Apply for tier-1 Maths PhD: what factors are important?

[panicking]

I just apply for a bunch of tier-1 Maths PhD program, so I guess it's kinda late to ask this. But I'm panicking right now, because my application is not strong at all, and I already put all my eggs in this tier-1 basket (ie. I don't have any safety school). So can someone tell me how important these factor are for the admission committee. If possible, provide also example of successful applicant that get into one of the tier-1 school (esp. MIT since it's my #1 right now) while being weak at some or many of the factors.

Here are the factors I find most worrying, so it's much better if you can address one of these, but feel free to add your own. Please don't just say that it's certain that I will fail; if you think a factor is intolerably weak, address other factors instead.

-Whether the application is submitted on time.

-Whether GRE general test have been taken.

-Not stellar GRE maths subject test.

-No REU.

-Only have 3 letters of rec.

-Whether recommenders are strong researcher.

-Undergrad is in liberal art instead of univ.

-Lacking graduate level maths course.

-Lacking basic maths course.

-Low cumulative GPA.

-Failed/low grade in many non-math course.

-Some maths course with not perfect grade.

 

I am pretty much banking on a perfect statement of purpose right now...except that they do not address specific school (I wrote it right on Dec 15th, did not have time) and I just found a grammar mistake. I have some hope that my letters of rec would not be too bad, but considering that the same letters was used on my latest failed REU application I have little faith in them.

 

Please give me some information. I'm panicking right now, and anything to end this uncertainty would be helpful.

[ratlab]

A perfect statement of purpose is not going to make up for that list (as it doesn't even demonstrate math skills). I think you're probably better off doing a funded masters if you can find one, and now would be the perfect time to look. Sorry it's not exactly an encouraging response - again though, there are exceptions to everything.

Edited December 18, 2013 by ratlab

[panicking]

Uh I am not asking whether the whole thing is a failure. I am asking how important each of these factors are, as in how much weight do they carry. If I fail, at least I know what to fix first. There is no way I am going to be content with just a master.

[ratlab]

Each of these factors is important. If you have listed these factors as weaknesses in your application, to be very blunt you haven't proven yourself capable of a math PhD program (especially a top 10 one - you should apply broadly). You really should reconsider doing a masters before a PhD, but my guess is that you'll see this in the school responses. You've listed like 10 faults (several of which will be kisses of death) and are basically asking for reassurance. I'm sorry, but I have none to offer (as I personally think you shot yourself in the foot by only applying to tier-1), and it's likely that the lack of other posts indicates the same.

 

-Whether the application is submitted on time. - Many programs won't even review your application if it's not submitted on time.

-Whether GRE general test have been taken. - This isn't negotiable, they either require it or do not. If you don't take it, they will throw you away. Plenty of others took it and followed directions (assuming the school requires it).

-Not stellar GRE maths subject test. - I don't know the importance of this subject test, but this is your field and I imagine they take it seriously (if they require it).

-No REU. - Not important as long as you have research experience elsewhere. If you have no research experience, then how do you know you'll even like a PhD?

-Only have 3 letters of rec. ​- Most schools only require 3.

-Whether recommenders are strong researcher. - Most likely it won't matter. What matters is that you did research under them, so they can comment on your skills.

-Undergrad is in liberal art instead of univ. - Not important.

-Lacking graduate level maths course. - Again, not important as long as you have extensive undergrad background. This is not the norm.

-Lacking basic maths course. - Extremely important. How does the committee know that you can do a math PhD if you haven't done math? This will weed you out.

-Low cumulative GPA. - Again, very important. Undergraduate is easier than Graduate school. Coupled with these others weakness it proves that one isn't ready to enter a PhD program. Really address why you didn't do well in undergraduate - try to gain some insight.

-Failed/low grade in many non-math course. - Not as important as failing math, but still alarming.

-Some maths course with not perfect grade. - Depends on what grade.

 

There is no way a perfect statement of purpose is going to make up for this list. My advice is to apply to masters programs in addition to these PhD applications.

Edited December 18, 2013 by ratlab

[panicking]

Thanks for at least pointing out that certain factor, which are very hard for me to change, are not importance. But still, it is possible that thing work differently between your field (behaviour neuroscience?) and maths, so I still held some hope. Maybe there are just too few people here for more to reply.

"Not important as long as you have research experience elsewhere" : I'm not sure what you meant by this. How else can one get research experience?

"Most schools only require 3" : I know, but lots of peoples send more, and I am afraid they would have an advantage

"How does the committee know that you can do a math PhD if you haven't done math?" : But math-heavy course such as some computer class or physics class count right? I meant, they can probably be classified as applied maths.

"Again, very important. Undergraduate is easier than Graduate school. Coupled with these others weakness it proves that one isn't ready to enter a PhD program. Really address why you didn't do well in undergraduate - try to gain some insight." : Even if the low GPA are due to failure in classes completely unrelated to maths? I meant it's undergrad, there are all sort of random classes totally unrelated to your major you have to take to fulfill requirement, which I assume you no longer need to deal with in grad school. Classes like foreign policy, or anthropology, or literature are pretty easy to fail.

"There is no way a perfect statement of purpose is going to make up for this list" : how much do you think the SOP would weight in the committee's eyes then? Especially one that boast all the intangible qualities?

[smootie]

Math major here.  I've talked at length with my department's graduate chair, and have helped him organize workshops on the topic of math graduate school.  We are not a tier-1 school so ignore this advice if you don't think it applies to your unique situation.

 

-Whether the application is submitted on time.  For my school, it's not super important because we don't get a ton of applicants.  For the more competitive programs in my university, late apps are not even considered.  If you're really concerend, you can simply call the departments you applied to and ask them if they accept late apps.

 

-Whether GRE general test have been taken.  For my department, the GRE is not required.  However, not submitting one counts against you, even if your scores are mediocre.  The way my chair explained it was that each piece of your application package gives him an idea of who you are.  When a piece is missing, it leaves a vacuum that must be filled by other things like your GPA and LoR.  Therefore, your GPA and LoR must work harder than if you submitted a GRE score.

