Profile Evaluation

[nicole2]

Hey everyone, I wanted to get some second opinion about the strength of my profile and which programs I would get into.

(See viewtopic.php?f=1&t=4950#p21850)

My adviser told me that I should be able to get into about half of these programs. So, which schools should I remove on this list to save myself on unnecessary fees? The deadlines are approaching I need to apply soon.

Help and feedback would be appreciated!

[nicole2]

Can someone provide me with some honest insight and advice?

[Integreat]

I think this really depends on what area you want to go into. I'd probably only consider the following if I were you:

Brown, Cornell, NYU, Carnegie Mellon, UW Madison, Minnesota, UIUC, UIC

But that's just based on the info you've provided. Again, depending on what area you like, you should adjust this accordingly.

[PhilippMainlander]

You have a lot of really really good schools on that list. I'm not saying you shouldn't apply to them, you should if you have the money, but also understand that people with better 'objective' stats than you have trouble getting into those schools. You should perhaps add more schools lower on the US news ranking(not an objective measure) unless you are adamant about going to those programs you have listed.

[jimmy]

Since your school is relatively unknown, the rigor of your courses may be questioned. Also, your mGRE score may be too low for schools you are applying for, which doesn't help. With this list, it's very likely you end up getting into nowhere. You should apply very broadly by adding some schools outside of top 50.

[nicole2]

hmmmm my advisor told me even though my scores and profile is weak I have a high chance of getting into at least 1 of them because I am a female so she told me I don't have to any 'safety schools'. What safety schools do you guys suggest, I want to do combinatorics or geometry.

[Cyclicduck]

University of Minnesota - Twin cities has a strong combinatorics program, including combinatorial algebraic geometry.

[ponchan]

All of the schools you've listed are extremely competitive, even for people with great mGRE scores, graduate coursework from top universities, and publications. Ask yourself this: If none accept you, would you be ok with waiting another year and reapplying to schools, perhaps after retaking the mGRE? If not, seriously consider applying to schools in the 50-150 range. Also, I am a bit confused by what you consider a "safety school". Safety might mean beyond 125 or so, not 35. With your current list, I'd say UIC and Minnesota are a reach and the others are "beyond reach". Even as a female, without (grad) coursework from a well-known university, you'd need a much higher mGRE score. I think your professor is doing you a disservice. You can look at the US News list, google the departments, and see which ones have people in the areas you're interested in. You should also look through the wealth of data on this site; the results of students from previous years can tell you what sort of schools people with your background have been accepted to. If you are interested in combinatorics, another obvious choice would be Michigan State (Bruce Sagan), which certainly is not a safety, but is reasonable. Emory has a great combinatorics program and doesn't even accept the mGRE. Again, still a competitive program, but you wouldn't be penalized for a low mGRE score. You might check out Syracuse as well.

[jimmy]

With your current profile, your chances of getting into Minnesota is almost nil, and I wouldn't waste money applying to schools above Minnesota. You should know that even as a female the competition is stiff, and no one gets in because he/she is lucky. The only school that you may have a shot at in your list is UIC.

[PhilippMainlander]

OP. You should listen to your advisor, but you should inform yourself by looking at the admissions thread and TheGradCafe.com. No one here can tell you where you can get in and what your chances are. Everyone here at best can guess, and their guesses could be totally wrong or maybe right? if you want to form an objective opinion then you are going to have to look at TheGradCafe.com and the acceptances threads. Everyone here is as lost and clueless as you.

viewtopic.php?f=1&t=4555

Start here, use the search function and type the schools' names and judge for yourself.

[temporaryacct]

[deleted]

[nicole2]

My advisor said my profile is strong and by applying to top 20 programs at least one of them will accept me.

I have taken two semesters of advanced calculus and modern algebra. I am also getting a honors degree with a written thesis. My GPA is 4.0. She said there is no need to apply to inferior schools because I deserve better, also easier to get in because I am female. She said it's a luck game apply to top 20 basically guarantees at least 1 acceptance because what are the chances getting denied by 20 out of 20? Probability = 0.

