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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 (login required)(opens in new window)
Contact information
Semester 1
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: 31 January 2024
Eligibility and requirements
Prerequisites
All of
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 |
Or equivalent
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: 31 January 2024
Assessment
Description | Timing | Percentage |
---|---|---|
Up to 60 pages of assignments (three assignments worth 20% each, due early, mid and late in semester)
| Throughout the teaching period | 60% |
A written examination
| During the examination period | 40% |
Last updated: 31 January 2024
Dates & times
- Semester 1
Coordinator Diarmuid Crowley Mode of delivery On Campus (Parkville) Contact hours Total time commitment 170 hours Teaching period 26 February 2024 to 26 May 2024 Last self-enrol date 8 March 2024 Census date 3 April 2024 Last date to withdraw without fail 3 May 2024 Assessment period ends 21 June 2024 Semester 1 contact information
Time commitment details
170 hours
What do these dates mean
Visit this webpage to find out about these key dates, including how they impact on:
- Your tuition fees, academic transcript and statements.
- And for Commonwealth Supported students, your:
- Student Learning Entitlement. This applies to all students enrolled in a Commonwealth Supported Place (CSP).
Subjects withdrawn after the census date (including up to the ‘last day to withdraw without fail’) count toward the Student Learning Entitlement.
Last updated: 31 January 2024
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 Doctor of Philosophy - Engineering Course Ph.D.- Engineering Course Master of Philosophy - Engineering Course Master of Science (Mathematics and Statistics) 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.
- Available to Study Abroad and/or Study Exchange Students
This subject is available to students studying at the University from eligible overseas institutions on exchange and study abroad. Students are required to satisfy any listed requirements, such as pre- and co-requisites, for enrolment in the subject.
Last updated: 31 January 2024