 

-Not stellar GRE maths subject test.  This one is important.  Grades give some indication of your math skills, but a high GPA only says that you are good at getting A's, not that you have any math knowledge.

 

-No REU.  Not a big deal.  But having a REU on your application makes you stand out.

 

-Only have 3 letters of rec.  This is standard.  Submitting more letters than required can count against you.  It depends on how busy the application screeners will be.  They are most likely swamped by applications, and would not appreciate having to process extra LoR.

 

-Whether recommenders are strong researcher.  What do you mean by "strong" researcher?  LoR are most meaningful from people who are respected in the field, who have worked with you closely (rather than someone who was your prof for one semester), who are full professors (rather than lecturers or adjunct faculty).

 

-Undergrad is in liberal art instead of univ.  Getting your undergrad from a more prestigious school helps, but it won't hurt your application if you did not.

 

-Lacking graduate level maths course.  Not a requirement but this would make you less competitive.  All the undergrads I know who are considering math graduate school all have several graduate level courses under their belt.  Keep in mind that we're not even a prestigious math program.  I imagine that the people competing for spots at tier-1 schools would be at the top of their game.

 

-Lacking basic maths course.  This one is bad.  At the very least, you should have a strong foundation in analysis and algebra.  My program will overlook this requirement for applicants to the master's program if the rest of the application is strong, but the student has to take these courses since they are pre-reqs for graduate courses.

 

-Low cumulative GPA.  GPA isn't as important as the other part of the application package, but my university won't consider graduate student applications with cumulative GPAs lower than 3.0 unless the department can justify why they want to accept the student.  Your application would have to be very compelling for the department to jump through those hoops for you.  Other schools will have different policies, I'm sure.

 

-Failed/low grade in many non-math course.  Any failed courses is cause for concern, but an F in a non-math courses isn't a dealbreaker if the rest of your app is strong, especially if the bad grade was from freshman year.  Again though, this is for my school and the level of our applicants are not in same league as MIT.  Most of my fellow math undergrads have 3.8-4.0 gpas, and we are required to take a LOT of classes outside of math to fulfill our general education requirements.  "Many" bad grades, even in non-math courses, looks really bad.

 

-Some maths course with not perfect grade.  B's are okay.  C's less so.  B/C's in lower level classes like calculus aren't as bad as B/C's in upper level classes.

 

Anyways, I hope that helped, and good luck on your app!

[RedPill]

Thanks for at least pointing out that certain factor, which are very hard for me to change, are not importance. But still, it is possible that thing work differently between your field (behaviour neuroscience?) and maths, so I still held some hope. Maybe there are just too few people here for more to reply.

"Not important as long as you have research experience elsewhere" : I'm not sure what you meant by this. How else can one get research experience?

"Most schools only require 3" : I know, but lots of peoples send more, and I am afraid they would have an advantage

"How does the committee know that you can do a math PhD if you haven't done math?" : But math-heavy course such as some computer class or physics class count right? I meant, they can probably be classified as applied maths.

"Again, very important. Undergraduate is easier than Graduate school. Coupled with these others weakness it proves that one isn't ready to enter a PhD program. Really address why you didn't do well in undergraduate - try to gain some insight." : Even if the low GPA are due to failure in classes completely unrelated to maths? I meant it's undergrad, there are all sort of random classes totally unrelated to your major you have to take to fulfill requirement, which I assume you no longer need to deal with in grad school. Classes like foreign policy, or anthropology, or literature are pretty easy to fail.

"There is no way a perfect statement of purpose is going to make up for this list" : how much do you think the SOP would weight in the committee's eyes then? Especially one that boast all the intangible qualities?

 

Umm what? Those electives should be easy As. 

[panicking]

Oh well, I got rejected from every places. Well, will eventually get rejected at least, there are still those that have not replied, but I don't think these would go any better now that it's almost April. Thanks you who had replied, especially ratlab and smootie who give detailed information. I would like to ask a few questions to prepare myself for next year, since it's now a near certainty that I won't get in any programmes.

 

-Which aspects can be improved that will help the most that don't cost much money? (e.g. I can't afford to go for another year in college, unless somehow getting a full scholarship)

 

-My philosophy this time is that if I go to a non-tier-1 school, I will never find a job even after I got a phd; which was why I only apply to those: I would rather retry than to go to a programmes that won't guarantee me a job (esp. research position). How true is that philosophy? Should I have some safety school next year?

 

-By next year, would grade after Dec this year get counted (it obviously cannot count for this year application). If I wait for 2 years, would the "last 2 year GPA" information that you need to provide in most application no longer applicable? If no longer applicable, is it good or bad? Because I just failed 2 classes this term (not in maths though, and are only D fail, not F fail).

 

-Despite getting rejected from everywhere, over half of them did not reject me until last week. Does that means I was actually on some waitlist, and could be almost good enough to get in? They are not strong tier-1 program of course (which reject pretty much as soon as possible), but weak tier-1 programmes such as Columbia.

 

-How much can connections help? I just learnt recently that one of my distance relative (but not even share last name) was one a phd student of a professor in a tier-1 programmes. Should I do any nudge nudge on my personal statement?

 

-If I claimed that I self-studied something on my statement, would they believe it? I can't figure out how to fix the lack-basic-maths-course problem now otherwise. I can at best take on Calculus next term, but not much more.

 

-Programmes frequently claimed that the chance of getting in won't improve with outside funding, but somehow I seriously doubted that (e.g. admitting a student with outside funding means they can still get all the student they want, and that extra one who have outside funding, which means more people doing research which is even better). How true is that claim? Should I try to get some outside funding?

 

-Would getting a master improve my chance at all? Just hypothetical, since I doubt any programmes give out master with funding, and I can't really afford it myself. But in case I can get some outside funding, or found a programmes that give out one.

 

-If I manage to solve an amazing unsolved problem, I should have no problems getting in to any programmes right? Anyone give enough maths expertise, can point me out to a big unsolved problem that have a chance to be solved by an undergrad like myself please?

 

Thank you for any helps.

