Key facts

UNE unit code: PMTH331

*You are viewing the 2024 version of this unit which may be subject to change in future.

Start
  • Trimester 1 - On Campus
  • Trimester 1 - Online
Campus
  • Armidale Campus
24/7 online support
  • Yes
Intensive schools
  • No
Supervised exam
  • No
Credit points
  • 6

Unit information

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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 1On Campus, Armidale Campus
Trimester 1Online

*Offering is subject to availability

Intensive schools

There are no intensive schools required for this unit.

Enrolment rules

Pre-requisites
PMTH212 and PMTH213 or candidature in a postgraduate award
Restrictions
PMTH431
Combined units

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)

David Robertson

Learning outcomes

Upon completion of this unit, students will be able to:

  1. apply an understanding of continuity to materials learnt in earlier study;
  2. apply continuity arguments to problems in number theory, algebra and geometry;
  3. recognise and apply the concepts of compactness, connectedness and separation to a range of important problems in analysis, geometry and algebra;
  4. recognise and apply properties of, and techniques for, metric spaces to problems in analysis, geometry, physical sciences, computing and functional analysis; and
  5. 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.

TitleMust CompleteWeightOfferingsAssessment Notes
Assessment 1Yes40%All offerings

Five problem-based assignments.

Final ExaminationYes60%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.

Topology

ISBN: 9780387908922

Jänich, K., Springer 1984

Note: Available from Dixson Library, UNE

Text refers to: All offerings

Introduction to Topology and Modern Analysis

ISBN: 9781575242385

Simmons, G.F., McGraw-Hill

Note: Older editions are available from Dixson Library and are also aceptable for use (Hardcover ISBN: 9781575242385, Paperback ISBN: 9780070597846).

Text refers to: All offerings

Introduction to Topology

ISBN: 9780486663524

Mendelson, B., Dover Publications 3rd ed. 2009

Note: Available from the Dixson Library, UNE.

Text refers to: All offerings

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