MTH3130 - Topology: The mathematics of shape

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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 … For more content click the Read More button below.

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

S1-01-CLAYTON-ON-CAMPUS

S1-FF-CLAYTON-FLEXIBLE

Requisites

Prerequisite

Contacts

Chief Examiner(s)

Dr Brett Parker

Unit Coordinator(s)

Dr Brett Parker

Learning outcomes

On successful completion of this unit, you should be able to:

Apply the basic definitions, concepts, examples, theorems and proofs of topology.

Construct and recognize topological spaces in various guises.

Apply some of the most famous theorems of topology such as the classification of surfaces and the Seifert-van Kampen theorem.

Demonstrate advanced problem solving and theorem proving skills.

Be aware of the scope of applications of topology in other areas of mathematics and the natural sciences.

Demonstrate advanced skills in the written and oral presentation of mathematical arguments that enable mathematical concepts, processes and results to be communicated effectively.

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.

Assessment summary

Examination (3 hours and 10 minutes): 60% (Hurdle)

Continuous assessment: 40% (Hurdle)

Hurdle requirement: If you would otherwise have passed the unit but you do not achieve at least 45% in the end of semester written examination and continuous assessment you will receive a Hurdle Fail (NH) grade and a mark of 45 on your transcript.

Workload requirements

Workload

Other unit costs

Costs are indicative and subject to change.
Miscellaneous Items Required (Unit Course Reader,Printing, Stationery)- $120.

Availability in areas of study

Applied mathematics
Mathematical statistics
Mathematics
Pure mathematics