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.
– 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.
– 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.
– 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.
– 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.