MTH5113 Low-dimensional topology
Faculty of Science
MTH5113 Low-dimensional topology is a level 5, 6-credit-point, postgraduate unit from the Faculty of Science. It isn't offered in 2023. It has no prerequisites.
- Credit points
- 6
- Offered in 2023
- Not offered
- Assessment
- Exam 40%
- and 1 other task
This is the 2023 handbook entry. See the 2027 entry.
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Requisites
Before MTH5113
No prerequisites or corequisites besides the enrolment rules below.
After MTH5113
No unit lists MTH5113 as a prerequisite in the 2023 handbook.
Enrolment rules
PROHIBITION: MTH4113
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 2023
The 2023 handbook lists no offerings for MTH5113.
Assessment
- Continuous assessmentOther60%
- Examination (3 hours and 10 minutes)ExamThreshold hurdle40%
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;
- 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
- Eight 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 MTH5113?
MTH5113 has no prerequisites, but enrolment rules apply.
When is MTH5113 offered?
MTH5113 has no offerings listed in the 2023 handbook.
Does MTH5113 have an exam?
Yes. The exam is worth 40% of the final mark, alongside 1 other task.