MATH7709 Topology

2016

4.5

3 x 1-hour lectures weekly
1 x 2-hour tutorial weekly

1 2 of MATH2701, MATH2711, MATH2014, MATH2111
1a ENGR2702 - Electrical Circuits and Machines
1b 2 of MATH2111, MATH1141
2 Admission into GCEB-Graduate Certificate in Engineering (Biomedical)
2a Admission into GDPEB-Graduate Diploma in Engineering (Biomedical)
2b Admission into MEB-Master of Engineering (Biomedical)
2c Admission into GCESI-Graduate Certificate in Engineering (Smart Instrumentation)
2d Admission into GDPESI-Graduate Diploma in Engineering (Smart Instrumentation)
2e Admission into MESI-Master of Engineering (Smart Instrumentation)
2f Admission into GCEE-Graduate Certificate in Engineering (Electronics)
2g Admission into GDPEE-Graduate Diploma in Engineering (Electronics)
2h Admission into MEE-Master of Engineering (Electronics)
2i Admission into HBIT-Bachelor of Information Technology (Honours)
2j Admission into HBSC-Bachelor of Science (Honours)
Must Satisfy: (((1 or 1a or 1b)) or ((2 or 2a or 2b or 2c or 2d or 2e or 2f or 2g or 2h or 2i or 2j)))

MATH4709 has been successfully completed

Students undertaking the one year honours programs should check to make sure they have the appropriate background from their undergraduate degree/s.

Topological spaces and continuous functions, connectedness and compactness, countability and separation axioms, the Tychonoff Theorem, metrization theorems and paracompactness, complete metric spaces and function spaces, the fundamental group and covering spaces.

This topic develops the theory of topology as a mathematical topic of interest in its own right, but also as it forms the theorectical foundations for mathematical analysis, geometry and algebraic topology.

At the completion of the topic, students are expected to be able to:

1. Have a sound knowledge of the fundamentals of topology
2. Understand how topology forms the theoretical foundations for mathematical analysis, geometry and algebraic topology