 

@RedPill: I'm not sure how they are easy A, at least not in my college. Over half of my philosophy class (on first order logic and lambda calculus) have to drop the class for example; I did not drop and end up with an F.

Edited March 27, 2014 by panicking

[pazuzu]

I am a fourth-year PhD student at a tier 1 mathematics program.  My advisor one of the faculty members that reviews graduate applications.  I am happy to give some insight, but I do have a few questions for you. 

 

-Which aspects can be improved that will help the most that don't cost much money? (e.g. I can't afford to go for another year in college, unless somehow getting a full scholarship)

It depends on your coursework and current grades.  Some post-bac programs are partially funded and can help get you into a better position for applying to graduate school.  Some other options (though expensive) could be to spend a year some place like Budapest Semesters in Mathematics.  You could definitely get more classes and experience, but it wouldn't be free.

 

 

-My philosophy this time is that if I go to a non-tier-1 school, I will never find a job even after I got a phd; which was why I only apply to those: I would rather retry than to go to a programmes that won't guarantee me a job (esp. research position). How true is that philosophy? Should I have some safety school next year?

 

I am not currently on the job market, but I have had many friends apply this year.  The academic job market for mathematicians isn't great, but you don't need to go to a top school to find a position. Likely you will be doing a  (even up to three ) post-docs, but there are jobs out there.  Tier 1 schools may make this job easier, but you need to have done meaningful research wherever you go to find a position. So, why do you want to be a professional mathematician?  What other positions with a mathematics PhD would be of interest to you (always good to know your options)?
 

 

-By next year, would grade after Dec this year get counted (it obviously cannot count for this year application). If I wait for 2 years, would the "last 2 year GPA" information that you need to provide in most application no longer applicable? If no longer applicable, is it good or bad? Because I just failed 2 classes this term (not in maths though, and are only D fail, not F fail). 

Failing several classes even in non-math is a huge red flag- especially so late in your degree. It says something about your ability to complete coursework.  There really isn't a way to hide this from your application.  The best bet would be to take another year of classes and absolutely rock them all.  Remember, the top programs have really good applicants (of course other programs do too!).  If you have poor grades and are otherwise equal to the other applicants you are not getting in.  You need to be very strong in the other parts of your application to make up the difference.  Realize that most tier 1 acceptances go to people with stellar understanding of mathematics and demonstrated research experience- any major flaw will be very difficult to overcome.

 

-Despite getting rejected from everywhere, over half of them did not reject me until last week. Does that means I was actually on some waitlist, and could be almost good enough to get in? They are not strong tier-1 program of course (which reject pretty much as soon as possible), but weak tier-1 programmes such as Columbia.

Not getting rejected out of hand is a good thing, but you would have to ask if you were waitlisted. Have you contacted the schools that rejected you and asked them what you can do to improve your application in the future?

 

 

-If I claimed that I self-studied something on my statement, would they believe it? I can't figure out how to fix the lack-basic-maths-course problem now otherwise. I can at best take on Calculus next term, but not much more. 

You should mention what you study in your free time.  They will believe it if it is true and you can demonstrate the knowledge you have gained from self-study.  I mentioned relevant papers that I read (not related to my undergrad coursework) in my application.  Showing the application committee that you are self-motivated is great, and will really hone your research statement because you will be reading enough to know what you want to work on.

 

However, the next statement really worries me, you should be well past the calculus sequence if you are applying for a PhD (if you are in your last year now- which I am assuming). Can you provide a list of the math classes have you taken? This would really help everyone understand your current standing.  You will not get into a math PhD program without skills in at least abstract algebra and real analysis.  A tier 1 PhD program will expect much much more.  Also, if you do not have a terrific foundation in writing proofs, you will not be able to pass the coursework- let alone do research.

 

 

-Programmes frequently claimed that the chance of getting in won't improve with outside funding, but somehow I seriously doubted that (e.g. admitting a student with outside funding means they can still get all the student they want, and that extra one who have outside funding, which means more people doing research which is even better). How true is that claim? Should I try to get some outside funding?

It doesn't hurt. You still must meet some minimum standards, but bringing in a full fellowship would be a great boon to your application.  You definitely can try for outside funding.  Be aware though, the outside funding sources will have the same concerns that the application committee may have with your application.

 

 

-Would getting a master improve my chance at all? Just hypothetical, since I doubt any programmes give out master with funding, and I can't really afford it myself. But in case I can get some outside funding, or found a programmes that give out one. 

I think so, this is the route I went. I earned my masters (funded) at a good tier 2 school before moving on to my PhD.  I would not have gotten into a tier 1 without the research experience my master's thesis afforded me.  Math research skills take a long time to develop (I'm still working on it myself!).  I definitely was not ready for a PhD right out of undergrad, though others may certainly have been.

 

-If I manage to solve an amazing unsolved problem, I should have no problems getting in to any programmes right? Anyone give enough maths expertise, can point me out to a big unsolved problem that have a chance to be solved by an undergrad like myself please? 

You mean solve a grand problem in spite of your application to gain admission? This really really really doesn't happen.  Math doesn't work as a start-from-nothing-and-get-a-big-result process.   Lots of undergrads have some results from REUs or directed studies.  These show you have the potential to be a researcher, but even with this experience they are unlikely to be solving massive open problems.  I can come back to this question when you have a chance to post your course work, but if I had a big important unsolved problem that I thought could be done by an undergrad, I'd be working on it. 

 

The real question is what are you interested in/good at?  What kind of math can you stare at for five years and still love (most of the time)?  My suggestion would be to read some research papers in fields you are interested in and see what mathematical research looks like-  you definitely need to have some idea of what you are getting into.  

 

 

 

To be quite blunt (and to repeat others above) it seems like you do not have the background necessary for a PhD in math.  Let's look at what you have done, but it sounds like a post-bac may be the best place to start if you want to pursue a PhD.

I really would also be curious to know why you want a PhD in math.  I don't mean this to sound belittling, I am genuinely interested. 

Edited March 28, 2014 by pazuzu

[pazuzu]

I should also say, my observations are assuming that your application had all of the issues from your initial post.  If that is incorrect, let us know.

