# MTH3130 - Topology: The mathematics of shape - 2019

## 6 points, SCA Band 2, 0.125 EFTSL

Refer to the specific census and withdrawal dates for the semester(s) in which this unit is offered.

Faculty

Science

Organisational Unit

School of Mathematical Sciences

Chief examiner(s)

Coordinator(s)

Unit guides

Offered

Clayton

• First semester 2019 (On-campus)

Prerequisites

Students must have passed: MTH2021 or MTH2025 and one of MTH2121, MTH2140, MTH3110, MTH3121 or MTH3140

## Synopsis

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.

## Outcomes

On completion of this unit students will 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.

## Assessment

Examination (3 hours): 60% (Hurdle)

Assignments: 40%

Hurdle requirement: To pass this unit a student must achieve at least 50% overall and at least 40% for the end-of-semester exam.