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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 |