Project proposals are due by April 29
Project reports are due by May 14
A project can either be a study project or a research project.
In a study project you focus on an important result, or set of results, that is not covered in detail in the course. Your proposal references the paper or set of papers that you will study, and a goal. Usually the goal will be to completely understand an important technical result, and to fill in the details of an important technical lemma that is only stated without proof (or with a sketchy proof) in the literature, or observe a simplified argument for a technical proof, or something along these lines. Your report will describe the big picture (the problem you are interested in, and the known results) and a report of what you achieved towards your goal. (A detailed exposition of a technical result, a simplified proof, etc.)
A research project starts with a general goal, like "improve the inapproximability result for Metric TSP," or "Prove P=/=NP." Towards this goal, you read the relevant papers, try various approaches, and then you may or may not reach your goal. At the end you write a report detailing your efforts. Obviously, regardless of the chosen problem, the chances of making interesting progress are not good. In the ideal case, one would come with a promising idea, show how it solves a non-trivial special case as a proof of concept, and then have something to think about during the summer. If no progress is made, any research project can become a study one.
Every student submitting a study project should submit an individual report. A group of two or three students can work together provided they find a way to study a broad question, and to divide up the work they plan to include in their individual reports.
A research project can be assigned to a team of two.
Any important result in complexity can be the base for a study project, and any interesting open question can the base for a research project.
Here are some examples of study projects. Ask me for the references.
Some examples of research projects [accessible only from within berkeley.edu]