Here is a list of suggested project topics. You and your team should check these out and pick one to work on. You may also choose something else if you like. Either way, please let me know what topic your team has selected before you get started.
There is a broad range represented in this list. Some of these topics are more algebraic than others, some lie in specific application domains, some are about algorithms, etc. Your team gets to pick what you want to do! The first step: google.
When gathering information about these topics, remember that you only have a short time to present in class (probably about 20-25 min). Thus necessarily you will be giving a very high level overview of anything you study. This means you shouldn't be intimidated by the depth of some of these topics; indeed, many lie at the forefront of research. Your task is to distill and synthesize information and present it to the class in a coherent and digestible form. For instance, don't worry about proving a theorem; instead explain it to us and show us illustrative examples. Don't try to blow us away with the full scope of a topic; instead try to find some nontrivial part that you can communicate to us.