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Algebraic Topology (MAST90023)
Graduate courseworkPoints: 12.5On Campus (Parkville)
About this subject
- Overview
- Eligibility and requirements
- Assessment
- Dates and times
- Further information
- Timetable(opens in new window)
Contact information
Overview
Availability | Semester 1 |
---|---|
Fees | Look up fees |
This subject studies topological spaces and continuous maps between them. It demonstrates the power of topological methods in dealing with problems involving shape and position of objects and continuous mappings, and shows how topology can be applied to many areas, including geometry, analysis, group theory and physics. The aim is to reduce questions in topology to problems in algebra by introducing algebraic invariants associated to spaces and continuous maps. Important classes of spaces studied are manifolds (locally Euclidean spaces) and CW complexes (built by gluing together cells of various dimensions). Topics include: homotopy of maps and homotopy equivalence of spaces, homotopy groups of spaces, the fundamental group, covering spaces; homology theory, including singular homology theory, the axiomatic approach of Eilenberg and Steenrod, and cellular homology.
Intended learning outcomes
After completing this subject, students should gain:
- an understanding of the concepts of homotopy and homotopy equivalence of topological spaces;
- an understanding of the fundamental group, homology groups, and covering spaces;
- the ability to calculate fundamental groups and homology of spaces;
- the ability to solve problems involving topological spaces and continuous maps by converting them into problems in algebra;
- the ability to pursue further studies in this and related areas.
Generic skills
In addition to learning specific skills that will assist students in their future careers in science, they will have the opportunity to develop generic skills that will assist them in any future career path. These include:
- problem-solving skills: the ability to engage with unfamiliar problems and identify relevant solution strategies;
- analytical skills: the ability to construct and express logical arguments and to work in abstract or general terms to increase the clarity and efficiency of analysis;
- collaborative skills: the ability to work in a team;
- time-management skills: the ability to meet regular deadlines while balancing competing commitments.
Last updated: 3 November 2022
Eligibility and requirements
Prerequisites
Both of the following, or equivalent:
Code | Name | Teaching period | Credit Points |
---|---|---|---|
MAST30005 | Algebra | Semester 1 (On Campus - Parkville) |
12.5 |
MAST30026 | Metric and Hilbert Spaces | Semester 2 (On Campus - Parkville) |
12.5 |
Corequisites
None
Non-allowed subjects
None
Inherent requirements (core participation requirements)
The University of Melbourne is committed to providing students with reasonable adjustments to assessment and participation under the Disability Standards for Education (2005), and the Assessment and Results Policy (MPF1326). Students are expected to meet the core participation requirements for their course. These can be viewed under Entry and Participation Requirements for the course outlines in the Handbook.
Further details on how to seek academic adjustments can be found on the Student Equity and Disability Support website: http://services.unimelb.edu.au/student-equity/home
Last updated: 3 November 2022
Assessment
Additional details
Up to 60 pages of assignments (60%: three assignments worth 20% each, due early, mid and late in semester), a 2-hour written examination (40%, in the examination period).
Last updated: 3 November 2022
Dates & times
- Semester 1
Principal coordinator Diarmuid Crowley Mode of delivery On Campus (Parkville) Contact hours Total time commitment 170 hours Teaching period 26 February 2018 to 27 May 2018 Last self-enrol date 9 March 2018 Census date 31 March 2018 Last date to withdraw without fail 4 May 2018 Assessment period ends 22 June 2018
Time commitment details
170 hours
Last updated: 3 November 2022
Further information
- Texts
Prescribed texts
None
Recommended texts and other resources
A. Hatcher. Algebraic Topology, Cambridge University Press (2002), available online at http://www.math.cornell.edu/~hatcher/AT/ATpage.html.
W. S. Massey. A Basic Course in Algebraic Topology, Springer (1997).James Munkres, Elements of Algebraic Topology, Westview Press, 1st edition
- Related Handbook entries
This subject contributes to the following:
Type Name Course Master of Science (Mathematics and Statistics) Course Master of Philosophy - Engineering Course Doctor of Philosophy - Engineering Course Ph.D.- Engineering Informal specialisation Mathematics and Statistics - Available through the Community Access Program
About the Community Access Program (CAP)
This subject is available through the Community Access Program (also called Single Subject Studies) which allows you to enrol in single subjects offered by the University of Melbourne, without the commitment required to complete a whole degree.
Entry requirements including prerequisites may apply. Please refer to the CAP applications page for further information.
Last updated: 3 November 2022