Undergraduate Course: Topics in Differential Topology (MATH10039)
Course Outline
| School |
School of Mathematics |
College |
College of Science and Engineering |
| Course type |
Standard |
Availability |
Available to all students |
| Credit level (Normal year taken) |
SCQF Level 10 (Year 4 Undergraduate) |
Credits |
10 |
| Home subject area |
Mathematics |
Other subject area |
Specialist Mathematics & Statistics (Honours) |
| Course website |
http://student.maths.ed.ac.uk |
|
|
| Course description |
Course for final year students in Honours programmes in Mathematics.
1. Define smooth manifolds and give lots of interesting
examples, perhaps concentrating on surfaces in 3-space.
2. Define de Rham cohomology and perhaps compare it with
simplicial cohomology.
3. Study the topology of manifolds (surfaces) via Morse
functions. |
Entry Requirements
| Pre-requisites |
|
Co-requisites |
|
| Prohibited Combinations |
|
Other requirements |
None
|
| Additional Costs |
None |
Course Delivery Information
Summary of Intended Learning Outcomes
1. Familiarity with simple examples of smooth manifolds.
2. Familiarity with differential forms, de Rham cohomology
and its relation with combinatorial definitions of
cohomology.
3. Familiarity with Morse functions and their use in the
calculation of topological invariants of a manifold.
4. Familiarity with further topics in differential
topology, such as the Hopf index theorem, Lefschetz
fixed-point theorem. |
Assessment Information
Examination only.
|
| Please see Visiting Student Prospectus website for Visiting Student Assessment information |
Special Arrangements
| Not entered |
Contacts
| Course organiser |
Dr Liam O'Carroll
Tel: (0131 6)50 5070
Email: L.O'Carroll@ed.ac.uk |
Course secretary |
Ms Jennifer Marshall
Tel: (0131 6)50 5048
Email: Jennifer.Marshall@ed.ac.uk |
|
copyright 2010 The University of Edinburgh -
1 September 2010 6:18 am
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