[panicking]

Thank you for the detailed reply pazuzu, which is especially useful coming from someone in a tier-1 programmes also in the same subject.

 

 

I should also say, my observations are assuming that your application had all of the issues from your initial post.  If that is incorrect, let us know.

Yes, almost all of them are there. Except for the GRE general test. I took it, but obviously, it was not part of the original application, but it could go in for next year. Both math and verbal are >95%, but I am somewhat worried about writing which I got merely 3.0. If needed for retake, I still have plenty of chance to do so.

 

To be quite blunt (and to repeat others above) it seems like you do not have the background necessary for a PhD in math.  Let's look at what you have done, but it sounds like a post-bac may be the best place to start if you want to pursue a PhD.

I really would also be curious to know why you want a PhD in math.  I don't mean this to sound belittling, I am genuinely interested. 

I love maths, and I want to study more, learn cutting edge research, and solve problems. I thought that's pretty much apply to everyone wanting to do PhD in maths isn't it? I am pretty sure I have a good background in maths (I just attempt Berkeley prelim exams on my own as practice; not sure how much time do they gave, but it took me 8 hours to solve both part, but remember that this exams have 3 optional questions each part, so it should be within time limit assuming that they give out a reasonable time limit; and got almost every question (once again, there are optionals)). Now I just need to convince people that I am capable somehow so that I can get in to prove myself.

 

I am not currently on the job market, but I have had many friends apply this year.  The academic job market for mathematicians isn't great, but you don't need to go to a top school to find a position. Likely you will be doing a  (even up to three ) post-docs, but there are jobs out there.  Tier 1 schools may make this job easier, but you need to have done meaningful research wherever you go to find a position. So, why do you want to be a professional mathematician?  What other positions with a mathematics PhD would be of interest to you (always good to know your options)?

 

I believe that tier-1 programmes give better connections (make it easier to get job) and also the strong research program mean I would have better chance of producing amazing work that can give me job. I read some statistics somewhere that claim that half of position in top 100 are occupied by those with PhD in top 10, and it's evident when I look through a number of faculty list. Which was why I picked to go with only tier-1, even my "safety" are still tier-1.

 

 

Failing several classes even in non-math is a huge red flag- especially so late in your degree. It says something about your ability to complete coursework.  There really isn't a way to hide this from your application.  The best bet would be to take another year of classes and absolutely rock them all.  Remember, the top programs have really good applicants (of course other programs do too!).  If you have poor grades and are otherwise equal to the other applicants you are not getting in.  You need to be very strong in the other parts of your application to make up the difference.  Realize that most tier 1 acceptances go to people with stellar understanding of mathematics and demonstrated research experience- any major flaw will be very difficult to overcome.

If only I can just give out grade from my 3rd year. I got straight A in 3rd years in every single courses. It helped that most of them are maths.

The problem is, even if I take 1 more year, I'm not so sure how well I would do, whether I can rock them all. I am somewhat unstable, and tend to crack under exams condition. Also, for subjects I don't like but have to take for requirement, I pretty much do no works (I can't even push myself to work when I'm bored, especially if it's a subject that make no sense like international relation). But that won't apply to PhD because I would get to study what I like all the time, and of course there is no exams except for a few formality.

 

Not getting rejected out of hand is a good thing, but you would have to ask if you were waitlisted. Have you contacted the schools that rejected you and asked them what you can do to improve your application in the future?

I am thinking of waiting until after Apr 15th, so it does not look like I'm haggling. I think subject GRE for maths is after that, so I should still have time to apply if they reply sufficiently fast and indicating that GRE score is a problem.

 

You should mention what you study in your free time.  They will believe it if it is true and you can demonstrate the knowledge you have gained from self-study.  I mentioned relevant papers that I read (not related to my undergrad coursework) in my application.  Showing the application committee that you are self-motivated is great, and will really hone your research statement because you will be reading enough to know what you want to work on.

 

 

You mean solve a grand problem in spite of your application to gain admission? This really really really doesn't happen.  Math doesn't work as a start-from-nothing-and-get-a-big-result process.   Lots of undergrads have some results from REUs or directed studies.  These show you have the potential to be a researcher, but even with this experience they are unlikely to be solving massive open problems.  I can come back to this question when you have a chance to post your course work, but if I had a big important unsolved problem that I thought could be done by an undergrad, I'd be working on it. 

 

The real question is what are you interested in/good at?  What kind of math can you stare at for five years and still love (most of the time)?  My suggestion would be to read some research papers in fields you are interested in and see what mathematical research looks like-  you definitely need to have some idea of what you are getting into. 

But people have managed to solve amazing problem as undergraduate right? I means, like Galois for example. Or for more modern example, those guys who proved that PRIME is in P, or Matiyasevich (Hilbert's 10th problem). Surely there is something within grasp, and it might just be in a somewhat less popular part of mathematics and so few are working on them. It does not have to be super important, just difficult unsolved problem that stand a long time.

I'm interested in number theory and algebraic geometry and discrete maths. I have read a number of paper, such as the above mentioned PRIME is in P, proof of Hilbert's 10th problem, and more. There are even more which I attempted, but can't because they are too hard or too long. I could mention those paper in SOP, and should have in retrospect, but I am afraid that they won't believe it and think I'm just overblown it (perhaps they might think that I only know the paper exist and not actually have read it through).

 

It doesn't hurt. You still must meet some minimum standards, but bringing in a full fellowship would be a great boon to your application.  You definitely can try for outside funding.  Be aware though, the outside funding sources will have the same concerns that the application committee may have with your application.

 

 

I think so, this is the route I went. I earned my masters (funded) at a good tier 2 school before moving on to my PhD.  I would not have gotten into a tier 1 without the research experience my master's thesis afforded me.  Math research skills take a long time to develop (I'm still working on it myself!).  I definitely was not ready for a PhD right out of undergrad, though others may certainly have been.

Would it be easier to apply for outside funding for PhD next year, or a funded master? I assume that as long as money is involved, they would scrutinize my application, but which tend to be more lenient?

