CS 598: Computational Topology (Fall 2009)

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Homeworks

There will be 3–5 written homeworks, released roughly every other week. I don't expect everyone to solve everything completely, but you should turn in at least a partial solution for each problem. This is a graduate special-topics class, so some homework problems may be open!

Homework solutions should be typeset in LaTeX, converted to PDF, and submitted by email as an attachment. (I will grudgingly accept at most one hardcopy printed or handwritten submission from each student, but I won't like it.)

Projects

The majority of the course grade will be based on a two-part semester project. The basic requirements of the project are quite open-ended:

Each open problem must combine both topology and algorithms, but it need not be directly related to any of the specific topics covered in class. Students are strongly encouraged to submit problems that draw on their prior research experience and interests.

The mid-semester summary should include a crisp statement of the problem, any relevant background definitions (so that the summary is self-contained), a sketch of existing related results, and a list of references. All summaries have now been posted, so that they can be mined by the class for the final project. (However, the final project problems need not come from these summaries.)

The ideal final outcome of the project is a publishable result. Any student who publishes work from this class, in a refereed conference or journal, will automatically get an A+. Moreover, this rule can be applied retroactively for several years after the course ends!

However, it is not reasonable (for most students) to expect to obtain publishable results on any problem after only one or two months of effort, especially in a new area. Thus, most final reports will describe the team's incomplete progress toward a solution. This progress can take several forms: a thorough literature survey, a complete solution for some interesting special case or necessary lemma, a plausible plan of attack, counterexamples that killed a seemingly plausible plan of attack, conjectures backed by experimental evidence, interesting approaches that didn't pan out, ideas that seemed smart at first but turned out to be stupid, and so on. You know, research.