Note: This is an archived Handbook entry from 2014.
|Dates & Locations:|| |
This subject is not offered in 2014.
|Time Commitment:||Contact Hours: 36 hours comprising two 1-hour lectures per week and one 1-hour practice class per week. |
Total Time Commitment:
3 contact hours plus 7 hours private study per week.
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 requests for Reasonable Adjustments under the Disability Standards for Education (Cwth 2005), and Students Experiencing Academic Disadvantage Policy, academic requirements for this subject are articulated in the Subject Description, Subject Objectives, Generic Skills and Assessment Requirements for this entry.
The University is dedicated to provide support to those with special requirements. Further details on the disability support scheme can be found at the Disability Liaison Unit website: http://www.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:
Master of Philosophy - Engineering |
Master of Science (Mathematics and Statistics)
Mathematics and Statistics |
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