How to get into a top Ph.D. program?

Forum for the GRE subject test in mathematics.
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z2xz2
Posts: 23
Joined: Sun Feb 11, 2024 3:24 pm

How to get into a top Ph.D. program?

Post by z2xz2 » Fri Feb 23, 2024 3:08 am

Does anyone know of anyone who’s gone from an unknown undergraduate/masters university to a top 15 Ph.D. program?

What did their application look like if so? Is it even worth trying to apply to such highly ranked schools?

fear_of_sheep
Posts: 7
Joined: Mon Jan 29, 2024 8:47 am

Re: How to get into a top Ph.D. program?

Post by fear_of_sheep » Fri Feb 23, 2024 11:06 am

I think trying to make your goal "top 15 PhD program" is a bad idea. I think instead you should ask yourself "how can I become the best mathematician I can?" This reframing is useful, because both questions have the same answer, but if you implement that answer motivated by getting into a top 15 phd program and do not get into one, you will probably be sad; but if you implement that answer thinking the goal is to just become better at math, then when you become better at math you will be happy, even if your PhD results disappoint you slightly.

The best way to become better at math as an undergraduate is to:
1. Take the most difficult coursework you can, and understand everything in your courses perfectly. As a corollary do not take a course you're not ready for -- if you lack prerequistes that are so extreme that you think you couldn't master everything in that course, then I would hesitate to suggest taking it.In In particular, at a lower ranked undergraduate instiution, I imagine this means being permitted to take upper level proof based electives as soon as possible. This is one of the main advantages people at fancier schools ahve -- students at Harvard are often allowed to learn analysis or abstract algebra in their first year, which is very helpful for their development. This is not essential to becoming a mathematician, but you should try to learn the foundational subjects of modern math quickly.
2. Study broadly -- take courses in real analysis, complex analysis, point-set topology, and abstract algebra.
3. Try to occupy yourself mathematically over the summer -- the most common way is doing an REU or some sort of reading course with a professor at your university, but if you do not get into one of those, try to find ways to study by yourself.
4. Talk to as many mathematicians as you can; in particular, go to your course's office hours as much as possible.

z2xz2
Posts: 23
Joined: Sun Feb 11, 2024 3:24 pm

Re: How to get into a top Ph.D. program?

Post by z2xz2 » Fri Feb 23, 2024 12:48 pm

deleted
The number was arbitrary. I just meant generally what people believe to be some of the top schools.

z2xz2
Posts: 23
Joined: Sun Feb 11, 2024 3:24 pm

Re: How to get into a top Ph.D. program?

Post by z2xz2 » Fri Feb 23, 2024 12:51 pm

fear_of_sheep wrote:
Fri Feb 23, 2024 11:06 am
I think trying to make your goal "top 15 PhD program" is a bad idea. I think instead you should ask yourself "how can I become the best mathematician I can?" This reframing is useful, because both questions have the same answer, but if you implement that answer motivated by getting into a top 15 phd program and do not get into one, you will probably be sad; but if you implement that answer thinking the goal is to just become better at math, then when you become better at math you will be happy, even if your PhD results disappoint you slightly.

The best way to become better at math as an undergraduate is to:
1. Take the most difficult coursework you can, and understand everything in your courses perfectly. As a corollary do not take a course you're not ready for -- if you lack prerequistes that are so extreme that you think you couldn't master everything in that course, then I would hesitate to suggest taking it.In In particular, at a lower ranked undergraduate instiution, I imagine this means being permitted to take upper level proof based electives as soon as possible. This is one of the main advantages people at fancier schools ahve -- students at Harvard are often allowed to learn analysis or abstract algebra in their first year, which is very helpful for their development. This is not essential to becoming a mathematician, but you should try to learn the foundational subjects of modern math quickly.
2. Study broadly -- take courses in real analysis, complex analysis, point-set topology, and abstract algebra.
3. Try to occupy yourself mathematically over the summer -- the most common way is doing an REU or some sort of reading course with a professor at your university, but if you do not get into one of those, try to find ways to study by yourself.
4. Talk to as many mathematicians as you can; in particular, go to your course's office hours as much as possible.
Thank you for your response. I completely agree.

MonsieurGalois
Posts: 8
Joined: Wed Jan 10, 2024 8:05 pm

Re: How to get into a top Ph.D. program?

