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DEGREE REGULATIONS & PROGRAMMES OF STUDY 2015/2016

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DRPS : Course Catalogue : School of Mathematics : Mathematics

Undergraduate Course: Topics in Differential Topology (MATH10039)

Course Outline
SchoolSchool of Mathematics CollegeCollege of Science and Engineering
Credit level (Normal year taken)SCQF Level 10 (Year 4 Undergraduate) AvailabilityAvailable to all students
SCQF Credits10 ECTS Credits5
SummaryCourse 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.
Course description Not entered
Entry Requirements (not applicable to Visiting Students)
Pre-requisites Co-requisites
Prohibited Combinations Other requirements None
Information for Visiting Students
Pre-requisitesNone
Course Delivery Information
Not being delivered
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.
Reading List
None
Additional Information
Course URL http://student.maths.ed.ac.uk
Graduate Attributes and Skills Not entered
KeywordsDTop
Contacts
Course organiserDr Liam O'Carroll
Tel: (0131 6)50 5070
Email: L.O'Carroll@ed.ac.uk
Course secretaryMs Jennifer Marshall
Tel: (0131 6)50 5048
Email: Jennifer.Marshall@ed.ac.uk
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© Copyright 2015 The University of Edinburgh - 18 January 2016 4:24 am