In this post, I will talk about the three most important parts of applying to grad school: choosing schools to apply to, writing the personal statement, and letters of recommendation. There are other components that go into the application, but there is not much to say about them. If you are an early undergrad interested in what you should do in order to be a strong applicant for grad schools in the future, then you should see this blog post instead.
Choosing schools to apply to
There are many things to consider while applying to grad school: location, research interests, faculty, graduate students, overall environment, etc. It can be super overwhelming to factor all of these into your decision making progress while coming up with a list of schools. In this section, I will talk about how to start forming a list of schools to apply to, how to choose which schools it makes sense to apply to, and how to choose a school once you are accepted!
First, we will discuss how to form a list of schools to apply to. If you are interested in applying to math PhD programs, then you have probably done some sort of research (maybe an REU or honors thesis or independent study with a professor). If you enjoyed the research you did, then a great place to start is by meeting with your REU mentor or honors thesis advisor or independent study professor to discuss what schools you should apply to. These professors know many people in their field and can best advise you on where to go if you’re interested in continuing similar work to what you did with them. If you have an idea of what area of math you’re interested in, then that’s even better. These professors know people in other fields and can put you in contact with professors who have similar interests and can guide you. This was definitely what helped me the most with compling a list of schools to apply to. It is also helpful if you can speak with someone at your school about where to apply to, because they might have a list of math PhD programs that students from there often get admitted to. This did not apply to me since no one from my school had gone to a math PhD program, but it is advice that I heard Keith Conrad say, so I figured I would mention it.
Fortunately, I knew I was interested in algebra/number theory, so after my number theory REU’s, I met with my mentors to discuss which schools I should apply to. My REU mentors and honors thesis advisor each gave me a list of schools that have strong algebra/number theory programs and also listed a few names of faculty who’s work I might be interested in. Of course there are many schools scattered all over the US that have can have good algebra/number theory programs, so this is where we have to start taking other things into account, like location for example. I preferred to stay on the East Coast so that I could be close to my family and easily come back to visit on holidays. This helped me narrow down the list of schools to consider a lot. I searched up each school from the list of schools that my advisors gave me and did thorough research on the algebra/number theory departments. I made sure that there were at least 2-3 professors that I would be interested in working with and that look like they are taking students. I also checked to see if the schools had an algebra/number theory seminar or reading group for grad students.
Some other things to take into account are: does the program seems competitive in a negative/positive way? Do the grad students get along? Do the faculty treat the students well? What is the TA work load like? Most of these questions are best answered by speaking to someone at the school. If you are considering going to a school, then feel free to email a grad student or professor asking to meet and discuss some of these things. In my experience, grad students tend to be the most honest and accurate about what the overall environment is like. They also tend to have the inside scoop on what’s going on, if anything is going on.
When choosing which school you will attend, you want to make sure you get to visit and speak to other people there. You are going to be living there for at least five years, so it’s super important that you like it there and will be happy in that environment. Personally, I would not pay too much attention to the rankings of schools. If there is a school that has people you want to work with who are publishing papers and doing well in their field, then that’s where you should go. It’s possible that a higher ranked school might not have anyone in your field who you want to work with, so at the end of the day, the rankings don’t mean too much. If anything, it probably matters more who you work with than where you go.
Overall, this is a very brief summary of what you should do:
- Speak to a professor you have done research with about which schools you should apply to.
- Determine where you are willing to go geographically and consider the schools in the locations you would go to.
- Research each schools math PhD department and make sure there are at least 2-3 professors you would be interested in working with, who are still doing research and taking students.
- Reach out to current grad students and professors to get more information about the program and environment.
- Visit and decide whether you would be happy there!
Writing the personal statement
The personal statement for grad apps can vary based on the application, but the format can be more or less the same. I am not sure what the best way to write a personal statement is, but I can share what I did. First, I stated which school I was applying to and what my mathematical interests were. I briefly stated how I became interested in math. I then talked about my undergrad experience and tried to show that I was self-motivated and constantly looking for opportunities to do more math, such as the REU’s I did, my study abroad in Budapest, and writing an honors thesis. It’s important to show, not tell the readers that you are passionate about math. I then, in a little more detail, described the research I did in my REU’s and honors thesis, and shared that I felt like I belonged in a research career and explained why. I also elaborated a bit on how I became interested in number theory and arithmetic geometry. Then I wrote a paragraph that specifically explained why I thought the school was a good fit for me and mentioned the faculty I was interested in working with and why. This part was easy to do after having researched the school beforehand, as mentioned in the previous section. I then concluded by stating why I think the school would help me thrive as a mathematician.
Overall, you want to make sure you express a few things:
- What areas of math you might be interested in studying.
- How you became interested in math and what you like about the areas you’re interested in.
- Past research you have done and what you learned/what skills you gained.
- Why the school would be a good fit for you and how you could contribute to the school’s program.
- Who you may be interested in working with if you are accepted. I think this helps schools realize that you took the time to really look into the program.
Letters of recommendation
Believe it or not, this is one of the most important parts of the application. Typically, you are allowed to submit 3 letters of recommendations. You should choose people who know you well and can best speak about your potential. The perfect people to ask for letters of recommendations are REU mentors, honors thesis advisors, professors who you’ve done independent studies with, or professors who you have taken difficult classes with and did well in and who have gotten to know you. It’s important to have at least one letter writer be able to speak on your ability to do research since that is a huge part of what you will be doing in grad school. It’s also important to have at least one letter writer who knows you well and can speak on your ability to work hard and ask questions. Ideally, your letter writers should be people who know you well and who you have worked with in some capacity, because they will have the best things to say.