Geometry II: Knots and Surfaces
Queen Mary, University of London
Area of Study
Taught In English
Course Level Recommendations
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Recommended U.S. Semester Credits4
Recommended U.S. Quarter Units6
Hours & Credits
Prerequisite: "MTH4101 MTH4103"
The module provides a first introduction to abstract ideas of differential geometry of curves and surfaces,
with some elements of knot theory and hyperbolic geometry. Building on experience with vectors in three
dimensions and elementary calculus, the modules asks what one can say of mathematical interest about an
arbitrary curve or surfaces. The module starts with the problem of how to tell if a curve or piece of string
is knotted (other than by pulling it about, ie. mathematically) before moving on to differential geometric
(calculus based) methods of measuring properties such as 'torsion' and 'curvature' of a curve or surface.
The module ends with exposure to more abstract hyperbolic surfaces and higher-dimensional spaces defined
by identifications and symmetries. There will be some proofs.
Assessment: 10.0% Coursework, 90.0% Examination
Semester 1 Associate Assessment: 100.0% Coursework
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