Considering Grad School

Why do a PhD in Math?

• Interested in a career in academia.
• Demonstrates your ability to do “hard problems”.
• It’s helpful for fInance, data science, coding, web design, operations research.
• About half of PhD students have remained in academia and half have entered industry.
• You have to be prepared to not be the smartest in your class anymore; there’s a huge ramp up in difficulty and speed, and you have to be aware of that to make the right decision.

What else did you consider?

• Both PhD students focused on applying to graduate school.
• The timing works out in such a way that if you get rejected from all your graduate programs, you’ll still have plenty of time to focus on job applications.

What’s the closest you got to dropping out, and why didn’t you?

• The COVID-19 year, and an advisor who was invested in her and helped her through the low point.
• The prelims: answering just one question on a five-question exam, and being part of a community and realizing that it wasn’t just them struggling.

What’s the happiest you’ve felt during grad school?

• Once I started working as a teaching assistant and realized that I was having an impact on students.
• When I was doing my first solo research problem, I had basically completed the problem up to some very tiny ridiculous computation that took me like 3 months. Finally solving that was the happiest I’ve been in grad school. All of the work that went into that final moment made it very rewarding. There will be a lot of grinding, hitting your head into the wall, for a little bit of success that is rewarding because it post-hoc justifies all the work you did.
• I did my qualifying exam on my original research rather than another paper, and my advisor Steve said he was proud of me.

Do you have to do math all the time? How much do you have to love it?

• You have to find your own level. There are people who fall asleep thinking about math and wake up thinking about math. But there are also people who have a wide variety of interests; it’s a common rule to refuse to do math after dinner. You should love math, but loving other things isn’t disqualifying in the slightest!

Applying to Programs

What does a typical application process look like?

• Many of the deadlines are around mid-December to January 1st.
• Some colleges will require both the general GRE and the Math Subject test, but some will require only the latter or even none.
• You need 2-3 letters of recommendation, and you
• One might also apply for the NSF fellowship, but it’s not typical to get it.

Letters of Recommendation

How do you choose letter-writers? What makes a good letter?

• People who know you ideally both as a student and as a researcher (though one or the other can be sufficient), and can speak to your capbilities in those areas.
• Doing reading courses is a great way to develop the relationship needed for a superb letter of recommendation.
• An aphorism: pick the person who you have spoken to the most outside of class.
• Don’t ask a professor who you haven’t interacted with (even if you did well) because even with excellent grades, there’s no meaningful thing that they can say. They will do fine with the generic part of the letter, but the real value-added is in the very specific and unique things that the letter-writer can say. Who are you? What can you do?
• The first two things that admissions officers look at are (1) grades in core math classes and (2) letters of recommendation.

When should you ask people for letters of recommendation?

• September is a good time to ask.
• Definitely at least a month or more than a month before the deadlines.
• It’s better to ask as soon as possible not just to avoid deadlines, but also so that interactions are fresh and ongoing, which makes the specificity aspects easier.

Adding to Your Resume

Given that I’m doing research programs such as an REU, how important is it to do a senior thesis?

• The answer depends on what letters you’re going to have: you can get a great letter-writer from a senior thesis, but if you have excellent letters anyways it might be fine.

Should I reach out to professors at places where you’re applying, and if so, when?

• It can be a good idea because you can get an idea of if professors are retiring, moving, not taking students, etc. This can be useful both before and after professors are being accepted.
• One substitute for this is using the word-of-mouth information that a faculty mentor has, but there’s still some value in writing to professors. It’s unlikely to boost your application by a lot, but it could make them look at your file.
• Thus, emailing people right after your application is submitted could be a useful approach.
• Northwestern gets about 350 applications for 15 spots (which is a 4.3% acceptance rate).

Choosing Programs

How do I choose where to study?

• Ask someone who knows you well (e.g. letter writer or faculty mentor) where you think will be happy?
• Think about the various aspects of the programs that are appealing to you: size is a major one, so is the location, so is the number of people at the university which are exploring topics that you’re interested in.
• It’s important to choose a department that has a number of people that you’re interested in, because if you fixate on one person, you can be screwed over by people leaving, retiring, dying, not taking graduate students at the time, changing interests, etc. ^bdc173

How do I choose what to study?

• There’s not much to go off of: just what classes you’ve enjoyed, and your research experiences, can be misleading (because graduate and professorial research is very different), but it’s also the only thing that you can use. See [[#^bdc173 |here]].
• Mention a concrete area in your personal statement, but it’s understood that you might change your mind; nobody will hold you to what you write, and that’s intentional. You won’t need to pick an advisor until your 2nd or 3rd year, and choosing that person is just as much a matter of personality as it is a matter of the very specific field that the advisor does.

You’ve been accepted. You’re visiting the campus. What should you look for?

• The location of the grad school. You’re not just studying here; you’ve living here.
• Talk to graduate students without faculty around. See if they’re happy even without hierarchical pressure to seem as such.
• Think about the size of the grad school. Some elite private schools are as small as 30 students, and some state universities have as many as 160 (e.g. at Berkeley). Consider the size of your cohort: if it’s much smaller than 10, there’s a lot of pressure to get along with those specific people.
• Look for opportunities to teach. Even though most of your time will be doing research (keep in mind that this is your full-time job), these can be very rewarding.

What will it be like?

• You’ll start out taking classes and preparing for the qualifying exams. However, once you pass your quals, you often don’t have to take classes anywhere. You’ll still be doing TA-ships, but you’re going to need to learn to structure your time. Set yourself deadlines, attend seminars, etc. to provide scaffolding around which you can organize.
• You’re not going to be identifying as a student anymore. Your priorities will be up to you. The independence can be a great blessing or an awful curse. You’ll need to get better at dealing with procrastination, because you don’t have external deadlines as a motivator anymore.
• There are, of course, all the elements of being an adult. Importantly, you’ll have to put more work into keeping in contact with your friends and making new ones.