[yeonK]

My advisor said my profile is strong and by applying to top 20 programs at least one of them will accept me.

I have taken two semesters of advanced calculus and modern algebra. I am also getting a honors degree with a written thesis. My GPA is 4.0. She said there is no need to apply to inferior schools because I deserve better, also easier to get in because I am female. She said it's a luck game apply to top 20 basically guarantees at least 1 acceptance because what are the chances getting denied by 20 out of 20? Probability = 0.

Well, I see that you have worked hard during your undergrad,
and it's impressive that you are finishing your thesis when you graduate. congrats for that.
But, I think it is still not a zero probability.
If the events are independent, and even if you suppose that the probability of getting a rejection is at most 90%, you still have more than 10 % probability of getting all rejected, which I think, is not negligible.
Also, no one can guarantee one's probability of getting admission from such good schools.
There are many competitive applicants all over the world.
Good luck with your application anyways.

ps. I hope you are not someone who hates female applicants, pretending to be someone else. We call such people "intelligent anti-fan" in my country.

[ponchan]

My advisor said my profile is strong and by applying to top 20 programs at least one of them will accept me.

I have taken two semesters of advanced calculus and modern algebra. I am also getting a honors degree with a written thesis. My GPA is 4.0. She said there is no need to apply to inferior schools because I deserve better, also easier to get in because I am female. She said it's a luck game apply to top 20 basically guarantees at least 1 acceptance because what are the chances getting denied by 20 out of 20? Probability = 0.

Again, what information is she basing this on? Previous students from your program who have a similar profile? It seems you have taken the bare minimum to be accepted to any program, let alone a top 20. Have you met any grad students from places like MIT, Princeton or Harvard? Many of them have been taking graduate level coursework since high school. I'm not saying this to discourage you from applying to grad school; but you asked for advice. If there is concrete evidence from your advisor that you're not sharing with us, then perhaps we're missing something. Otherwise, you're interested in math, right? Then that means you're interested in things like proof and data. Well, this website and grad cafe have lots of data -- archiving acceptance outcomes of students over the last decade -- so that you may draw a conclusion yourself.

Saying you "deserve better" gives me pause. Are you interested in math or are you interested in telling people you go to a fancy school? If it's the latter, perhaps you should interrogate your motivations for wanting to go to grad school in the first place. People who do good work, regardless of the school they're at, will get job offers. There's evidence of this! And people who do mediocre work at top schools will be forced to leave academia (or, if they can't pass qualifying exams, will be kicked out of their programs). But putting blind faith in someone who says you will get accepted to a top 20 school, without knowing her reasoning, doesn't seem like a good idea. Good luck!

[jimmy]

My advisor said my profile is strong and by applying to top 20 programs at least one of them will accept me.

I have taken two semesters of advanced calculus and modern algebra. I am also getting a honors degree with a written thesis. My GPA is 4.0. She said there is no need to apply to inferior schools because I deserve better, also easier to get in because I am female. She said it's a luck game apply to top 20 basically guarantees at least 1 acceptance because what are the chances getting denied by 20 out of 20? Probability = 0.

I am not saying this to discourage you but unfortunately there is a quite high probability that you get rejected by all top 20 programs, even top 50 programs. Have you taken grad level analysis and algebra? You have the bare minimum background for math phd. As a Statistics PhD applicant from a well-known Canadian school, I have more coursework than you do. I have functional analysis/measure theory under my belt and am planning on taking a harmonic analysis course next term. All of my friends who got into top 20 Statistics PhD have similar background as mine. They all have strong gpa, grad level coursework, multiple research experiences and >80% mGRE and still got rejected by a lot of programs. My supervisor told me the competition was very stiff and even with my background she still suggested me apply to some schools ranked around 50 just to be safe. With that said, I am gonna assume math PhD demands more grad level coursework and your math background is not even sufficient for many Statistics PhD programs. This, along with your 500 (14th percentile) mGRE score, make your admissions to top 50 programs very unlikely.

