Undergraduate - UnitMTH3160 - Analysis and topology

This unit entry is for students who completed this unit in 2013 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.

print version

6 points, SCA Band 2, 0.125 EFTSL

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Level	Undergraduate
Faculty	Faculty of Science
Organisational Unit	School of Mathematical Sciences
Offered	Clayton First semester 2013 (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:

Understand the basic topological properties of metric spaces, and their applications to problems in other areas of mathematics;

Understand and appreciate some important basic theorems in analysis and their applications, such as the Ascoli-Arzela Theorem, the Weierstrass approximation theorem, the inverse and implicit function theorems;