Key facts
UNE unit code: PMTH331
*You are viewing the 2025 version of this unit which may be subject to change in future.
- Trimester 1 - On Campus
- Trimester 1 - Online
- Armidale Campus
- Yes
- No
- No
- 6
Unit information
Topology studies continuity in its broadest context, exploring the properties of curves and surfaces – the ways surfaces bend and how curves shape and twist in space. Impacting almost all other branches of mathematics, topology provides you with a foundation to solve problems in analysis, geometry, the physical sciences and computing.
This unit introduces you to the central concepts of topology: compactness, connectedness and separation. Using familiar concepts of continuity from calculus, you will first trace continuity through Euclidean space and metric space, bringing you to the notion of open sets and topological spaces, the setting for this unit.
You will examine applications to number theory, algebraic geometry, algebra, functional analysis, metric spaces and the notion of completeness. You will also learn how to apply topology to central proofs such as the Fundamental Theorem of Algebra, the Extreme Value Theorem and the Intermediate Value Theorem.
Offerings
For further information about UNE's teaching periods, please go to Principal Dates.
Teaching period | Mode/location |
---|---|
Trimester 1 | On Campus, Armidale Campus |
Trimester 1 | Online |
*Offering is subject to availability
Intensive schools
There are no intensive schools required for this unit.
Enrolment rules
Notes
This unit is essential for students wishing to continue to honours or postgraduate mathematics.
Please refer to the student handbook for current details on this unit.
Unit coordinator(s)
Learning outcomes
Upon completion of this unit, students will be able to:
- apply an understanding of continuity to materials learnt in earlier study;
- apply continuity arguments to problems in number theory, algebra and geometry;
- recognise and apply the concepts of compactness, connectedness and separation to a range of important problems in analysis, geometry and algebra;
- recognise and apply properties of, and techniques for, metric spaces to problems in analysis, geometry, physical sciences, computing and functional analysis; and
- apply advanced concepts and techniques from modern mathematics.
Assessment information
Assessments are subject to change up to 8 weeks prior to the start of the teaching period in which you are undertaking the unit.
Title | Must Complete | Weight | Offerings | Assessment Notes |
---|---|---|---|---|
Assessment 1 | Yes | 40% | All offerings | Five problem-based assignments. |
Final Examination | Yes | 60% | All offerings |
Learning resources
Textbooks are subject to change up to 8 weeks prior to the start of the teaching period in which you are undertaking the unit.
Note: Referenced material is held in the University Library — purchase is optional.
Introduction to Topology
ISBN: 9780486663524
Mendelson, B., Dover Publications 3rd ed. 2009
Text refers to: All offerings
Introduction to Topology and Modern Analysis
ISBN: 9781575242385
Simmons, G.F., McGraw-Hill
Text refers to: All offerings
Topology
ISBN: 9780387908922
Jänich, K., Springer 1984
Text refers to: All offerings
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