[dujiahan]

Hey everyone, I wanted to get some second opinion about the strength of my profile and which programs I would get into.

Undergrad Institution: Middle sized state school. Not known outside of region.
Major(s): Mathematics
Minor(s): Computer Science
GPA: 4.00/4.00
Type of Student: Domestic White Female

GRE Revised General Test:
Q: 168 (89%)
V: 167 (93%)
W: 5.5 (91%)
GRE Subject Test in Mathematics:
M: 500 (I think 25%)

Program Applying: All Pure Math PhD

Research Experience: 1 REU and honors senior thesis
Awards/Honors/Recognitions: Deans lists, 'best undergraduate student in the department' award.
Pertinent Activities or Jobs: Work as a tutor, math club president.
Any Miscellaneous Points that Might Help: Senior thesis adviser is from Cornell.
Any Other Info That Shows Up On Your App and Might Matter: I was a mathematical education and switched to math major last year. We have a masters program but not a doctorate. My adviser's letter should be very strong.

Applying to Where: (Color use here is welcome)
Harvard
Princeton
MIT
Yale
Brown
Cornell
Stanford
NYU
Chicago
Carnegie Mellon
UW Madison
Minnesota
UCLA
UCB
UIUC
UIC

My adviser told me that I should be able to get into about half of these programs. So, which schools should I remove on this list to save myself on unnecessary fees? The deadlines are approaching I need to apply soon.

Help and feedback would be appreciated!

Even if you are a girl, your standard test scores are not good enough for schools like Harvard, unless you have extremely strong publications/recommendations/connections. It is true that UCB/UCLA sometimes accept girls with low test scores,
but 25% is probably too low.

[dujiahan]

hmmmm my advisor told me even though my scores and profile is weak I have a high chance of getting into at least 1 of them because I am a female so she told me I don't have to any 'safety schools'. What safety schools do you guys suggest, I want to do combinatorics or geometry.

I think you made a grammar mistake, you should have said "scores and profile are weak" not "is weak".

I wonder if your profile is fake, maybe you made this all up to confuse other people.

[ponchan]

They put Carnegie Mellon as a safety. This is a troll thinking they're being subtle.

[cc119]

nicole2, have you already got decisions from Chicago and Yale?

[dujiahan]

nicole2, have you already got decisions from Chicago and Yale?

Yes, she was rejected, I checked all her posts.

[MathParent]

nicole2, have you already got decisions from Chicago and Yale?

Yes, she was rejected, I checked all her posts.

Come on. Yale didn't announce the decisions yet. Neither did UChicago.

[MathParent]

nicole2, have you already got decisions from Chicago and Yale?

Yes, she was rejected, I checked all her posts.

I take it back. I guess, the institutions started to announce some obvious decisions, like obvious admits and obvious rejections.

[nicole2]

nicole2, have you already got decisions from Chicago and Yale?

Yes, she was rejected, I checked all her posts.

I take it back. I guess, the institutions started to announce some obvious decisions, like obvious admits and obvious rejections.

What are you trying to say? You aren't the first person that insulted me because of my gender, what is wrong with everyone. At school others joked about me getting As credited to (((fill in the blank here for nasty things people say about me being a female))) not actually because of my ability, even some professors mocked me for being slow at learning. And now even at an online math forum I am being stereotyped? It's only fair that we get easier admission for all the sexism we've been through.

[dujiahan]

Yes, she was rejected, I checked all her posts.

I take it back. I guess, the institutions started to announce some obvious decisions, like obvious admits and obvious rejections.

