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Topology, colloquially known as “rubber-sheet geometry”, is the study of continuity in an abstractsetting. Topological notions underpin, or are used in, many areas of mathematics, both pure and applied. In this course, we study some of the main concepts of point set topology, and provide abrief introduction to algebraic topology.The topics will cover: Metric and topological spaces; continuous functions and homeomorphism; compact and connected spaces; quotient and product topology; surfaces, manifolds and knots; homotopy, the fundamental group and applications.
This course will provide students with an opportunity to develop the Graduate Attributes specified below:
Critically competent in a core academic discipline of their award
Students know and can critically evaluate and, where applicable, apply this knowledge to topics/issues within their majoring subject.
Subject to approval of the Head of School.
Assessment:Two assignments, each worth 20%Final exam, worth 60%
Recommended texts:Topology, Klaus Jänich, Springer-Verlag, 1984Basic Topology, M. A. Armstrong. Springer, 1983.Renzo’s Math490, .pdf available online.
School of Mathematics and Statistics Postgraduate Handbook
General information for students
Domestic fee $950.00
International Postgraduate fees
* Fees include New Zealand GST and do not include any programme level discount or additional course related expenses.
For further information see
Mathematics and Statistics.