Topics List for Graduate Presentations

Only those enrolled in this course on the graduate level are required to do a presentation.

The following are suggestions for presentation topics. You are welcome to choose your own topic, subject to my approval. The comments on each topic give you a place to look for preliminary information on which to base your decision. Once you have decided, I will (in most cases) have other resources I can loan you. I am more than happy to work closely with you on deciding what you should (and should not) discuss in your presentation. You should plan on your talk taking about 20 minutes.


Space-Filling Curves See Armstrong, Section 2.3, for an example; additional info is on the Wikipedia page on space-filling curves.
Manifold Embeddings See the wikipedia pages on the Whitney embedding theorem and the Nash embedding theorem, for example. A good goal would be to sketch a proof of Whitney's theorem.
Separation Axioms See the Wikipedia page on separation axioms for a start (although it's more interesting than that page makes it appear); a good goal would be to give examples showing the strict containment of the various axioms.
Knots See the Wikipedia page on knot theory for a start; a good goal would be to prove (using three-colorability, for instance) that non-trivial knots exist.
Metric Spaces & Metrizability See the first bit of Armstrong, Section 2.4, for definitions; a good goal would be to state and discuss the Urysohn metrization theorem.
Topological Groups & Orbit Spaces See Armstrong 4.3 and 4.4.
Wallpaper Groups See the Wikipedia page on wallpaper groups. A good goal would be a sketch of the classification.

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USA Math Dept USA Last Modified 13th Oct 08