What are you trying to say? You aren't the first person that insulted me because of my gender, what is wrong with everyone. At school others joked about me getting As credited to (((fill in the blank here for nasty things people say about me being a female))) not actually because of my ability, even some professors mocked me for being slow at learning. And now even at an online math forum I am being stereotyped? It's only fair that we get easier admission for all the sexism we've been through.

Certainly no one should insult you, and sexism will not be tolerated.

I think people are just trying to say that even for girls, the competition is fierce, and maybe you will benefit by applying to schools like Syracuse. It is a good school, but easier to get in. Nevertheless, I wish you all the best.

[nicole2]

... maybe you will benefit by applying to schools like Syracuse. It is a good school, but easier to get in. Nevertheless, I wish you all the best.

It ranks 74, how is that a good school? I think I deserve to go to a better school with my credentials.

[MathParent]

... maybe you will benefit by applying to schools like Syracuse. It is a good school, but easier to get in. Nevertheless, I wish you all the best.

It ranks 74, how is that a good school? I think I deserve to go to a better school with my credentials.

Nicole. I think the guys here are concentrated on your Math GRE score, which is admittedly low, and may be even more on your words that "subject GRE is too hard." The problem is, subject GRE is NOT too hard for those who are good candidates to get into good schools, especially in **pure** math. If you were applying to Applied Math, I think it would have been a bit better, but you see, the guys who are easily getting scores of 700, 800, 850 - are looking at your score and can't just get it - why do you think you "have credentials" to get into any of the top schools? Truly, Math GRE covers basic math needed for a pure mathematician. Saying that it is too hard, bringing the score of 500, and being surprised why they (the guys here) advise Syracuse - I mean... You know... get realistic...!! And you know, I am a woman too. I had my share of everything. I got my PhD in Engineering, not in Math, but I do NOT think we, women, are entitled to just come and get a place at Harvard or whatnot, having a score that barely beats 25% of applicants... Sorry. If they admit you to a top school - good for you. I'll be happy for you, honestly. But it will be a fluke, in my book.

[ponchan]

If we're all being perfectly honest here, I'm not sure why we're speaking of Syracuse as if it's a shoe-in for her. It's not, and frankly it's an insult to Syracuse to say so.

[mathmcspirit]

There is no such thing as “deserving” to go to a school. The question is whether or not you will be realistically admitted, and by and large that is what these replies have reflected. Admissions committees are looking for a number of things when evaluating applicants, good GRE scores being one of them. When there are applicants with your same GPA, coursework, great research, and great GRE scores, likely those are who will be admitted before you. Further, there are plenty of women with the same or better credentials, so even at schools who are making real efforts to diversify their programs wrt gender (of which there are not as many as one would hope), the competition is stiff. Of course, none of us can know for sure, but based on previous years, I wouldn’t expect your anticipated outcome, regardless of whether or not you are a promising young mathematician.

Further, even at these programs that you seem to think are beneath you, there are fantastic professors that any young mathematician could learn a great many things from. That is not to say prestige doesn’t matter when it comes to opening certain doors, but it isn’t everything. I implore you to keep this in mind when talking about schools that many of us here would be thrilled to attend.

[nicole2]

I think I underestimated the difficulty of getting into these programs now, gonna drop couple unsubmitted and instead apply to some safeties instead as a plan b.

But I think my chances are not that bad, I did an reu, and currently writing a senior thesis with someone from Cornell and also have excellent GPA. Though you guys make a valid point - I should apply to some programs where I will certainly get in.

Sure I bombed the gre but they 'll probably think I am just a bad test taker. There are so many advanced topics on the gre that were simply not taught/exposed to undergraduates, like I was stuck on this one vector space and span question on the nov gre (probably due to stress, we are allowed over 2 hours to complete our linear algebra tests in school) and then this other question about some group thing which I've never heard until after the exam. Srs they shouldn't put so many graduate materials on the math gre we are not all putnam fellows. How do they expect us answer these questions in less than 3 minutes?

Syracuse doesn't require a gre!! Yay!!

