MTH3130 Topology: The mathematics of shape
Faculty of Science
MTH3130 Topology: The mathematics of shape is a level 3, 6-credit-point, undergraduate unit from the Faculty of Science, offered in 2020 in Semester 1 at Clayton. It needs (MTH2021 or MTH2025) and (MTH2121, MTH3140, MTH2140, MTH3110 or MTH3121) and unlocks 4 units.
- Credit points
- 6
- Offered in 2020
- Semester 1
- Clayton
This is the 2020 handbook entry. See the 2027 entry.
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Requisites
Before MTH3130
Prerequisites
Pass these before you enrol.
After MTH3130
4 units list MTH3130 as a prerequisite or corequisite.
Overview
From point-set topology to manifolds: sets, topological spaces, basis of topology, and properties of spaces such as compact, connected, and Hausdorff. Maps between spaces and their properties, including continuity, homeomorphism, and homotopy.
Constructing spaces via subspace, product, identification, and cell complexes. Manifolds. Additional topics from algebraic and low-dimensional topology may include fundamental group and Seifert-van Kampen theorem, classification of surfaces, and topics in knot theory. Throughout, examples of spaces will include Euclidean spaces, surfaces (real projective plane, Klein bottle, Mobius strip), complexes, function spaces, and others.
Offerings in 2020
| Teaching period | Campus | Mode |
|---|---|---|
| First semester | Clayton | On campus |
| First semester (Fully flex) | Clayton | Flexible |
Learning outcomes
When you finish this unit, you should be able to:
- 1
Apply the basic definitions, concepts, examples, theorems and proofs of topology.
- 2
Construct and recognize topological spaces in various guises.
- 3
Apply some of the most famous theorems of topology such as the classification of surfaces and the Seifert-van Kampen theorem.
- 4
Demonstrate advanced problem solving and theorem proving skills.
- 5
Be aware of the scope of applications of topology in other areas of mathematics and the natural sciences.
- 6
Demonstrate advanced skills in the written and oral presentation of mathematical arguments that enable mathematical concepts, processes and results to be communicated effectively.
- 7
Work both individually and collectively with staff and fellow students on the synthesis of mathematical knowledge and the application of mathematical skills to problem solving.
Workload and teaching
- Three 1-hour lectures
- One 2-hour applied class per week
Where it fits
MTH3130 is part of 6 areas of study in the 2020 handbook.
- APPLMTH07Additional extended major elective unitsApplied mathematicsNo reviews yet
- MTHSTAT07Mathematical statistics elective unitsMathematical statisticsNo reviews yet
- MATHS05Mathematics elective unitsMathematicsNo reviews yet
- MATHS06Mathematics elective unitsMathematicsNo reviews yet
- MATPURE05Pure mathematics elective unitsPure mathematicsNo reviews yet
- MATPURE07Pure mathematics elective unitsPure mathematicsNo reviews yet
Contacts
- Unit Coordinators
- Dr Brett Parker
- Chief Examiners
- Dr Brett Parker
Common questions
What are the prerequisites for MTH3130?
You need (MTH2021 or MTH2025) and (MTH2121, MTH3140, MTH2140, MTH3110 or MTH3121) before you enrol.
What can I take after MTH3130?
MTH3130 is a prerequisite or corequisite for 4 units, including MTH4113, MTH4115, MTH5113 and MTH5115.
When is MTH3130 offered?
In 2020, MTH3130 runs in Semester 1 at Clayton.
Which majors and minors include MTH3130?
MTH3130 is part of Applied mathematics, Mathematical statistics, Mathematics and Pure mathematics.