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

Requisites

Prerequisite

Contacts

Chief Examiner(s)

Dr Wenhui Shi

Unit Coordinator(s)

Dr Wenhui Shi

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.

Teaching approach

Active learning

Peer assisted learning

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.

Assessment

1 - Continuous assessment

2 - Examination (3 hours and 10 minutes)

Scheduled and non-scheduled teaching activities

Applied sessions

Lectures

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