Post by MonsieurGalois » Fri Feb 23, 2024 5:21 pm

I’ve only been waitlisted at a T15 so definitely take my opinion with a grain of salt! However, my undergraduate degree was from an international university that doesn’t even appear on most math ranking websites, and my master’s, while at an Ivy, is just coursework in CS so totally irrelevant. I would say that the single most important thing you need to do, other than the obvious such as perfect grades in the most advanced courses possible, is to strategically pick your REUs and senior thesis in areas that are currently popular in T15 institutions, and ideally under supervisors whose names some of the faculty at T15s will recognize. Note that the two points are actually self supporting in some sense since, if you do all your undergrad research in areas that aren’t popular in T15 institutions, it’s unlikely that the faculty at these institutions will have ever had a reason to read a paper from your supervisor working in that area. One of the main reasons why choosing REUs that align well with the faculty research interests at T15 institutions is so important, other than getting LoRs from supervisors who are more likely to be known by the faculty, is that your REUs and undergraduate thesis will form the core of your SoP. And, assuming you have perfect grades in tough courses and great LoRs, your SoP will end up becoming very important when coming from a no name school since what you’re really trying to do when applying is to gain the support from as many of the graduate committee faculty members as possible - a much easier task if most of the faculty members are familiar with the areas of research you talk about in your SoP and are therefore able to get a sense of how deeply you went into each of these topics and how much potential the research demonstrates about your ability to complete a PhD at a T15 standard. In saying all of this, I wasn’t really able to follow my own advice due the lack of mathematicians working in such areas in my country. Instead, I did most of my research in operator algebras, topological K-theory and Khovanov homology. Maybe my waitlist at UChicago would’ve been an admit if my REUs were more relevant :lol: Best of luck in preparing for your applications!!

z2xz2
Posts: 23
Joined: Sun Feb 11, 2024 3:24 pm

Re: How to get into a top Ph.D. program?

Post by z2xz2 » Sat Feb 24, 2024 3:07 am

MonsieurGalois wrote:
Fri Feb 23, 2024 5:21 pm
I’ve only been waitlisted at a T15 so definitely take my opinion with a grain of salt! However, my undergraduate degree was from an international university that doesn’t even appear on most math ranking websites, and my master’s, while at an Ivy, is just coursework in CS so totally irrelevant. I would say that the single most important thing you need to do, other than the obvious such as perfect grades in the most advanced courses possible, is to strategically pick your REUs and senior thesis in areas that are currently popular in T15 institutions, and ideally under supervisors whose names some of the faculty at T15s will recognize. Note that the two points are actually self supporting in some sense since, if you do all your undergrad research in areas that aren’t popular in T15 institutions, it’s unlikely that the faculty at these institutions will have ever had a reason to read a paper from your supervisor working in that area. One of the main reasons why choosing REUs that align well with the faculty research interests at T15 institutions is so important, other than getting LoRs from supervisors who are more likely to be known by the faculty, is that your REUs and undergraduate thesis will form the core of your SoP. And, assuming you have perfect grades in tough courses and great LoRs, your SoP will end up becoming very important when coming from a no name school since what you’re really trying to do when applying is to gain the support from as many of the graduate committee faculty members as possible - a much easier task if most of the faculty members are familiar with the areas of research you talk about in your SoP and are therefore able to get a sense of how deeply you went into each of these topics and how much potential the research demonstrates about your ability to complete a PhD at a T15 standard. In saying all of this, I wasn’t really able to follow my own advice due the lack of mathematicians working in such areas in my country. Instead, I did most of my research in operator algebras, topological K-theory and Khovanov homology. Maybe my waitlist at UChicago would’ve been an admit if my REUs were more relevant :lol: Best of luck in preparing for your applications!!
Thanks for the response! I think you made good points but I wouldn’t say my school has anybody who has the kind of name recognition you mention.

Also, I plan to start a funded masters program soon. Do you have similar advice since I’m no longer an undergrad (so can’t participate in REU’s)?

fear_of_sheep
Posts: 7
Joined: Mon Jan 29, 2024 8:47 am

Re: How to get into a top Ph.D. program?

Post by fear_of_sheep » Sat Feb 24, 2024 10:59 am

MonsieurGalois wrote:
Fri Feb 23, 2024 5:21 pm
I’ve only been waitlisted at a T15 so definitely take my opinion with a grain of salt! However, my undergraduate degree was from an international university that doesn’t even appear on most math ranking websites, and my master’s, while at an Ivy, is just coursework in CS so totally irrelevant. I would say that the single most important thing you need to do, other than the obvious such as perfect grades in the most advanced courses possible, is to strategically pick your REUs and senior thesis in areas that are currently popular in T15 institutions, and ideally under supervisors whose names some of the faculty at T15s will recognize. Note that the two points are actually self supporting in some sense since, if you do all your undergrad research in areas that aren’t popular in T15 institutions, it’s unlikely that the faculty at these institutions will have ever had a reason to read a paper from your supervisor working in that area. One of the main reasons why choosing REUs that align well with the faculty research interests at T15 institutions is so important, other than getting LoRs from supervisors who are more likely to be known by the faculty, is that your REUs and undergraduate thesis will form the core of your SoP. And, assuming you have perfect grades in tough courses and great LoRs, your SoP will end up becoming very important when coming from a no name school since what you’re really trying to do when applying is to gain the support from as many of the graduate committee faculty members as possible - a much easier task if most of the faculty members are familiar with the areas of research you talk about in your SoP and are therefore able to get a sense of how deeply you went into each of these topics and how much potential the research demonstrates about your ability to complete a PhD at a T15 standard. In saying all of this, I wasn’t really able to follow my own advice due the lack of mathematicians working in such areas in my country. Instead, I did most of my research in operator algebras, topological K-theory and Khovanov homology. Maybe my waitlist at UChicago would’ve been an admit if my REUs were more relevant :lol: Best of luck in preparing for your applications!!
From what I've heard, I am unsure if SOP is all too important -- I am not sure if it's looked at closely by many people. I think you're right that what does matter is getting good letters from mathematicians who people at a t15 know about.

