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
fields 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.
The final project should be an in-depth exploration of a particular
application of differential equations. It may 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 components
to the project
Other Comments on the Research Projects:
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:
- Initial Presentation:
Thursday of 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.
- 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.
- Paper or Technical Report: Due on the last day of spring
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
A few of these discussions may seem tedious, but I ask for your
patience. I think whatever mild tedium we endure will be worth it in
the long run.
- The difference between interests, topics, questions, and problems.
- The mechanics of peer-reviewed journals and academic publishing.
- How to search for sources, including using the science and social
science citation indexes, and the citation lists available in Google
- How to give an effective technical presentation.
- Ethics in research, plagiarism and academic fraud, issues
surrounding research on human subjects.
- How the internet and "web 2.0" tools alter how research is done.
As part of this you will need to get accounts on del.icio.us and citeulike.
- Software for 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
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