Note: This is an archived Handbook entry from 2016.
|Dates & Locations:|| |
This subject is not offered in 2016.
|Time Commitment:||Contact Hours: 36 hours comprising three 1-hour lectures per week |
Total Time Commitment:
Both of the following, or equivalent.
Study Period Commencement:
Semester 1, Semester 2
|Recommended Background Knowledge:||None|
|Non Allowed Subjects:|| |
|Core Participation Requirements:||
For the purposes of considering request for Reasonable Adjustments under the Disability Standards for Education (Cwth 2005), and Student Support and Engagement Policy, academic requirements for this subject are articulated in the Subject Overview, Learning Outcomes, Assessment and Generic Skills sections of this entry.
It is University policy to take all reasonable steps to minimise the impact of disability upon academic study, and reasonable adjustments will be made to enhance a student's participation in the University's programs. Students who feel their disability may impact on meeting the requirements of this subject are encouraged to discuss this matter with a Faculty Student Adviser and Student Equity and Disability Support: http://services.unimelb.edu.au/disability
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.
After completing this subject, students will gain:
Up to 60 pages of written assignments (60%: three assignments worth 20% each, due early, mid and late in semester), a two-hour written examination (40%, in the examination period).
|Prescribed Texts:|| |
N. Hitchin. Differentiable Manifolds, available online at: people.maths.ox.ac.uk/~hitchin/hitchinnotes/hitchinnotes.html
|Breadth Options:|| |
This subject is not available as a breadth subject.
|Fees Information:||Subject EFTSL, Level, Discipline & Census Date|
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:
Doctor of Philosophy - Engineering |
Master of Philosophy - Engineering
Master of Science (Mathematics and Statistics)
Mathematics and Statistics |
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