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Unit of study_

Metric Spaces (Advanced) - MATH3961

Year - 2018

Topology, developed at the end of the 19th Century to investigate the subtle interaction of analysis and geometry, is now one of the basic disciplines of mathematics. A working knowledge of the language and concepts of topology is essential in fields as diverse as algebraic number theory and non-linear analysis. This unit develops the basic ideas of topology using the example of metric spaces to illustrate and motivate the general theory. Topics covered include: Metric spaces, convergence, completeness and the contraction mapping theorem; Metric topology, open and closed subsets; Topological spaces, subspaces, product spaces; Continuous mappings and homeomorphisms; Compact spaces; Connected spaces; Hausdorff spaces and normal spaces, Applications include the implicit function theorem, chaotic dynamical systems and an introduction to Hilbert spaces and abstract Fourier series.

Three 1 hour lectures and one 1 hour tutorial per week.

2 hour exam, assignments, quizzes (100%)

Assumed knowledge
MATH2923 or MATH2962


Credit average or greater in 12 credit points of Intermediate Mathematics units


MATH3001 or MATH3901


Faculty: Science

Semester 1

05 Mar 2018

Department/School: Mathematics and Statistics Academic Operations
Study Mode: Normal (lecture/lab/tutorial) day
Census Date: 31 Mar 2018
Unit of study level: Senior
Credit points: 6.0
EFTSL: 0.125
Available for study abroad and exchange: Yes
Faculty/department permission required? No
Courses that offer this unit

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