 

 

However, the next statement really worries me, you should be well past the calculus sequence if you are applying for a PhD (if you are in your last year now- which I am assuming). Can you provide a list of the math classes have you taken? This would really help everyone understand your current standing.  You will not get into a math PhD program without skills in at least abstract algebra and real analysis.  A tier 1 PhD program will expect much much more.  Also, if you do not have a terrific foundation in writing proofs, you will not be able to pass the coursework- let alone do research.

I answer this last because it's gonna be rather long. I did not put these details into my first post of this thread, partly because of that and also because I was panicking back then. Anyway...

 

My school is a small college, so obviously there are no graduate classes. The maths department, especially are tiny; there are 3 professor (not counting one who was just hired this calendar year) (so just enough for LOR), and 1 is visiting, and 1 is on tenure track but not full professor yet. Maths department tend to have to teach important basic classes frequently as well as those that are required for major, so pretty much the professors are tied up doing those classes. Classes like Calculus, Stats, and so on. There are still advanced classes almost every term, but each particular classes get offered rather rarely. Another problem is that if there are too few people attend a class (typical problem with advanced maths classes, since there are few maths major in the first place) the class is cancelled. Some of the classes I took was because friends are asking me to get in.

Now the worst thing is that due to sharing space, classes of one department tend to clump together into a few time slot. What this means is that very frequently, advanced classes conflict time with basic classes. Since advanced classes get offered so rarely, I always pick the advanced classes when it is offered. The professors are understanding enough (and also some time to just fill up the class) so they pretty much throw the prereqs into the wind and let anyone in.

 

So my list of class goes like this:

Intro to number theory

Classical & differential geometry (though it's more like 80% classical, 20% differential)

Complex analysis

Abstract algebra 2 (ring, field, Galois)

Measure theory & Lebesgue integration & probability theory & stats theory (yeah it's 1 class)

Topology (metric space & point-set topology)

A class that is just a bag of unrelated topics (a bit of dynamical system, some advanced point-set topology, some optimization, some set theory, a bit of group theory, and some generating functions); the name of this class is literally just Advanced Topics in Mathematics, and I don't think they even have a consistent syllabus each time this class is taught (but then again, it's only offered once during my time here)

Theory of computation (we don't even have a Comp Sci department or the major, but this is mathy enough, classify as computer science course, but taught by maths professors)

Numerical analysis (also classify as computer science, but taught by maths professors)

 

So these classes are available, and I think I should had took them, but I really have no clues how important each of these are. It's too late now anyway, the only thing that's available next term are either one of the 2 calculus classes, or some stats classes which are clearly irrelevant:

Calculus

Multivariable calculus

Elementary set theory

Abstract algebra 1

Real analysis

Linear algebra

Ordinary differential equation

Partial differential equation

Optimization theory

 

(except for linear algebra, optimization and set theory, the rest is offered every year; single variable calculus even every term)

 

But...my school have a much better physics department with many more professors. I have been taking classes from them, and might graduate with a physics degree if I don't do those calculus classes and just finish the requirement for physics. I hope that the following classes in physics could help:

Advanced electromagnetism

Quantum mechanics (heavy on linear algebra)

Mathematics for physicists (have all sort of stuff, from Fourier transform to various ODE and PDE, and some linear algebra too)

Thermodynamics

Fluid dynamics

 

And next term if I don't take the calculus class, I can take instead:

Particle physics and gauge theory

 

From philosophy department there are:

Logic (first order logic and lambda calculus)

 

As for grade, I got C on complex analysis because I partied too hard the night before the finals and overslept. Adv electromagnetism got B because I took it in my freshman year and get basically no preparation. Maths for physicist got B+ because it have some oral speaking component and I got stage fright. Logic I got F first time because I never come to class (too early in the morning), and naturally fail the finals; but got A on second try. All other maths/physics classes are A.

 

So yeah, I'm very sure that I have a rather strong background in maths. I just need to convince admission committee, somehow, that please give me a chance to prove myself.

Edited March 28, 2014 by panicking

[Crucial BBQ]

Pardon my confusion, but you were able to take higher level math courses without taking the basics first?  

[HKsai]

I just want to chime in and say that your application is whole package that represents you. It shows the committee who you are, how you value education and the dedication to the subject you intend to pursue. I will say that yes math grades are important but the other grades can be just as important because it tells different parts of you. It may not tell the committee about your math ability but it tells the committee your study ability, your mental flexbility...It just seems like you are making a lot of excuses to a lot of stuff that you didn't do well. "As for grade, I got C on complex analysis because I partied too hard the night before the finals and overslept. Adv electromagnetism got B because I took it in my freshman year and get basically no preparation. Maths for physicist got B+ because it have some oral speaking component and I got stage fright." I'm not saying that you can't party or you can't get stage fright, but considering PhD applicant pool is so competitive and you don't stand a chance against them. I think the general consensus that with your current application there's no way that you can get into a PhD program not to mention tier 1 program. I think you need to move beyond your mistake and accept the flaws that you made. Stop giving excuses about your mistakes because what's done is done. Because right now I feel like the committee can see not just the lack of ability but also the lack of dedication to the subject. You talk about how much you love the subject but from the application it doesn't even show that you are dedicated to academia at all (i'm not saying that you are not but your application doesn't show that's the problem)

[pazuzu]

 

But people have managed to solve amazing problem as undergraduate right? I means, like Galois for example. Or for more modern example, those guys who proved that PRIME is in P, or Matiyasevich (Hilbert's 10th problem). Surely there is something within grasp, and it might just be in a somewhat less popular part of mathematics and so few are working on them. It does not have to be super important, just difficult unsolved problem that stand a long time.

I'm interested in number theory and algebraic geometry and discrete maths. I have read a number of paper, such as the above mentioned PRIME is in P, proof of Hilbert's 10th problem, and more. There are even more which I attempted, but can't because they are too hard or too long. I could mention those paper in SOP, and should have in retrospect, but I am afraid that they won't believe it and think I'm just overblown it (perhaps they might think that I only know the paper exist and not actually have read it through).

