The slides of a talk I gave at the 2014 SIAM meeting about the Imposter Syndrome, based on a survey amongst Stanford graduate students in science and engineering.
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In each math or engineering course I teach, beit at the freshmen or advanced graduate level, I hear students lament they lack the innate ability to do math at the required level. “I’m just not that good at math”, or “I was OK at lower level math, but I do not have the ability to perform well at this higher level”.
I’ve never believed that mathematics was something you either could or could not do. I’d say that it is a myth that mathematical ability is genetically determined, and a really rotten one at that as it has caused many perfectly capable students to shy away from mathematics at their first weak performances.
Google “mathematics innate ability” and you can find references to a long list of papers on this topic. In the last years, sufficient evidence has been gathered that mathematics is something you can learn to be good at: practice makes the mathematician.
I see this also in my classes. For the students that struggle, I often offer bootcamps: intense periods in which the students practice mathematical concepts every day, consistently. Nearly all students who participate in bootcamps improve, sometimes significantly.
I am not claiming that talent does not come into the picture. For some, mathematics will come easier, or at least certain types of mathematics will come easier. But I do strongly believe that everyone can be pretty good, if they persist, helped by good instructors.
For all of you who doubt your ability, read about the growth mindset (e.g. Carol Dweck’s book “Mindset”), and do not give up. Mathematics is wonderful, powerful and beautiful, and you can all come to see that.
A brain dump inspired by a recent meeting with ICME graduate students, during which we discussed the academic job application and interview process.
A wee disclaimer: these are general observations and my own point of view based on my experiences in (quite a few) searches on campus and outside. There are of course always exceptions to the rules stated and there will be other opinions out there.
Application and selection process:
- Academic job openings are typically posted in the Fall for jobs starting Fall the year after
- Most universities require four documents in the initial application: a cover letter, a CV, a research statement and a teaching statement
- A search committee will often make a first selection (reducing the number of applicants from x00 to around 20-40) based on these four documents alone.
- Reference letters (usually 3 or 4) will usually be solicited after the first cut, but in some cases I’ve seen reference letters asked before the cut (but this is not common as it creates a lot of work for many people)
- Based on the letters and the four documents, a short list of 7-10 candidates is formed (plus or minus). These short listed applicants will be invited to interview.
- Most universities will finalize the list of interviewees some time between December and late January.
- Interviews are held over the span of several weeks.
What do search committees look for in the four documents (not in order of priority, but all important):
- Proof of excellence in research, or proof of potential for excellence in research
- Clear and interesting vision for research
- Evidence of teaching and good communication skills
- A good sense of why you are interested in the position at that particular institution (this means that you should always tailor your documents and not send generic statements)
- A good sense of what you can offer the institution in research, teaching and community building
How do you write a research statement?
- Probably the most important part of the application
- Do not just talk about research you have done or research you are about to do: look further. What would you like to build in the next 5-10 years? What are the big dreams and aspirations you have? In other words, give the search committee a good idea of what kind of colleague you will be and what you can bring the institution in the future
- Developing a vision is not easy. It requires that you have a very good understanding of the broader field you work in. You need to know what people are doing and why, and then find your own niche in it. You do not want to be a clone of your advisor: it must be very clear that you are your own person, with your own style and dreams and capabilities.
How to develop a vision
Before you can write a vision statement, answer the following questions, in order. At the time of your thesis defense, you should be able to answer them all:
- Why are you working on your particular PhD topic (and do not say that your advisor asked you to)?Why do you enjoy working on this topic (assuming that you are enjoying it!)?
- What can be the broader impacts of your PhD work? If you are working on one particular application, are their others to which your ideas could be applied?
- What are straightforward, or less straightforward extensions of your work? These could be topics you would work on during your PhD if you had just a bit more time, or that you could work on during a postdoc or your first year as assistant professor.
- What are the broader and harder challenges you would like to work on? In other words: expand your research further. Include new directions, new ideas. Start mapping out a possible strategic research plan for your future students. A good guiding question is: what do you envision your first 5 graduate students to work on?
