Differential Topology (MAST90029)
Graduate courseworkPoints: 12.5On Campus (Parkville)
Overview
| Availability | Semester 1 |
|---|---|
| Fees | Look up fees |
This subject extends the methods of calculus and linear algebra to study the topology of higher dimensional spaces. The ideas introduced are of great importance throughout mathematics, physics and engineering. This subject will cover basic material on the differential topology of manifolds. Topics include: smooth manifolds, tangent spaces, inverse and implicit function theorems; differential forms, integration on manifolds and de Rham cohomology; submersions and fibre bundles; immersions and transversality; examples coming from Lie groups and homogeneous spaces. Additional topics may include: Morse theory; intersection theory; characteristic classes and Chern-Weil theory; the Thom isomorphism; bordism theory.
Intended learning outcomes
On completion of this subject, students should be able to:
- Demonstrate understanding of the basic notions of Differential Topology, including smooth manifolds, vector bundles, differential forms and integration on manifolds;
- Calculate with smooth manifolds, smooth maps, and differential forms in local coordinates;
- Compute global invariants of manifolds;
- Explain and apply major foundational results in differential topology;
- Demonstrate knowledge of important examples of Lie groups and homogeneous spaces; and
- Pursue further studies in differential topology 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; and
- Time-management skills: the ability to meet regular deadlines while balancing competing commitments.
Last updated: 4 March 2025
Eligibility and requirements
Prerequisites
One of
| Code | Name | Teaching period | Credit Points |
|---|---|---|---|
| MAST20009 | Vector Calculus |
Semester 2 (On Campus - Parkville)
Semester 1 (On Campus - Parkville)
|
12.5 |
| MAST20032 | Vector Calculus: Advanced | Semester 1 (On Campus - Parkville) |
12.5 |
AND
| Code | Name | Teaching period | Credit Points |
|---|---|---|---|
| MAST30026 | Metric and Hilbert Spaces | Semester 2 (On Campus - Parkville) |
12.5 |
Corequisites
None
Non-allowed subjects
MAST90054 Differential Topology
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
| Description | Timing | Percentage |
|---|---|---|
A written assignment
| Early in the teaching period | 20% |
A written assignment
| Second half of the teaching period | 20% |
A written assignment
| Late in the teaching period | 20% |
Written Examination
| During the examination period | 40% |
Last updated: 4 March 2025
Dates & times
- Semester 1
Coordinator Diarmuid Crowley Mode of delivery On Campus (Parkville) Contact hours 36 hours comprising of 3x 1-hour lectures per week Total time commitment 170 hours Teaching period 3 March 2025 to 1 June 2025 Last self-enrol date 14 March 2025 Census date 31 March 2025 Last date to withdraw without fail 9 May 2025 Assessment period ends 27 June 2025 Semester 1 contact information
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
N. Hitchin. Differentiable Manifolds, available online at: http://people.maths.ox.ac.uk/~hitchin/files/LectureNotes/Differentiable_manifolds/manifolds2014.pdf
- Related Handbook entries
This subject contributes to the following:
Type Name Course Ph.D.- Engineering Course Master of Science (Mathematics and Statistics) Course Doctor of Philosophy - Engineering Course Master of Philosophy - 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.
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
Last updated: 4 March 2025