[MathParent]

I think I underestimated the difficulty of getting into these programs now, gonna drop couple unsubmitted and instead apply to some safeties instead as a plan b.

But I think my chances are not that bad, I did an reu, and currently writing a senior thesis with someone from Cornell and also have excellent GPA. Though you guys make a valid point - I should apply to some programs where I will certainly get in.

Sure I bombed the gre but they 'll probably think I am just a bad test taker. There are so many advanced topics on the gre that were simply not taught/exposed to undergraduates, like I was stuck on this one vector space and span question on the nov gre (probably due to stress, we are allowed over 2 hours to complete our linear algebra tests in school) and then this other question about some group thing which I've never heard until after the exam. Srs they shouldn't put so many graduate materials on the math gre we are not all putnam fellows. How do they expect us answer these questions in less than 3 minutes?

Syracuse doesn't require a gre!! Yay!!

Good luck Nicole, it is a good idea to add safeties. As for GRE - it is my impression that none of the material is/was of the graduate level. `All of it is covered in the undergraduate courses that a **PhD candidate** is/was supposed to take.
I truly wish you get into a school you will enjoy studying at. I am rooting for you!

[nicole2]

I think I underestimated the difficulty of getting into these programs now, gonna drop couple unsubmitted and instead apply to some safeties instead as a plan b.

But I think my chances are not that bad, I did an reu, and currently writing a senior thesis with someone from Cornell and also have excellent GPA. Though you guys make a valid point - I should apply to some programs where I will certainly get in.

Sure I bombed the gre but they 'll probably think I am just a bad test taker. There are so many advanced topics on the gre that were simply not taught/exposed to undergraduates, like I was stuck on this one vector space and span question on the nov gre (probably due to stress, we are allowed over 2 hours to complete our linear algebra tests in school) and then this other question about some group thing which I've never heard until after the exam. Srs they shouldn't put so many graduate materials on the math gre we are not all putnam fellows. How do they expect us answer these questions in less than 3 minutes?

Syracuse doesn't require a gre!! Yay!!

Good luck Nicole, it is a good idea to add safeties. As for GRE - it is my impression that none of the material is/was of the graduate level. `All of it is covered in the undergraduate courses that a **PhD candidate** is/was supposed to take.
I truly wish you get into a school you will enjoy studying at. I am rooting for you!

Not sure if you're being sarcastic .... but thanks. I just want to succeed by going to a top school. I added Syracuse and Iowa as safeties.

Would you mind clarify as to why the materials on the math gre is not of graduate level?

Okay, if you people believe that I am being too ambitious, then doesn't that mean my advisor is purposely setting me up for failure by telling me I have an excellent chance of getting into these schools?

Also, what is the point of doing a PHD at a bottom tier school? I don't think there are any good mathematicians out there coming from tier 3 schools.

[dujiahan]

I think I underestimated the difficulty of getting into these programs now, gonna drop couple unsubmitted and instead apply to some safeties instead as a plan b.

But I think my chances are not that bad, I did an reu, and currently writing a senior thesis with someone from Cornell and also have excellent GPA. Though you guys make a valid point - I should apply to some programs where I will certainly get in.

Sure I bombed the gre but they 'll probably think I am just a bad test taker. There are so many advanced topics on the gre that were simply not taught/exposed to undergraduates, like I was stuck on this one vector space and span question on the nov gre (probably due to stress, we are allowed over 2 hours to complete our linear algebra tests in school) and then this other question about some group thing which I've never heard until after the exam. Srs they shouldn't put so many graduate materials on the math gre we are not all putnam fellows. How do they expect us answer these questions in less than 3 minutes?

Syracuse doesn't require a gre!! Yay!!

Good luck Nicole, it is a good idea to add safeties. As for GRE - it is my impression that none of the material is/was of the graduate level. `All of it is covered in the undergraduate courses that a **PhD candidate** is/was supposed to take.
I truly wish you get into a school you will enjoy studying at. I am rooting for you!

