Note: This is an archived Handbook entry from 2011.
|Dates & Locations:|| |
This subject is not offered in 2011.
|Time Commitment:||Contact Hours: 36 hours comprising 2 one-hour lectures per week and 1 one-hour practical class per week. |
Total Time Commitment: 3 contact hours and 7 hours private study per week
|Recommended Background Knowledge:||It is recommended that students have completed third year subjects in algebra (equivalent to 620-321 Algebra) and metric spaces (equivalent to 620-329 Metric and Hilbert Spaces).|
|Non Allowed Subjects:||None.|
|Core Participation Requirements:||
For the purposes of considering requests for Reasonable Adjustments under the Disability Standards for Education (Cwth 2005), and Students Experiencing Academic Disadvantage Policy, academic requirements for this subject are articulated in the Subject Description, Subject Objectives, Generic Skills and Assessment Requirements for this entry.
The University is dedicated to provide support to those with special requirements. Further details on the disability support scheme can be found at the Disability Liaison Unit website: http://www.services.unimelb.edu.au/disability/
|Subject Overview:||This subject studies topological spaces and continuous maps between them. It demonstrates the power of topological methods in dealing with problems involving shape and position of objects and continuous mappings, and shows how topology can be applied to many areas, including geometry, analysis, group theory and physics. The aim is to reduce questions in topology to problems in algebra by introducing algebraic invariants associated to spaces and continuous maps. Important classes of spaces studied are manifolds (locally Euclidean spaces) and CW complexes (built by gluing together cells of various dimensions). Topics include: homotopy of maps and homotopy equivalence of spaces, homotopy groups of spaces, the fundamental group, covering spaces; homology theory, including singular homology theory, the axiomatic approach of Eilenberg and Steenrod, and cellular homology.|
After completing this subject, students should gain:
|Assessment:||Up to 60 pages of assignments (60%: three assignments worth 20% each, due |
early, mid and late in semester), a two-hour written examination (40%, in the examination period).
|Prescribed Texts:|| |
|Recommended Texts:||A. Hatcher. Algebraic Topology, Cambridge University Press (2002), available online at |
W. S. Massey. A Basic Course in Algebraic Topology, Springer (1997).
|Breadth Options:|| |
This subject is not available as a breadth subject.
|Fees Information:||Subject EFTSL, Level, Discipline & Census Date|
In addition to learning specific skills that will assist students in their future careers in science, they will have the opportunity to develop generic skills that will assist them in any future career path. These include:
Master of Science (Mathematics and Statistics) |
Download PDF version.