Generating Ideas of Undergraduate Research Projects

How do Joe Gallian, Katie Johnson, Stephan Garcia and Colin Adams generate ideas for their many undergraduate research projects? Pamela Harris put together a panel and this is what they had to say.

Joe Gallian:

– Do original research, have high expectations, expect some frustration, and always ask students to write their results as they get them.

– Use computers to generate data. Some projects don’t need to involve proofs. They can analyze interesting data.

– Look at Math Magazine, Involve, and other journals that publish work done with undergraduates.

Katie Johnson:

– Any time you think of an idea that might work for an undergraduate research project, write it in a notebook. Bring the notebook with you to conferences and events.

– Keep a folder with interesting papers that undergraduates could read.

– Stay current, attend conferences, seminars, and colloquia (and bring your notebook).

– Once students are working with you, ask them to think of 3 to 5 questions that might lead to other research projects.

Stephan Garcia:

– When needed, stretch your research area a bit. Try new topics. Search for fertile ground. Trust yourself.

– Encourage your students to find variants of existing questions.

– Ask students to read a paper and come back with 20 questions about it. Many won’t be “good” questions but some might lead to interesting projects.

– Be flexible, if something is not working, be willing to pivot and adapt. Change assumptions; be creative.

Colin Adams:

– Have the antenna up. While you are at math events, always think about if there is a project that can be done by students.

– Find something students can compute (even if they don’t understand the math). Fill in the details later.

– Learn about related areas to your research. One way to do this is to teach courses related to these areas.

– At the end of courses, collect papers and give them to students to present on them. Often interesting projects arise in this way.

– Think about whether you can generalize results or change assumptions a bit.

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