Not sure if you're being sarcastic .... but thanks. I just want to succeed by going to a top school. I added Syracuse and Iowa as safeties.

Would you mind clarify as to why the materials on the math gre is not of graduate level?

Okay, if you people believe that I am being too ambitious, then doesn't that mean my advisor is purposely setting me up for failure by telling me I have an excellent chance of getting into these schools?

Also, what is the point of doing a PHD at a bottom tier school? I don't think there are any good mathematicians out there coming from tier 3 schools.

None of the stuff on GRE subject is graduate level... and Syracuse is not at the bottom of all schools. Your advisor is not doing you any favor in my opinion. Please listen to the advices on the forum instead of your advisor.

[Cyclicduck]

Would you mind clarify as to why the materials on the math gre is not of graduate level?

Okay, if you people believe that I am being too ambitious, then doesn't that mean my advisor is purposely setting me up for failure by telling me I have an excellent chance of getting into these schools?

Also, what is the point of doing a PHD at a bottom tier school? I don't think there are any good mathematicians out there coming from tier 3 schools.

As to the gre question, the most advanced subjects covered are point-set topology, groups and rings, linear algebra, and some real analysis. I think the standard is to take a linear algebra, abstract algebra, analysis, and topology class by the fourth year of undergrad that covers these subjects.

I also wouldn't necessarily trust everyone on this anonymous forum more than your advisor, but I think it's important to get second and third opinions. Other faculty members would probably be your best bet. My opinion, for what it's worth, is that it's not a waste to apply to schools in the ~20-30 range, but you should research schools that fit well with your interests and strengths (instead of just looking at ranking) and write tailored statements for them.

You're probably right about no good mathematicians coming from tier 3 schools, but having a PhD in math can lead to plenty of other job opportunities. Being a good mathematician purely in terms of research, though, is a rare thing.

One additional point that I feel hasn't been discussed enough is the importance of having good armwrestling clubs near your graduate institution. For instance, Syracuse is a great school for this reason, as the great CNY armwrestling club is located there. (See here) to find a list of clubs by location.)

[AugmentedSeventh]

I think I underestimated the difficulty of getting into these programs now, gonna drop couple unsubmitted and instead apply to some safeties instead as a plan b.

But I think my chances are not that bad, I did an reu, and currently writing a senior thesis with someone from Cornell and also have excellent GPA. Though you guys make a valid point - I should apply to some programs where I will certainly get in.

Sure I bombed the gre but they 'll probably think I am just a bad test taker. There are so many advanced topics on the gre that were simply not taught/exposed to undergraduates, like I was stuck on this one vector space and span question on the nov gre (probably due to stress, we are allowed over 2 hours to complete our linear algebra tests in school) and then this other question about some group thing which I've never heard until after the exam. Srs they shouldn't put so many graduate materials on the math gre we are not all putnam fellows. How do they expect us answer these questions in less than 3 minutes?

Syracuse doesn't require a gre!! Yay!!

Good luck Nicole, it is a good idea to add safeties. As for GRE - it is my impression that none of the material is/was of the graduate level. `All of it is covered in the undergraduate courses that a **PhD candidate** is/was supposed to take.
I truly wish you get into a school you will enjoy studying at. I am rooting for you!

Not sure if you're being sarcastic .... but thanks. I just want to succeed by going to a top school. I added Syracuse and Iowa as safeties.

Would you mind clarify as to why the materials on the math gre is not of graduate level?

Okay, if you people believe that I am being too ambitious, then doesn't that mean my advisor is purposely setting me up for failure by telling me I have an excellent chance of getting into these schools?

Also, what is the point of doing a PHD at a bottom tier school? I don't think there are any good mathematicians out there coming from tier 3 schools.

