# MATH30090 Metric Spaces

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.

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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 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
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.

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

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

30

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

70

No

Carry forward of passed components
No

Resit In Terminal Exam
Spring Yes - 2 Hour