MonsieurGalois
Posts: 8
Joined: Wed Jan 10, 2024 8:05 pm

Re: How to get into a top Ph.D. program?

Post by MonsieurGalois » Sat Feb 24, 2024 5:39 pm

z2xz2 wrote:
Sat Feb 24, 2024 3:07 am
Thanks for the response! I think you made good points but I wouldn’t say my school has anybody who has the kind of name recognition you mention.

Also, I plan to start a funded masters program soon. Do you have similar advice since I’m no longer an undergrad (so can’t participate in REU’s)?
I think when you come from an unknown school, it helps to get research experience at other, more well known, institutions whenever possible. In fact, my research experience was spread across three different universities and two different countries, none of which were from my undergraduate institution. Although, in saying this, a friend of mine who did his undergraduate and master’s at my undergraduate institution was admitted to Minnesota recently and that was the only place he applied. He had a couple publications, I think one of which was published in the Proceedings of the American Mathematical Society. So I guess if you do stay at the same place, getting a publication in a good journal will definitely help!

One thing to keep in mind about doing a master’s degree in math is that completing a master’s won’t necessarily increase how competitive your application is in the US. A great example of this is June Huh - a recent Fields medalist who, as a journalism major, stumbled into studying mathematics while attending the lectures of a visiting Fields medalist, Heisuke Hironaka, whom he was hoping to interview. He ended up befriending Hironaka and completed a master’s degree under his supervision. And yet, despite having a very strong LoR from a Fields medalist, he got rejected from everywhere he applied to in the States except for UIUC due largely to his undergraduate transcript. In saying this, there’s plenty of fantastic universities outside of the States where a master’s degree is a prerequisite for a PhD, so don’t let this paragraph deter you from pursuing your master’s!

KovenFan
Posts: 4
Joined: Sun May 21, 2023 2:22 am

Re: How to get into a top Ph.D. program?

Post by KovenFan » Tue Mar 05, 2024 12:52 am

Even if you solve RH, you have no chance of getting into top 15 if you don't come from a fancy school.

greenface1998
Posts: 22
Joined: Wed Feb 21, 2024 7:02 am

Re: How to get into a top Ph.D. program?

Post by greenface1998 » Tue Mar 05, 2024 1:25 am

KovenFan wrote:
Tue Mar 05, 2024 12:52 am
Even if you solve RH, you have no chance of getting into top 15 if you don't come from a fancy school.
Thus is a very silly take. Take a look at the current PhD students of top schools. There’s no shortage of people who didn’t come from top 50 undergrad programs.

superfluousviolinist
Posts: 4
Joined: Wed Jan 10, 2024 1:53 am

Re: How to get into a top Ph.D. program?

Post by superfluousviolinist » Tue Mar 05, 2024 11:11 pm

Though Huh had a strong LOR, but he apparently didn't get good grades even as a master's student. https://www.quantamagazine.org/a-path-l ... -20170627/

MonsieurGalois wrote:
Sat Feb 24, 2024 5:39 pm
z2xz2 wrote:
Sat Feb 24, 2024 3:07 am
Thanks for the response! I think you made good points but I wouldn’t say my school has anybody who has the kind of name recognition you mention.

Also, I plan to start a funded masters program soon. Do you have similar advice since I’m no longer an undergrad (so can’t participate in REU’s)?
I think when you come from an unknown school, it helps to get research experience at other, more well known, institutions whenever possible. In fact, my research experience was spread across three different universities and two different countries, none of which were from my undergraduate institution. Although, in saying this, a friend of mine who did his undergraduate and master’s at my undergraduate institution was admitted to Minnesota recently and that was the only place he applied. He had a couple publications, I think one of which was published in the Proceedings of the American Mathematical Society. So I guess if you do stay at the same place, getting a publication in a good journal will definitely help!

One thing to keep in mind about doing a master’s degree in math is that completing a master’s won’t necessarily increase how competitive your application is in the US. A great example of this is June Huh - a recent Fields medalist who, as a journalism major, stumbled into studying mathematics while attending the lectures of a visiting Fields medalist, Heisuke Hironaka, whom he was hoping to interview. He ended up befriending Hironaka and completed a master’s degree under his supervision. And yet, despite having a very strong LoR from a Fields medalist, he got rejected from everywhere he applied to in the States except for UIUC due largely to his undergraduate transcript. In saying this, there’s plenty of fantastic universities outside of the States where a master’s degree is a prerequisite for a PhD, so don’t let this paragraph deter you from pursuing your master’s!



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