Mathman's Retrospectives: Applying to Math PhD Programs

 

For this blog, let's take a brief break from making silly blogs about topology and graph theory and focus on the math PhD application process!

Hopefully, as someone who has just applied and gotten into a couple of math PhD programs, I can give my few nuggets of wisdom to you. While I could ramble all day about the process, I'll try to limit myself to 10 pieces of advice. 

As you read this, keep in mind that you should take all my advice with a grain of salt and every applicant's experience is different! Additionally, there is no standard way that a math department conducts their PhD admissions, so any of this advice could not be true for some departments. Anyways, I will split my general advice into 3 sections: applying to grad school, the grad school cycle, and deciding your future.

Applying to Grad School

Advice #1: Don't look for schools until you figure out the areas of research that you want to focus on!

Before you run off to find schools to apply to, you need to at least figure out the areas of math you want to research first. Unlike undergrad, the PhD is all about research once you get your coursework out of the way, so going to a program with research you want to pursue is extremely important. Take some time to thoroughly explore your interests. You want to do more theoretical work or try to be more interdisciplinary? If you like applied math research, what fields (like biology, chemistry, physics, etc.) do you want to focus on? All these questions are valuable to figuring out the schools that you would be a good research fit for. 

Advice #2: Only apply to schools that have at least three professors in your research area.

This is a classic piece of advice that always gets thrown around that I think is true! While researching schools, try to find three active professors that take on PhD students that are within your research area. After all, you want to have a few options for potential advisors in just case your dream advisor isn't taking students (or is a terrible advisor). Additionally, these application committees are looking for students are are a great research fit for the department. So, if you mention research areas in your statement of purpose that aren't the departments specialty, they will most likely reject you in favor of students that are a better fit. 

Advice #3: Only apply to schools that you actually want to go to...

While this may seem like obvious advice, first time applicants like me may fall back to the college application mindset of applying to "safety schools". While there are PhD programs that will be easier to get into than others, there is no such thing as safety schools! For pretty much any funded PhD program, there are hundreds of applicants fighting for a small amount of fully funded positions.

Given this, there is a decent chance that you might only get into one program. So, make sure that whatever program that is, it will be a school that you would be excited to go to. You don't want to be in a situation where you have to decide to either go to a school you hate or apply again next year.

The Grad School Cycle (December-April)

Now that you've submitted your application, the long wait begins...

Advice #4: Don't check your email/application portals/GradCafe every 10 seconds...

Believe me, the moment you press submit on your first application, any emails you receive will give you a mini heart attack. However, nothing good ever comes from checking. Even though I checked my email countless times a day, all my grad school decisions arrived when I wasn't looking. 

While I'm dooming you to look because I'm mentioning it, don't look at GradCafe or the Mathematics GRE forum. While both of those sites seem great at the surface because people post when they hear back from schools and sometimes their application profiles, but it's not worth it. It will give you nothing but anxiety when you realize that other applicants have heard back from a school that you've applied to. Just live in ignorance. I know you won't listen, but don't forget that I've told you so. If you really want to look, I will admit that both sites are useful for figuring out when the schools you're applying to release decisions in general and what profiles applicants have when accepted. However take everything posted there with a huge grain of salt. 

Advice #5: There will be a long silence. Don't think too much about it.

While the rest of the world moves at the speed of light, academia reviews and makes decisions at a snail's pace. There's several factors to why (professors are busy, waiting for funding, etc), but don't expect a speedy response. While the year I applied was a bit of an outlier (programs in general took longer to release decisions), expect to wait until at least the end of January to February on average for those first waves of decisions. I recommend to find a hobby to fill the void of waiting. I painted a lot of paintings...

Advice #6: Rejections will hurt and you will take it personally. Please don't.

I received 7 rejections, and the first few of those rejections were hard to emotionally manage. In my mind, those committees must of looked at my application and laughed at how dumb I was to apply there before throwing it in the bin.

Spoiler alert: It's not that personal. Those professors have to flick through hundreds of applications and somehow narrow it down to less than a dozen spots. Plus every math department at different schools are picking applicants based on what the department needs. Maybe the math department you applied to accepted too many applicants in your research area last year, or maybe the professor you wanted to work with is only accepting one student. As you can imagine, all of these factors make applying to grad school like gambling. So, don't be too hard on yourself if you don't get in.

Deciding Your Future

Getting acceptances are amazing, and you should celebrate whenever you get one. However, after you are done celebrating, you should take a closer look at that funding package.

Advice #7: If you were accepted to a PhD program without guaranteed funding, run away.

Even if your PhD offer letter has funding, definitely check if that funding is guaranteed for 5 years and if funding is guaranteed if your advisor somehow loses funding. Doing a PhD is enough stress already, suddenly losing all your funding is a nightmare. 

Additionally, if you were accepted into a PhD program and you get no funding, RUN AWAY. 

Advice #8: Not all funding looks the same.

While every school is different, and some just offer a general stipend, many schools create stipends with different types of funding. There are usually three types of funding offered to you: TA funding, RA funding, and fellowships.

TA funding: Every program is different, but being a TA (teaching assistant) usually involves some sort of mix of grading, tutoring, teaching recitation sections, teaching classes, etc for a certain amount of hours a week. If you are offered a TAship, look into the typical workload for a TA. While this is valuable experience if you want to become a professor, it also eats away at any time spent doing research/classes. 

RA funding: RA stands for research assistantship, and is usually provided by your advisor. As the name implies, you are funded to do research on the particular project they are funding you for.

Fellowships: Fellowships are a sacred type of funding. While every fellowship is different, usually there isn't a necessarily a "service" you have to provide to the university in return. If you are offered a fellowship, keep that in mind when you choose between your offers. 

Advice #9: Try to visit the school if you can!!!

If it is possible (and the school funds your visit), please go! Going to visits allows you to get a brief close look into what the program is like, and could give you valuable insight into whether or not this program is right for you. While every applicant has different priorities, you want to hopefully end up with a program that is supportive and is will provide a fulfilling experience. 

Advice #10: Cost of living is a thing, make sure you don't have to live with 12 roommates.

That's a bit of an exaggeration, but 20k stipend in NYC is very different from a 20K stipend in rural Illinois. While no stipend will allow you to live like a king, talk to the grad students and see how comfortably they live on their stipend. While there's a pretty good chance that you have to live with a roommate, make sure that the school doesn't provide a stipend that forces you to live in a cardboard box.

Conclusion:

There is so much more to talk about, but I didn't want to overload you with too much information. I hope that these small pieces of wisdom don't scare you away from pursuing a PhD if you want it, but I hope that helped give a clearer picture on the application process! If you decide to apply to PhD programs, good luck!