From
(1):
The notion of mentoring is ancient. The original Mentor was described
by Homer as the "wise and trusted counselor" whom Odysseus left in
charge of his household during his travels. Athena, in the guise of
Mentor, became the guardian and teacher of Odysseus' son Telemachus.
Warning: Mentoring is individual. Don't follow all advice.
Finding good projects:
- Consider involving an undergraduate in your research (this can help you keep up with your research as it is very hard to find time when you are adjusting to a new place). One possibility is to explore a specific example related to your research
- Explore an known unsolved problem. You may not expect to solve it, but one can still illustrate how one can approach the unknown. It may also lead you to a smaller result.
- Consider turning a math game into research projects.
- Send students to REU's and have student bring problems back.
- For data analysis, use Kaggle.
Recruiting Students
- Hang out on math chat boards such as
- Check out the honors program at your university
Sometimes you should turn down students
Initiation
When meeting mentor for first time:
- Make appropriate eye contact and be enthusiastic.
- Ask
about math background. In what areas do they feel weak and need
improvement. Be careful to not be judgmental, but let them know that
everyone comes in with different backgrounds and that they should feel
free to share their mathematical background so that together you can
work to improve it or make project fit background.
- Emphasize
that if they feel lost, confused, overwhelmed, they should let you
know. Coming to you would be a sign of maturity when overwhelmed. And
getting lost is typical. They should take time to think about things,
but one can progress faster when discussing with others. When to
discuss is up to student, advisor, and time restraints (ie summer REU vs
longer research period).
- Let
the student decide how personal they want to get. Not all students
want to share personal details even such as where they are from.
- You can share your experiences and let them determine what they want to share.
- Can ask them to share one unusual thing about themselves or what is their favorite TV show
Preparing students for graduate school
- Let students know that most graduate schools in math and science offer TAships and other funding so that loans are unnecessary (at least for those willing to live cheap and those without families).
- Financially, it may be difficult to have/start a family, but many graduate students do so. In fact some say that the best time to start a family is while a graduate student when your schedule is most flexible.
- Students should not be trying to get into the best possible school they can get into, but rather the best school that they can succeed at. Advisers should be very honest with their students on where they think they can do well and make suggestions based on their background.
Preparing students for industry
SIAM for students
Advising students on applying to graduate school
- Ask professors of proofs courses/recent professors for letters of recommendation. A letter from a Dean will count less than a professor who taught the student recently in an advanced course.
- Transcripts are very important. Students should focus on having proofs classes and a wider variety of classes and steer clear of independent studies unless they are well planned out and that professor is going to write them a letter. At some smaller colleges, independent studies may be where a student can get rigorous proofs courses. In this case, the student should get a letter of recommendation from that professor and ask them to describe the course as well as how they did in the course. Similarly for REUs
- Some departments look for people who could be leaders within the department, so they will take note of students' activities.
- Personal statement should not be superficial. For example, don't say you want to work with a prefessor who is no longer at that university.
- Apply to a safety school.
- Apply to PhD program, not masters if the university has a PhD program.
Writing letters of recommendation
- State how long and in what capacity you have known the student.
- Specifics are more helpful than generalities.
- Letters in the USA often "embellish" a student's accomplishments, but be careful of over embellishing. Letters written for previous students can affect how your letters for future students are considered. Also over-embellishments not backed up by specifics can appear insincere.
- Be careful of including negative qualities. It can make your letter sound more honest, but it can also be misinterpreted. When discussing negative qualities, put a positive slant on it.
- Possibly discuss if student is a good match for that school.
- Consider using a limited amount of boldface to emphasize important characteristics. Some readers will appreciate this as they quickly read letters, but if you use too much, others might think you are screaming at them.
- Give comparisons to other students (without giving names you know
who have succeeded at other graduate schools (name the graduate
schools). For example. Student X is comparable to another student who
went to university X and has since passed all their quals.
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- See additional advice at https://owl.english.purdue.edu/owl/resource/982/02/
