UnitLevel 3Undergraduate

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 2025 in Semester 1 at Clayton. It has no prerequisites and unlocks 7 units, leading on to 9 units in all.

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 MTH3130

No prerequisites or corequisites besides the enrolment rules below.

After MTH3130

7 units list MTH3130 as a prerequisite or corequisite.

Enrolment rules

PREREQUISITE: You must have passed one unit from MTH2021 or MTH2025 and one unit from MTH2121 or MTH3121 or MTH3140 or MTH3141 or MTH2140 or MTH2141 or MTH3110, or be enrolled in 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 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 2025

Teaching period	Campus	Mode
First semester	Clayton	On campus

Assessment

Continuous assessmentDemonstration
50%
Final assessment - Exam (3 hours and 10 minutes)Examination
50%

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

Applied sessions22 hours
Seminars36 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.

Where it fits

MTH3130 is part of 6 areas of study in the 2025 handbook.

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 7 units, including MTH3170, MTH3175, MTH4113, MTH4115, MTH5113 and MTH5115. Those lead on to 9 units in all.

When is MTH3130 offered?

In 2025, 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.

Which majors and minors include MTH3130?

MTH3130 is part of Applied mathematics, Mathematical statistics, Mathematics and Pure mathematics.

More details

Credit points: 6
Level: 3
Study level: Undergraduate
Faculty: Faculty of Science
Organisational unit: School of Mathematics

Type: Coursework
EFTSL: 0.125
Student contribution: SCA Band 1
Study abroad: Available
Handbook years: 2020 2021 2022 2023 202420252026 2027