Undergraduate - UnitMTH3160 - Analysis and topology

This unit entry is for students who completed this unit in 2012 only. For students planning to study the unit, please refer to the unit indexes in the the current edition of the Handbook. If you have any queries contact the managing faculty for your course or area of study.

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6 points, SCA Band 0 (NATIONAL PRIORITY), 0.125 EFTSL

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

Level	Undergraduate
Faculty	Faculty of Science
Offered	Clayton First semester 2012 (Day)
Coordinator(s)	Dr Gilbert Weinstein

Synopsis

This unit will explore the power of mathematical generalisation, by showing how rather elementary techniques from the theory of abstract metric spaces, lead directly to proofs of fundamental results on ordinary differential equations and in geometry. Extending linear algebra to infinite-dimensional topological vector spaces leads to the general theory of Hilbert spaces, which has important applications in all areas of mathematics and the physical sciences.

Outcomes

On completion of this unit students will be able to demonstrate: an understanding of the basic topological properties of metric spaces, and their applications to problems in other areas of mathematics; an understanding of Hilbert spaces and some of their applications; and communication skills and team work as appropriate for the discipline of mathematics.