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Differential Topology and Geometry (MAST90029)
Graduate courseworkPoints: 12.5Dual-Delivery (Parkville)
Please refer to the return to campus page for more information on these delivery modes and students who can enrol in each mode based on their location.
About this subject
- Overview
- Eligibility and requirements
- Assessment
- Dates and times
- Further information
- Timetable(opens in new window)
Contact information
Semester 1
Overview
| Availability | Semester 1 - Dual-Delivery |
|---|---|
| Fees | Look up fees |
This subject extends the methods of calculus and linear algebra to study the geometry and 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 including integration on manifolds, and give an introduction to Riemannian geometry. Topics include: Differential Topology: smooth manifolds, tangent spaces, inverse and implicit function theorems, differential forms, bundles, transversality, integration on manifolds, de Rham cohomology; Riemanian Geometry: connections, geodesics, and curvature of Riemannian metrics; examples coming from Lie groups, hyperbolic geometry, and other homogeneous spaces.
Intended learning outcomes
After completing this subject, students will gain:
- An understanding of the basic notions of Differential Topology, including smooth manifolds, vector bundles, differential forms and integration on manifolds;
- An understanding of the basic notions of Riemannian Geometry, including connections, curvature and geodesics;
- The ability to work with smooth manifolds, smooth maps, differential forms and Riemannian metrics;
- The ability to do geometric calculations in local coordinates;
- A knowledge of important examples of Lie groups and symmetric spaces; and
- 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; and
- Time-management skills: the ability to meet regular deadlines while balancing competing commitments.
Last updated: 3 November 2022
Eligibility and requirements
Prerequisites
All of
| Code | Name | Teaching period | Credit Points |
|---|---|---|---|
| MAST20009 | Vector Calculus |
Semester 1 (Dual-Delivery - Parkville)
Semester 2 (Dual-Delivery - Parkville)
|
12.5 |
| MAST30026 | Metric and Hilbert Spaces | Semester 2 (Dual-Delivery - Parkville) |
12.5 |
Or equivalent
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: 3 November 2022
Assessment
| Description | Timing | Percentage |
|---|---|---|
Continuing assessment of up to 60 hours work, worth 60% of the mark, throughout the semester
| Throughout the teaching period | 60% |
A written examination
| During the examination period | 40% |
Last updated: 3 November 2022
Dates & times
- Semester 1
Principal coordinator Craig Hodgson Mode of delivery Dual-Delivery (Parkville) Contact hours 36 hours comprising of 3x 1-hour lectures per week Total time commitment 170 hours Teaching period 1 March 2021 to 30 May 2021 Last self-enrol date 12 March 2021 Census date 31 March 2021 Last date to withdraw without fail 7 May 2021 Assessment period ends 25 June 2021 Semester 1 contact information
Last updated: 3 November 2022
Further information
- Texts
Prescribed texts
None
Recommended texts and other resources
N. Hitchin. Differentiable Manifolds, available online at: people.maths.ox.ac.uk/~hitchin/hitchinnotes/hitchinnotes.html
M. P. do Carmo, Riemannian Geometry, Birkhäuser (1992). - 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: 3 November 2022