AMS Group II schools really aren't that bad. Sure, it may be near impossible to land a tenured position at a prestigious research university with a PhD degree from those schools, but it is incredibly difficult to do that regardless of where you attend. Most people with mathematics PhD degrees end up working either in industry or at state schools/LACs without mathematics graduate departments. If those professions are not good enough for you, then you might be setting yourself up for disappointment in the future.

[nicole2]

Good luck Nicole, it is a good idea to add safeties. As for GRE - it is my impression that none of the material is/was of the graduate level. `All of it is covered in the undergraduate courses that a **PhD candidate** is/was supposed to take.
I truly wish you get into a school you will enjoy studying at. I am rooting for you!

Not sure if you're being sarcastic .... but thanks. I just want to succeed by going to a top school. I added Syracuse and Iowa as safeties.

Would you mind clarify as to why the materials on the math gre is not of graduate level?

Okay, if you people believe that I am being too ambitious, then doesn't that mean my advisor is purposely setting me up for failure by telling me I have an excellent chance of getting into these schools?

Also, what is the point of doing a PHD at a bottom tier school? I don't think there are any good mathematicians out there coming from tier 3 schools.

AMS Group II schools really aren't that bad. Sure, it may be near impossible to land a tenured position at a prestigious research university with a PhD degree from those schools, but it is incredibly difficult to do that regardless of where you attend. Most people with mathematics PhD degrees end up working either in industry or at state schools/LACs without mathematics graduate departments. If those professions are not good enough for you, then you might be setting yourself up for disappointment in the future.

Your (as in plural) comments are making me nerve wrecking. Should I apply to more safety schools? How much weight are given to statement of purpose, GPA, letters and math GRE, individually speaking? .... Maybe I shouldn't have sent my math GRE scores.

Would anyone recommend applying to a masters program? Would having a masters degree improve chances of getting into a better program?

And how competitive are Canadian masters programs for American citizens? Which ones would you guys recommend for me to apply?

[ponchan]

Not sure if you're being sarcastic .... but thanks. I just want to succeed by going to a top school. I added Syracuse and Iowa as safeties.

Would you mind clarify as to why the materials on the math gre is not of graduate level?

Okay, if you people believe that I am being too ambitious, then doesn't that mean my advisor is purposely setting me up for failure by telling me I have an excellent chance of getting into these schools?

Also, what is the point of doing a PHD at a bottom tier school? I don't think there are any good mathematicians out there coming from tier 3 schools.

AMS Group II schools really aren't that bad. Sure, it may be near impossible to land a tenured position at a prestigious research university with a PhD degree from those schools, but it is incredibly difficult to do that regardless of where you attend. Most people with mathematics PhD degrees end up working either in industry or at state schools/LACs without mathematics graduate departments. If those professions are not good enough for you, then you might be setting yourself up for disappointment in the future.

Your (as in plural) comments are making me nerve wrecking. Should I apply to more safety schools? How much weight are given to statement of purpose, GPA, letters and math GRE, individually speaking? .... Maybe I shouldn't have sent my math GRE scores.

Would anyone recommend applying to a masters program? Would having a masters degree improve chances of getting into a better program?

And how competitive are Canadian masters programs for American citizens? Which ones would you guys recommend for me to apply?

I suggest the following: Apply to a terminal MA program. Miami University, Wake Forest, and UVM all have these (and they're fully funded). Then you'll get more grad courses under your belt and hopefully boost your mGRE score substantially with more preparation. This will also give you the opportunity to do more research. If you do that I think you'd have a much better shot at some of these programs.

[AugmentedSeventh]

The importance of each part of the application is different for each school. Some schools (for example Stony Brook University and UC Riverside) don't even ask you to send your math GRE score, so clearly those schools place a very low weight on the math GRE. Worst case scenario, you could always take a gap year and apply for Fall 2021. This is what I did (except I didn't apply to any schools last year) since, like you, I went to a small school without a math graduate department and thus had to learn a lot of material on my own in order to score somewhat competitively on the math GRE.