MTH4130 Topology: The mathematics of shape
Faculty of Science
MTH4130 Topology: The mathematics of shape is a level 4, 6-credit-point, undergraduate and postgraduate unit from the Faculty of Science, offered in 2025 in Semester 1 at Clayton. It has no prerequisites.
- Credit points
- 6
- Offered in 2025
- Semester 1
- Clayton
- Assessment
- Exam 50%
- and 1 other task
This is the 2025 handbook entry. See the 2027 entry.
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Requisites
Before MTH4130
No prerequisites or corequisites besides the enrolment rules below.
After MTH4130
No unit lists MTH4130 as a prerequisite in the 2025 handbook.
Enrolment rules
Prohibition: MTH3130
You must be enrolled in the Graduate Certificate in Mathematics or the Master of Mathematics
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 delta 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 2025
| Teaching period | Campus | Mode |
|---|---|---|
| First semester | Clayton | On campus |
Assessment
- Continuous assessmentDemonstration50%
- Final assessment - Exam (3 hours and 10 minutes)Examination50%
Learning outcomes
When you finish this unit, you should be able to:
- 1
Critically evaluate and synthesise definitions, concepts, examples, theorems, and proofs of topology.
- 2
Design and construct topological spaces in various guises, recognising their underlying structures and properties
- 3
Apply some of the most famous theorems of topology, such as the classification of surfaces and the Seifert-van Kampen theorem, to solve complex problems.
- 4
Exhibit mastery in advanced problem-solving and theorem-proving techniques, demonstrating creativity and rigour in the approach to complex topological problems
- 5
Explore and assess the extensive applications of topology across advanced areas of mathematics and the natural sciences, identifying potential interdisciplinary connections and contributions.
- 6
Communicate sophisticated mathematical arguments and concepts related to topology with clarity and precision, both in written and oral forms, suitable for academic and professional contexts.
- 7
Collaborate effectively with staff and fellow students in the synthesis of advanced mathematical knowledge and the application of topological methods to complex problem-solving scenarios, demonstrating leadership and initiative in group settings
Workload and teaching
- Applied sessions22 hours
- Seminars36 hours
- 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 MTH4130?
MTH4130 has no prerequisites, but enrolment rules apply.
When is MTH4130 offered?
In 2025, MTH4130 runs in Semester 1 at Clayton.
Does MTH4130 have an exam?
Yes. The exam is worth 50% of the final mark, alongside 1 other task.