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Differential Geometry (MAST90143)
Graduate courseworkPoints: 12.5Dual-Delivery (Parkville)
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About this subject
- Overview
- Eligibility and requirements
- Assessment
- Dates and times
- Further information
- Timetable(opens in new window)
Contact information
Semester 2
Overview
Availability | Semester 2 - Dual-Delivery |
---|---|
Fees | Look up fees |
This subject extends notions from calculus, linear algebra and differential equations to study spaces with geometric structures. The concepts introduced are of great importance in mathematics, physics, and all areas in which local properties of spaces are used to model systems.
Topics include: smooth manifolds, vector bundles, multilinear algebra; Frobenius’ theorem, exterior differentiation, Lie differentiation, flows of vector fields; connections and curvature; bilinear forms, metrics, length, volume, Levi-Civita connection; parallel transport, geodesics, holonomy; connections on principal bundles; examples including Lie groups, hyperbolic geometry and homogeneous spaces.
Additional topics may include: second fundamental form and minimal submanifolds; Jacobi fields and applications to topology; constant curvature and Einstein metrics; Hodge star operator, Hodge Laplacian and harmonic forms; Lorentzian geometry and Einstein's equations; Kähler geometry; symplectic geometry; gauge theory.
Intended learning outcomes
After completing this subject, student should be able to:
- demonstrate understanding of the basic notions of Differential Geometry, including smooth manifolds, vector bundles, Riemannian metrics, connections and curvature;
- functionally use connections, curvature and geodesics;
- perform geometric calculations in local coordinates;
- explain and apply major foundational results in differential geometry;
- demonstrate knowledge of important examples of Lie groups and homogeneous spaces; and
- pursue further studies in differential geometry 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: 31 January 2024
Eligibility and requirements
Prerequisites
Code | Name | Teaching period | Credit Points |
---|---|---|---|
MAST30026 | Metric and Hilbert Spaces | Semester 2 (Dual-Delivery - Parkville) |
12.5 |
AND
One of
Code | Name | Teaching period | Credit Points |
---|---|---|---|
MAST20009 | Vector Calculus |
Semester 2 (Dual-Delivery - Parkville)
Semester 1 (Dual-Delivery - Parkville)
|
12.5 |
MAST20032 | Vector Calculus: Advanced | Semester 1 (Dual-Delivery - Parkville) |
12.5 |
Corequisites
None
Non-allowed subjects
Code | Name | Teaching period | Credit Points |
---|---|---|---|
MAST90029 | Differential Topology and Geometry | Not available in 2024 |
12.5 |
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 |
---|---|---|
Written assignment
| Early in the teaching period | 20% |
Written Assignment
| Second half of the teaching period | 20% |
Written Assignment
| Late in the teaching period | 20% |
Final exam
| During the examination period | 40% |
Last updated: 31 January 2024
Dates & times
- Semester 2
Coordinator Volker Schlue Mode of delivery Dual-Delivery (Parkville) Contact hours 3 one-hour interactive lectures per week Total time commitment 170 hours Teaching period 25 July 2022 to 23 October 2022 Last self-enrol date 5 August 2022 Census date 31 August 2022 Last date to withdraw without fail 23 September 2022 Assessment period ends 18 November 2022 Semester 2 contact information
Last updated: 31 January 2024
Further information
- Texts
Prescribed texts
Recommended texts and other resources
J. M. Lee, Riemannian manifolds: an introduction to curvature, Springer, 1997.
M. P. do Carmo, Riemannian geometry, Birkhäuser, 1992.
B. O'Neill, Semi-Riemannian geometry with applications to relativity, 1983.
- 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