The following is a list of some possible topics for the course project. You can choose topics outside this list; in this case, you must talk with me and we should agree on the project. I strongly suggest you start your search for a topic that fits your interests as soon as possible.
The kind of topics in the list are mainly theoretical but you may consider implentations too. Indeed, a project involving both components (some implementations together with some theoretical explanations) could be very interesting. However, if a topic is essentially an implementation of some algorithm, then it must include a report explaining how and why the program works, and must contain well-justified data testing.
A portion of the marks go to how your project is written and organized. I suggest you consider the following scheme: include a title with an abstract. In a first section, explain the problem you are addressing, the background (if needed), and clearly state your results and conclusions. No proof of theorems or programming code must appear in the first section. Then, describe the problem, the method you used (if applicable), how and why it works, and tables summarizing your experiments (if applicable) with clear explanations of the results. Finally, a list of references should appear. Programs (if applicable) should appear in an appendix.
Of course, there is no need of new results, but if you do have something that is new explicitly point this out.
We include a list of possible references for most of the topics. In general, this is intended as a starting point for the search but in some cases is self-contained. When a reference contains only a section or a chapter, the relevant information is in that book. In case there is no reference included you must consult me. In any case, you should consult the instructor to clear out doubts, suggest lines of action, help you on decisions about the topic, etc. Just come to office hours, or send me mail, or drop by my office and we talk.
The project must be your own work. In particular, you must cite everything you are taking from the literature. You can take proofs, explanations, etc, from papers and books but the final writing must be only yours. One possible way to enhance (and show) your understanding of some work is giving new proofs of results, filling some missing steps in theorems, adding examples, and so on.
You must have a meeting with the instructor to discuss your project before February 29, 2008. That will ensure that everything is in order with your project. By February 29, 2008, a two page extended abstract should be submitted. The final paper is due on March 30, 2006. The presentations (30 minutes) will take place in class on April 1 and 3, 2008 and your slides should be also handed in before your presentations.For example, here is a list of topics.
and many more....