MATH30090 Metric Spaces

Academic Year 2021/2022

This module is an introduction to the theory of metric spaces: sets equipped with a metric, which measures the distance between two elements of the set. Metric spaces are of fundamental importance in many areas of mathematics, including analysis and topology.

Show/hide contentOpenClose All

Curricular information is subject to change

Learning Outcomes:

The student should learn how to recognize, manipulate and apply the foundational concepts of metric analysis: metric spaces and metrics; isometries; the distance between points and sets; the boundary, closure and interior of sets; open and closed sets and balls; the topology of a metric space, convergence of sequences and continuity of functions; Cauchy sequences; compactness, completeness, fixed point theorems and a selection of additional topics as covered in the course (for example, normed vector spaces, isolated points and accumulation points, the diameter of a set, connectedness).

Student Effort Hours: 
Student Effort Type Hours
Lectures

18

Practical

11

Specified Learning Activities

44

Autonomous Student Learning

41

Total

114

Approaches to Teaching and Learning:
Lectures, tutorials, enquiry and problem-based learning. 
Requirements, Exclusions and Recommendations
Learning Requirements:

The student is required to have attained the learning outcomes of a module in elementary real analysis such as MATH10320, which includes the rigorous definitions of the convergence of a sequence of real numbers and the continuity of a function on the real numbers.

All questions about eligibility should be addressed to the module coordinator.


Module Requisites and Incompatibles
Pre-requisite:
MATH10320 - Mathematical Analysis


 
Assessment Strategy  
Description Timing Open Book Exam Component Scale Must Pass Component % of Final Grade
Continuous Assessment: In-trimester assignments Unspecified n/a Standard conversion grade scale 40% No

20

Examination: Written examination 2 hour End of Trimester Exam No Standard conversion grade scale 40% No

80


Carry forward of passed components
No
 
Resit In Terminal Exam
Spring Yes - 2 Hour
Please see Student Jargon Buster for more information about remediation types and timing. 
Feedback Strategy/Strategies

• Group/class feedback, post-assessment

How will my Feedback be Delivered?

Not yet recorded.

Name Role
Dr Myrto Manolaki Lecturer / Co-Lecturer
Konstantinos Maronikolakis Tutor
Timetabling information is displayed only for guidance purposes, relates to the current Academic Year only and is subject to change.
 
Autumn
     
Lecture Offering 1 Week(s) - Autumn: All Weeks Mon 12:00 - 12:50
Tutorial Offering 1 Week(s) - Autumn: All Weeks Mon 16:00 - 16:50
Lecture Offering 1 Week(s) - Autumn: All Weeks Wed 14:00 - 14:50
Autumn