I was speaking in absolutes, undergraduates can certainly solve open problems.  My issue is that you want to solve a problem that will guarantee you admission to a tier 1 school, but this presents a catch-22.  If you are as good as Galois, you are going to have done enough to get into a tier 1 school.  If you aren't as good as Galois you aren't going to solve a singular problem which will allow you to get in anywhere you want.  This goes into the following...

 

 

 

does not have to be super important, just difficult unsolved problem that stand a long time.

There is no magic way to get into graduate school.  You are highly highly unlikely to find and solve an "instant admission" problem.   You are looking for a problem which professional mathematicians know about and cannot solve, but an undergraduate comes along and solves.  I am not going to argue that such a situation is impossible- it isn't- but such a situation is incredibly rare. 

 

If you do solve an open problem this will be part of your application material.  It will make you look better, but almost all applicants in tier 1 programs have solved some open problem.   Graduate programs at all levels want you to demonstrate what your research potential is.  This can be done in many ways (REU, directed study, or even publishing something), but a tier 1 (and even any PhD) program is going to expect some record of research.  It sounds like you are looking for a quick and easy fix.  Mathematics does not move forward this way, save for a few brilliant and rare minds.

This whole situation feels like a student who is failing going into the final exam and asking if they get an A on the final if they can pass the course.  If you are failing the class you very likely aren't going to get an A on the final, and if you could get an A on the final there is no reason for you to be failing the class.  

 

I love maths, and I want to study more, learn cutting edge research, and solve problems. I thought that's pretty much apply to everyone wanting to do PhD in maths isn't it? 

Sure, but what did you research statement say?  You don't need to know exactly what you want to do, but you should have (and communicate) a much better idea than this.

 

 

 

 

Your math background is lacking.  Any school which funds students by TA positions is going to expect you to have completed the calculus sequence.  I have no idea how your school let you do, for example, complex analysis before calculus or multivariate calculus, but that will be something that needs to be explained to any program.  A bare minimum of the basics is going to include calc 1-3, linear algebra, and differential equations.  This is why your transcript is so strange, how did you do topology, measure theory, and differential geometry without calculus?  How did you do topology without linear algebra?  I guarantee you every admission committee is going to be highly skeptical of such a transcript.

For reference, for my funded masters program I applied with 18 courses (6 basic courses like calculus, and 12 upper level courses) in mathematics from undergraduate school ( a tiny liberal arts school in the midwest).  I did have to study at a math program abroad to pick up so many math courses.  This may be a bit high, but is not uncommon in top programs.

 

Hopefully you can understand these concerns, but as the poster above me said, your current application package is not good enough to go to a top program, and you would have a hard time at some of the low ranked PhD programs.  If you can explain the strange lack of basic math courses, and can demonstrate research potential you may be able to gain admission into a masters program.  In terms of funding though, it is cutthroat.  There are a lot of people with more classes, more research, and better grades looking for the same positions you are.

 

If you want to be a mathematician that is great, and you can get there.  However, the path you want to take will very likely not work for you.  I would really recommend post-bac or trying for a masters.

 

Edited March 29, 2014 by pazuzu

[panicking]

Your math background is lacking.  Any school which funds students by TA positions is going to expect you to have completed the calculus sequence.  I have no idea how your school let you do, for example, complex analysis before calculus or multivariate calculus, but that will be something that needs to be explained to any program.  A bare minimum of the basics is going to include calc 1-3, linear algebra, and differential equations.  This is why your transcript is so strange, how did you do topology, measure theory, and differential geometry without calculus?  How did you do topology without linear algebra?  I guarantee you every admission committee is going to be highly skeptical of such a transcript.

 

Pardon my confusion, but you were able to take higher level math courses without taking the basics first?  

 

 

But wouldn't the very fact that I took maths courses (and physics courses) that are dependent on both calculus and multivariable calculus, and did well in almost all of them, show that I know calculus? I don't understand why would anyone be skeptical about that. As I mentioned, the professors let anyone in. Yes the course did in fact have those as prereqs, but I was let in anyway. Of course, I still have to know those stuff (from physics classes, and self-study). Just because I don't have the class on the official transcript does not means I do not know the stuff. The prereqs are merely suggestions than rules, because otherwise classes won't fill up to minimum, and the students might not see that course ever get offered again. I'm not sure why would the transcript look strange. I'm sure there are non-math major who apply too, and thus they can expect some classes to be missing. I don't really miss out on anything except for set theory (which you did not mention as being important), since maths for physicists course cover pretty much everything. I'm not sure how to even explain why some classes are missing, I meant I didn't take them, what else can I say?

 

 

If you can explain the strange lack of basic math courses, and can demonstrate research potential you may be able to gain admission into a masters program.  In terms of funding though, it is cutthroat.  There are a lot of people with more classes, more research, and better grades looking for the same positions you are.

 

If you want to be a mathematician that is great, and you can get there.  However, the path you want to take will very likely not work for you.  I would really recommend post-bac or trying for a masters.

 

Is there anything I can fix without using a post-bac or a masters? I tried applying for REU multiple times but never got any. Now that I'm about to graduate, and since REU is usually for current undergrad, I think that options is pretty much non-existence now. I don't really want to do a post-bac (cost money, and don't show research potential) or a master (cost even more money). Surely there are way to show that I am capable of a PhD despite the lack of maths course right? In fact, since I self-studied many of those stuff, wouldn't that means I have even better research potential than those who have to take the classes? Can I turn that into an advantage? My maths grade is extremely good, as long as you ignore that one C. And my general GPA is still very high as long as only 2nd and 3rd grade are counted. Most of my fail come from 1st year, and this year I only failed 2 courses so far in completely irrelevant classes.

 

 

Hopefully you can understand these concerns, but as the poster above me said, your current application package is not good enough to go to a top program, and you would have a hard time at some of the low ranked PhD programs.

 

So which PhD programmes would be more feasible? Would top 25 more viable? Top 30 guaranteed? What about small programmes vs big one? Perhaps small programmes are more understanding of lacking of basic courses, or perhaps big programmes admit a lot more people. Is there any programmes that is meant for say, "late-bloomer", like they have for undergraduate?

