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DRPS : Course Catalogue : School of Mathematics : Mathematics

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 Taught in Gaelic? No
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
Information for Visiting Students
Pre-requisites None
Displayed in Visiting Students Prospectus? Yes
Course Delivery Information
Not being delivered
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.
Special Arrangements
None
Additional Information
Academic description Not entered
Syllabus Not entered
Transferable skills Not entered
Reading list Not entered
Study Abroad Not entered
Study Pattern Not entered
Keywords DTop
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
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copyright 2011 The University of Edinburgh - 31 January 2011 7:59 am