6 points, SCA Band 2, 0.125 EFTSL
Undergraduate - Unit
Refer to the specific census and withdrawal dates for the semester(s) in which this unit is offered.
- First semester 2017 (Day)
From point-set topology to manifolds: sets, topological spaces, basis of topology, and properties of spaces such as compact, connected, and Hausdorff. Maps between spaces and their properties, including continuity, homeomorphism, and homotopy.
Constructing spaces via subspace, product, identification, and cell complexes. Manifolds. Additional topics from algebraic and low-dimensional topology may include fundamental group and Seifert-van Kampen theorem, classification of surfaces, and topics in knot theory. Throughout, examples of spaces will include Euclidean spaces, surfaces (real projective plane, Klein bottle, Mobius strip), complexes, function spaces, and others.
On completion of this unit students will be able to:
- Apply the basic definitions, concepts, examples, theorems and proofs of topology.
- Construct and recognize topological spaces in various guises.
- Apply some of the most famous theorems of topology such as the classification of surfaces and the Seifert-van Kampen theorem.
- Demonstrate advanced problem solving and theorem proving skills.
- Be aware of the scope of applications of topology in other areas of mathematics and the natural sciences.
- Demonstrate advanced skills in the written and oral presentation of mathematical arguments that enable mathematical concepts, processes and results to be communicated effectively.
- Work both individually and collectively with staff and fellow students on the synthesis of mathematical knowledge and the application of mathematical skills to problem solving.
Three 1-hour lectures + one 2-hour support class per week
See also Unit timetable information