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 2027 in Semester 1 at Clayton. It has no prerequisites and unlocks 6 units, leading on to 7 units in all.
- Credit points
- 6
- Offered in 2027
- Semester 1
- Clayton
- Assessment
- Exam 50%
- and 1 other task
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Requisites
Before MTH3130
No prerequisites or corequisites besides the enrolment rules below.
After MTH3130
6 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 2027
| Teaching period | Campus | Mode |
|---|---|---|
| First semester | Clayton | On campus |
Assessment
- Continuous assessmentDemonstration50%
- Final assessment - Exam (3 hours and 10 minutes)Examination50%
Assessment details may change. Please refer to the assessment information in Moodle closer to the start of the teaching period.
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
- Seminars36 hours
- Applied sessions22 hours
- Teaching approachActive learning
- Teaching approachPeer assisted learning
- Three 1-hour seminars;
- One 2-hour applied class (in weeks 2-12) and
- 7 hours of independent study per week.
Each week you will need to prepare and present some material to a small group of 3 or 4 students, and actively participate (by asking questions, and helping out) when the other students in your group present. Being able to clearly explain mathematics is an important skill that needs practice, and nothing cements mathematics in your mind like teaching it. These activities count as a kind of active, peer assisted learning. You will solve problems in small groups during contact hours. Solving these problems together is a kind of active, peer assisted learning, and a good source practice and instant feedback. You will also submit written solutions to problems, to practice careful written explanations of mathematics, and to get feedback on your writing.
Contacts
- Unit Coordinators
- Dr Andy Hammerlindl
- Chief Examiners
- Dr Andy Hammerlindl
Common questions
What are the prerequisites for MTH3130?
MTH3130 has no prerequisites, but enrolment rules apply.
What can I take after MTH3130?
MTH3130 is a prerequisite or corequisite for 6 units, including MTH3170, MTH3175, MTH4113, MTH5113, MTH5115 and MTH5510. Those lead on to 7 units in all.
When is MTH3130 offered?
In 2027, MTH3130 runs in Semester 1 at Clayton.
Does MTH3130 have an exam?
Yes. The exam is worth 50% of the final mark, alongside 1 other task.