 

I think the general consensus that with your current application there's no way that you can get into a PhD program not to mention tier 1 program. I think you need to move beyond your mistake and accept the flaws that you made. Stop giving excuses about your mistakes because what's done is done. Because right now I feel like the committee can see not just the lack of ability but also the lack of dedication to the subject. You talk about how much you love the subject but from the application it doesn't even show that you are dedicated to academia at all (i'm not saying that you are not but your application doesn't show that's the problem)

I think that excuse is pretty much the only way I can explain those bad grade. It's done, and is on my record, so there is nothing I can do about those bad grade except explaining why it happened. For example, I could request one of the professors to explain in the LOR that I actually did very well on the complex analysis course until the final blunder (not sure if it's a good idea, just a thought, did not try).

 

 

Sorry if I am somewhat agitated. I just got another rejection. But I think for the rejection to come so late it does means for a long time I was on the table. Now I just need a bit more of something to stand out.

[HKsai]

The thing is there's no guaranteed.... This is PhD not undergraduate. You should really do some research and look at the acceptance rate for different tier of school. The problem is no one is willing to take a risk nor give money to you to do research when your application is weak no matter which school you are talking about. I'm not trying to be negative but I think you should be a little bit more realistic. I understand your frustration but maybe there's a different way to achieve what you want. People here are just trying to help you maximize your potential with what you have.

[bsharpe269]

Is there anything I can fix without using a post-bac or a masters? I tried applying for REU multiple times but never got any. Now that I'm about to graduate, and since REU is usually for current undergrad, I think that options is pretty much non-existence now. I don't really want to do a post-bac (cost money, and don't show research potential) or a master (cost even more money). Surely there are way to show that I am capable of a PhD despite the lack of maths course right? In fact, since I self-studied many of those stuff, wouldn't that means I have even better research potential than those who have to take the classes? Can I turn that into an advantage? My maths grade is extremely good, as long as you ignore that one C. And my general GPA is still very high as long as only 2nd and 3rd grade are counted. Most of my fail come from 1st year, and this year I only failed 2 courses so far in completely irrelevant classes.

 

 

Most people applying to grad school will never have failed a course in their life. Many, have never earned a C in their life and some (the ones getting into top 10 schools) have mostly straight As. Failing only 2 courses is really really bad.

[Kleene]

But wouldn't the very fact that I took maths courses (and physics courses) that are dependent on both calculus and multivariable calculus, and did well in almost all of them, show that I know calculus? I don't understand why would anyone be skeptical about that. As I mentioned, the professors let anyone in. Yes the course did in fact have those as prereqs, but I was let in anyway. Of course, I still have to know those stuff (from physics classes, and self-study). Just because I don't have the class on the official transcript does not means I do not know the stuff. The prereqs are merely suggestions than rules, because otherwise classes won't fill up to minimum, and the students might not see that course ever get offered again. I'm not sure why would the transcript look strange. I'm sure there are non-math major who apply too, and thus they can expect some classes to be missing. I don't really miss out on anything except for set theory (which you did not mention as being important), since maths for physicists course cover pretty much everything. I'm not sure how to even explain why some classes are missing, I meant I didn't take them, what else can I say?

Yes, some adcoms might be lenient with your lack of basic classes if you aced advanced classes that require the basic material. Have you got A's in all your advanced classes?

 

My maths grade is extremely good, as long as you ignore that one C. And my general GPA is still very high as long as only 2nd and 3rd grade are counted. Most of my fail come from 1st year, and this year I only failed 2 courses so far in completely irrelevant classes.

IMO failing classes is just not okay. Failing classes and low grades tell adcoms more than you would wish about dedication, perseverance and the ability to complete (uninteresting) work. Your transcripts will reflect an apparent lack of care. To be honest, the fact that in your posts you try to trivialize this, makes it seem to me there might be some truth it in. Please read my reaction to the following quote w.r.t. this. I agree with bsharpe that failing classes is rare and quite bad.

 

 

I think that excuse is pretty much the only way I can explain those bad grade. It's done, and is on my record, so there is nothing I can do about those bad grade except explaining why it happened. For example, I could request one of the professors to explain in the LOR that I actually did very well on the complex analysis course until the final blunder (not sure if it's a good idea, just a thought, did not try).

No. You should definitely not make excuses. That would probably make you come across as immature. There are no excuses for bad grades. The best way is to acknowledge that you made these mistakes, and try your best not to make them again. In your LORs and especially in your SOP you might want to elaborate a bit on what you learnt/gained from these failures and how you have improved yourself such that you will not make these mistakes again. Plus, do not bother to explain individual grades. That would be definitely seen as making excuses. It is okay to give a general reason for your tendency to underachieve (personal circumtances, or whatever) if there is one.

 

 

Sorry if I am somewhat agitated. I just got another rejection. But I think for the rejection to come so late it does means for a long time I was on the table. Now I just need a bit more of something to stand out.

This all depends on the program/department. Some programs inform all accepted applicants first and then all rejects in on batch at the end. I am not sure if you have more indications than just the mere fact that you got your rejection late, but in general it is not helpful to try and make up explanations for things that happen in the application process.

 

So, what is your actual major? Physics? In that case you might want to go with a Master's on the verge of physics and maths as a sort of conversion. No sure if they exist, though. If you do well in your Master's, you will be in a significantly better position to apply for PhDs, especially if you can get some research experience too. Mind you that there are no safety schools for PhDs. Virtually all schools are highly competitive. There is no way to say if you would be able to get in any top 30 school, even if you applied to all of them. Not now, but also not if you managed to improve your application. There are guarantees whatsoever.

 

Best of luck to you, whatever you decide to do!

Edited March 29, 2014 by Kleene

[panicking]

Well thanks everyone for your comments. I'm still at a loss at what to do. I just realized that many top school don't even have Master programmes, and those that do (such as Berkeley), it seems like they have the same deadline as PhD. So it's pretty much a non-options for now.

