2 (April/May)MATH10101 Metric Spaces2:00
Learning Outcomes
On completion of this course, the student will be able to:
  1. Demonstrate an understanding of metric spaces by proving unseen results using the methods of the course.
  2. Correctly state the main definitions and theorems in the course.
  3. Produce examples and counterexamples illustrating the mathematical concepts presented in the course.
  4. 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
Course organiserDr Nikolaos Bournaveas
Tel: (0131 6)50 5063
Course secretaryMiss Greta Mazelyte
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