This class is designed to help you transition from being a reader, to being read, from being someone who listens, to someone who is listened to.

Research is an essential component of almost any area of study and field of work. Learning what research is, how to think about it, and how to do it well, are extremely important skills---ones that you will use in many, many areas beyond differential equations and mathematics. I think research skills are important enough that it is worth devoting a considerable fraction of this class to them.

Overview: The research project should be an in-depth exploration of a particular application of differential equations. It may also be possible to do a more theoretical project. We will spend the first few weeks of the term talking about what research is, how to move from an area of interest to a topic, and how to relate a research question to a broader set of questions or concerns. There are three major "deliverables" associated with the project:

1. Initial Presentation: During week five you will give an initial presentation in which you introduce your topic. You should give a sense of what you'll be doing the next several weeks and the questions you'll wish to address. There are three reasons for this initial presentation.
   • It will force you to choose a topic early rather than later.
   • It will let other people in the class know what you're up to, so you can get feedback and ideas from others.
   • It will give you a chance to practice giving technical presentations. You'll get feedback on your presentation from both me and classmates.
2. Final Presentations: Sometime during week 10 we will give presentations in a session open to the community. These talks will follow the format of contributed talks at a scientific meeting.
3. Paper or Technical Report: Due on the last day of the term. This will be a 5-20 page paper on your research question. You should write in a style appropriate for publication in peer-reviewed journal of your choosing. (If you want to explore another form, this is possible, but you should clear this with me early on.) Your paper must be well-formatted, include figures and graphs as appropriate, and correctly use the citation format standard for whichever journal you choose.

Throughout the term we will spend time discussing a number of issues and ideas in research, and also cover some specific research skills. This will likely include:

• The difference between interests, topics, questions, and problems
• The mechanics of peer-reviewed journals and academic publishing
• The rhetorical style of research papers
• How to search for sources, including using the citation lists available in Google scholar
• How to give an effective technical presentation
• Ethics in research, plagiarism and academic fraud, issues surrounding research on human subjects
• Software for organizing and automating bibliographies

I probably will also divide you up into small groups based on similarity of interests and ask your groups to meet and/or share resources.

A few of these discussions may sound not that interesting, but give them a shot. In the past students have found these topics to be useful and quite helpful.

It is inevitable that some of you will "get farther" in your projects than others, since some of you are farther along in your studies. Also, some research topics are harder to make progress on than others. This diversity is fine. The point of the projects is not to come up with publishable original research or even have an amazing and polished final result. Rather, the idea is to strive toward as good a result as possible, and learn a lot (and challenge yourself and have fun) while doing so.

Finally, as you may have guessed, I suspect that these research projects will be a lot of work. But with a good topic and the right attitude, I think this work can be very fun and rewarding. And I think doing a term-long project like this will be very helpful before undertaking your final project or a research internship somewhere.