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MATH30090

Academic Year 2024/2025

Metric Spaces (MATH30090)

Subject:
Mathematics
College:
Science
School:
Mathematics & Statistics
Level:
3 (Degree)
Credits:
5
Module Coordinator:
Dr Hermann Render
Trimester:
Autumn
Mode of Delivery:
On Campus
Internship Module:
No
How will I be graded?
Letter grades

Curricular information is subject to change.

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.

About this Module

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 diameter of a set; the boundary, closure and interior of sets; balls; open and closed sets; density; the topology of a metric space; convergence of sequences; continuity of functions; Cauchy sequences; completeness and a selection of additional topics that will be covered in the course (for example, isolated points and accumulation points, fixed point theorems, compactness, connectedness).

Student Effort Hours:
Student Effort Type Hours
Specified Learning Activities

44

Autonomous Student Learning

41

Lectures

18

Practical

11

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 Component Scale Must Pass Component % of Final Grade In Module Component Repeat Offered
Exam (In-person): Two hour exam in exam centre End of trimester
Duration:
2 hr(s)
Standard conversion grade scale 40% No
70
No
Exam (In-person): Midterm exam Week 7 Standard conversion grade scale 40% No
30
No

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
Andrew Mullins 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
Autumn Tutorial Offering 1 Week(s) - Autumn: All Weeks Mon 16:00 - 16:50
Autumn Lecture Offering 1 Week(s) - Autumn: All Weeks Wed 14:00 - 14:50