MTH4121 Analysis on manifolds
Faculty of Science
MTH4121 Analysis on manifolds is a level 4, 6-credit-point, postgraduate unit from the Faculty of Science, offered in 2020 in Semester 2 at Clayton. It has no prerequisites.
- Credit points
- 6
- Offered in 2020
- Semester 2
- Clayton
- Assessment
- Exam 60%
- and 1 other task
This is the 2020 handbook entry. See the 2021 entry.
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Requisites
Before MTH4121
No prerequisites or corequisites besides the enrolment rules below.
After MTH4121
No unit lists MTH4121 as a prerequisite in the 2020 handbook.
Equivalent units
The same content under another code. Only one of them counts.
Overview
In this course, you will investigate manifolds using the tools of analysis. In this setting, curvature and topology become crucial. The topics covered may include Riemann surfaces, Lie derivatives, Hodge theory, spectral theory on manifolds, comparison theorems, topics in mathematical physics, and geometric differential equations such as the minimal surface equation, geometric evolution equations, and harmonic maps. You will also examine some foundational theorems in the field, such as the uniformisation theorem, the resolution of the Yamabe problem, or the positive mass theorem.
Offerings in 2020
| Teaching period | Campus | Mode |
|---|---|---|
| Second semester | Clayton | On campus |
Assessment
- In-semester assessment40%
- Examination (3 hours and 10 minutes)Threshold hurdle60%
Learning outcomes
When you finish this unit, you should be able to:
- 1
Apply sophisticated tools of mathematical analysis to understand manifolds in a variety of settings
- 2
Demonstrate a profound understanding of connections between the geometry of a manifold, and the analytic properties of the manifold.
- 3
Communicate complex information and results with clarity.
Workload and teaching
- Lectures36 hours
- Applied sessions11 hours
- Teaching approachActive learning
- 3 hours of lectures
- 1-hour tutorial and
- 8 hours of independent study per week
Active learning will occur in lectures and applied classes.
Contacts
- Chief Examiners
- Dr Julie Clutterbuck
- Unit Coordinators
- Dr Julie Clutterbuck
Common questions
What are the prerequisites for MTH4121?
MTH4121 has no prerequisites, but enrolment rules apply.
When is MTH4121 offered?
In 2020, MTH4121 runs in Semester 2 at Clayton.
Does MTH4121 have an exam?
Yes. The exam is worth 60% of the final mark, alongside 1 other task.
More details
- Credit points
- 6
- Level
- 4
- Study level
- Postgraduate
- Faculty
- Faculty of Science
- Organisational unit
- School of Mathematics
- Type
- Coursework
- EFTSL
- 0.125
- Student contribution
- SCA Band 2
- Study abroad
- Not available
- Handbook years
- 20202021