Algebraic Topology (MAST90023)

Graduate courseworkPoints: 12.5Not available in 2025

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Overview

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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: 4 March 2025

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: 4 March 2025

Assessment

DescriptionTimingPercentage

Up to 60 pages of assignments (three assignments worth 20% each, due early, mid and late in semester)

  • 60 pages
Throughout the teaching period60%

A written examination

  • 2 hours
During the examination period40%

Last updated: 4 March 2025

Dates & times

Not available in 2025

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: 4 March 2025

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:

    TypeName
    CoursePh.D.- Engineering
    CourseDoctor of Philosophy - Engineering
    CourseMaster of Philosophy - Engineering
    CourseMaster of Science (Mathematics and Statistics)
    Informal specialisationMathematics 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.

    Please note Single Subject Studies via Community Access Program is not available to student visa holders or applicants

    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: 4 March 2025