MTH4113 Low-dimensional topology
Faculty of Science
MTH4113 Low-dimensional topology is a level 4, 6-credit-point, postgraduate unit from the Faculty of Science, offered in 2022 in Semester 2 at Clayton. It has no prerequisites.
- Credit points
- 6
- Offered in 2022
- Semester 2
- Clayton
- Assessment
- Exam 60%
- and 1 other task
This is the 2022 handbook entry. See the 2027 entry.
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Requisites
Before MTH4113
No prerequisites or corequisites besides the enrolment rules below.
After MTH4113
No unit lists MTH4113 as a prerequisite in the 2022 handbook.
Enrolment rules
PROHIBITION: MTH5113
PREREQUISITE: MTH3130
COREQUISITE: Enrolment in the Master of Mathematics.
Equivalent units
The same content under another code. Only one of them counts.
Overview
The study of low-dimensional topology is the study of spaces of dimensions 2, 3, and 4, including the study of surfaces and their symmetries, knots and links, and structures on 3 and 4-manifolds. It has applications to mathematical fields such as geometry and dynamics; it also has modern applications to fields such as microbiology, physics, and computing. The unit will cover core concepts in low-dimensional topology such as surfaces and the mapping class group, descriptions of 3-manifolds by Heegaard splittings and Dehn fillings, cobordism in 4-dimensions. Additional topics may include prime and torus decompositions of 3-manifolds, knot and link invariants, contact and symplectic structures on manifolds, foliations, 3-manifold geometries, and applications to mathematical physics.
Offerings in 2022
| Teaching period | Campus | Mode |
|---|---|---|
| Second semester | Clayton | On campus |
Assessment
- Continuous assessmentOther40%
- Examination (24:00 hours)ExamThreshold hurdle60%
Learning outcomes
When you finish this unit, you should be able to:
- 1
Formulate complex mathematical arguments using ideas from low-dimensional topology.
- 2
Apply sophisticated tools of low-dimensional topology to tackle novel problems, for example, to distinguish or classify new spaces, etc.
- 3
Communicate mathematical concepts and arguments.
- 4
Apply critical thinking to judge the validity of mathematical reasoning.
Workload and teaching
- Lectures36 hours
- Applied sessions11 hours
- Teaching approachActive learning
- Two 1.5 -hour lectures;
- One 1-hour applied class (in weeks 2-12) and
- 8 hours of independent study per week.
Active learning will occur in lectures and applied classes.
Contacts
- Chief Examiners
- Professor Jessica Purcell
- Unit Coordinators
- Professor Jessica Purcell
Common questions
What are the prerequisites for MTH4113?
MTH4113 has no prerequisites, but enrolment rules apply.
When is MTH4113 offered?
In 2022, MTH4113 runs in Semester 2 at Clayton.
Does MTH4113 have an exam?
Yes. The exam is worth 60% of the final mark, alongside 1 other task.