- Now extend these thoughts all the way out to 5 or 10 years after PhD. Of course you can not predict this far out, but you can always have dreams!
Answering these questions is not so easy. Here are some ways to help you. Start these early (do them regularly during the last two years of your defense, at least):
- Read extensively. Be familiar with the research done at sister research groups (research groups at other universities in similar areas). Maybe set one afternoon a week aside to just read papers
- Discuss vision questions with your advisor. Beware: do not adopt everything he/she tells you. You don’t want to be a clone of your advisor. Develop your own opinions. However, your advisor is of course pretty knowledgeable and will have strong, and no doubt pretty solid, ideas.
- Volunteer to review papers for journals in your area. A fantastic way to find out about new research directions
- Go to conferences in your field, even if you are not presenting. ICME has travel money to support this
- Visit research groups that work in similar areas to yours. Aim to visit all research groups you would be interested in joining after your PhD. Make connections during conferences, or just swing by if you happen to be in the neighborhood. Volunteer to give a talk when you visit, and hang around for a while so you can talk to grad students and postdocs, as well as faculty, at the place you are visiting. If you need some financial support for these visits, ask us as we have some travel funds available
- Form a thesis committee early (at least two years out). Involve your thesis committee members in your PhD research: brief them regularly (each quarter, or twice per year) and solicit feedback and suggestions. Your PhD defense will be very smooth and easy if the committee members have been involved and have been able to give directions
When you have gone through all these steps, you will find that writing a vision statement is easier. You now have a lot of oversight, your understand more than your own thesis work, you know how your work relates to that of others and most importantly: you know where the big gaps are in your field at this point in time. Gaps that you may be able to fill.
How do you provide evidence of teaching skills?
- If you apply for academic positions directly after your PhD, you will likely compete with candidates that have a few more years of experience, including teaching experience
- It is still quite uncommon for a fresh PhD to have good teaching skills, and teaching experience
- In ICME, we build a teaching program for PhD students. Take advantage: you can start as a TA, move on to teaching in the refresher courses, continue as a co-teacher or teacher of a 1-unit course (such as the 19x series), participate in our professional certificate program, or teach summer short courses, create Jolts in our studio for online modules
- At Stanford, we have a wonderful Center of Teaching and Learning. Take advantage
- In ICME, we have now set up a system to track your teaching experiences: the teaching portfolio. Start building one. It is a place to put teaching evals, thoughts on teaching/teaching statements, pdfs of materials, videos of lectures you have given, and you can also collect endorsements
- Do teach during your PhD, and give as many talks as you can. Practice makes better. Practice, practice, practice
During the interview
- A typical academic interview takes two or one and a half days
- On the first day, often in the afternoon, you give your interview talk, which is probably the most important part of the interview
- In some places you will be asked to also give a (shorter but separate) vision talk, and occasionally you are asked to give a lecture on some topic
- The rest of the days is filled with one-on-one interviews. Interview days are exhausting: you have to be on the ball all the time
- If you have not been asked to give a vision talk, your interview talk must contain vision as well. An interview talk is not the same as a typical seminar talk. you cannot just discuss one part of your thesis in detail. You really must spend some time talking about your general passions, your ideas for future research, and help the audience put things in perspective.
- Remember that in an interview talk you must tailor your talk to the audience. Who will attend? Do you have connections to the audience? Are their overlaps in interest? Can you relate your work to what’s done in the department you are visiting? Will there be people from outside the department (most search committees have outside faculty also and these people may not at all be familiar with your research area)? Can you jump straight into details or should you give a general intro first? All these things are important to think about. The main thing to remember is: at the end of the talk, the audience must know what you like to work on, what you accomplished thus far, why you like this area so much, they must see passion, they must be convinced that you understand the general research area well and know what other people are working on, they must see vision and understand where this research is going and why
- In the talk and interviews also stay pleasant, enthusiastic, listen well and be patient when answering questions (even if you get the same question in ten different discussions). After all, the committee/department wants to find out if they like the idea of having you as a colleague for many years to come
In a next Watzegtzenou, some thoughts on how to write effective research and teaching statements
Added talks and books