MAT 364 Syllabus
Here is a list of possible topics from which the course material
will be selected:
1. Basic topology in Rn
- Open and closed sets, compactness, connectivity, continuity,
homeomorphisms, isotopies
2. Elementary knot theory
- Knots and their diagrams, isotopy of knots, Reidemeister moves,
invariants of knots and links, classification problems
3. Topology of surfaces
- Basic definitions, orientability, examples of surfaces, cut
and paste techniques, triangulations, Euler characteristic,
fundamental group, classification of compact surfaces
4. Geometry of smooth curves and surfaces in R3
- Parametrization of curves and surfaces, arclength and area,
curvature and torsion of curves, Gauss map and curvature of surfaces
5. Global invariants of surfaces
- Vector fields on surfaces, index of a singularity,
Poincare-Hopf and Gauss-Bonnet theorems
6. Symmetries and groups
- Tilings, lattices, solids of Plato, introduction to
Group Theory
7. Geometry in the hyperbolic plane
- Elementary properties, lines and reflections, the
hyperbolic metric, isometries, comparison with Euclidean geometry
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Math 364