 

Just wondering, are we talking about the same thing when we say "tier-1" programmes. Because everyone seems to make it sounds like it's something super super impossible to get to, so I was wondering if you are thinking of something very high at the top. Just want to clarify this so that we're on the same page, since I may have had a lower expectation of what "tier-1" means. For me, tier-1 programmes is just have to be in top 15. On average each programmes probably accept 20 PhD students per year. That means 300 spots. Let's say only 5000 students (count by number of actual human, not number of application) apply in total to those programmes (I can't imagine more than that many students have good enough application to even bother applying in the first place), then the competition is more like 5%. Sure it's still hard, but isn't all that impossible.

 

 

no one is willing to take a risk nor give money to you to do research when your application is weak no matter which school you are talking about

I was wondering if this is a good strategy. Applying but do not ask for financial support to get in. Borrow some $$$ for the first year. In first year, show great ability. Then ask for financial aid for 2nd year onward. Do you think it would work?

 

Most people applying to grad school will never have failed a course in their life. Many, have never earned a C in their life and some (the ones getting into top 10 schools) have mostly straight As. Failing only 2 courses is really really bad.

I only got 1 F fail, and 3 D fail. Now I was wondering if I could spin this around on a SOP, or ask a recommender to write this on the LOR. For example, I could say that the fact that I failed show that the school is extremely rigorous, and so the fact that I got an A on maths course means a lot more than someone else's A when they got perfect grade in every course. After all, grades ARE relative.

 

 

Yes, some adcoms might be lenient with your lack of basic classes if you aced advanced classes that require the basic material. Have you got A's in all your advanced classes?

Almost. There are some exception, all happened in my freshman year, which I hope they do not mind as much consider I was taking upperclassman courses as a freshman. The rest of them are all A.

 

IMO failing classes is just not okay. Failing classes and low grades tell adcoms more than you would wish about dedication, perseverance and the ability to complete (uninteresting) work. Your transcripts will reflect an apparent lack of care. To be honest, the fact that in your posts you try to trivialize this, makes it seem to me there might be some truth it in.

But I like maths. There is no ways it's going to be boring for me. Very different from those classes which I clearly don't like at all. I means, part of why I don't care is also that I did not thought it would come back to bite me now. If people can forgive criminal after merely 2 years (statute of limitation expire), surely adcoms would not dwell on something happen long ago and I can do nothing about right? As for the recent fails, well I thought that doesn't matter either since I think I'm going to grad school.

 

No. You should definitely not make excuses. That would probably make you come across as immature. There are no excuses for bad grades. The best way is to acknowledge that you made these mistakes, and try your best not to make them again. In your LORs and especially in your SOP you might want to elaborate a bit on what you learnt/gained from these failures and how you have improved yourself such that you will not make these mistakes again. Plus, do not bother to explain individual grades. That would be definitely seen as making excuses. It is okay to give a general reason for your tendency to underachieve (personal circumtances, or whatever) if there is one.

 

No I means if I ask my recommender to give excuse for me, it won't come across that I was giving excuse, but rather it will come across as the recommender think I'm good enough that he will explain it for me. I means, one of my recommender taught complex analysis, and he still remind me of that blunder.

 

 

This all depends on the program/department. Some programs inform all accepted applicants first and then all rejects in on batch at the end. I am not sure if you have more indications than just the mere fact that you got your rejection late, but in general it is not helpful to try and make up explanations for things that happen in the application process.

 

Well for most of my rejections that is indeed the only fact. But for this particular latest one, I find certain encouraging thing about it: (a) I was reminded (through email, and it appears to be a rather personal letter since it addressed exactly whose LOR is missing and contains typos) that I am still missing a LOR well into early Feb, which means that I already got throw enough hoop and it come down to the point where everything is needed for tie breaker; ( there are already rejections posted up on the result page long before mine, but after some acceptance; and © the rejection letter mentioned "difficult decision", something which is not seen in any rejection emails I have seen so far.

 

 

So, what is your actual major? Physics? In that case you might want to go with a Master's on the verge of physics and maths as a sort of conversion. No sure if they exist, though. If you do well in your Master's, you will be in a significantly better position to apply for PhDs, especially if you can get some research experience too. Mind you that there are no safety schools for PhDs. Virtually all schools are highly competitive. There is no way to say if you would be able to get in any top 30 school, even if you applied to all of them. Not now, but also not if you managed to improve your application. There are guarantees whatsoever.

 

Well currently Philosophy, but if I finish the requirement for Physics next term I would get that too. Yes I do agree that there are no guarantees, which is why I want to mention an earlier question which people seems to have neglected:

-Would my application be guaranteed if I had connections? Specially, one of my distance relative was once PhD student of a professor in tier-1 school. Is there anyway I could exploit that?

[pazuzu]

Of course it isn't impossible to get into a top program, people do it every year.  However you are underestimating how good the applicants are that are accepted.  These programs are incredibly competitive and often self-selective.  Don't think you will have much luck getting in by playing a numbers game.  All accepted students have taken the basic and advanced courses, have good GRE scores, and have demonstrated research ability. There may be a 5% acceptance rate (I don't know the exact number), but I know people with much stronger backgrounds than you who were rejected from tier 1 schools.

 

 

 

The prereqs are merely suggestions than rules, because otherwise classes won't fill up to minimum, and the students might not see that course ever get offered again. I'm not sure why would the transcript look strange. I'm sure there are non-math major who apply too, and thus they can expect some classes to be missing. I don't really miss out on anything except for set theory (which you did not mention as being important), since maths for physicists course cover pretty much everything. I'm not sure how to even explain why some classes are missing, I meant I didn't take them, what else can I say?

Your transcript looks strange because you have to know the pre-reqs and you have no proof that you so.

 

 

Let me speak as an adcom member for a second. Math is built on foundations.  For example not having linear algebra, but doing well in courses which use, it implies an ad hoc knowledge of the subject.  Your record does not show you have mastered linear algebra.  Secondly, not having the calc sequence means you might understand some calculus, but I cannot trust (pay) you to teach a calc one class to a bunch of undergrads. Further, not knowing your school, if they let you take classes without prerequisites those classes must not go very deep into the advanced topics.

 

This last paragraph is meant to give you an idea of what the adcoms are going to say. This isn't personal, I am to trying to attack you or belittle your knowledge.  I can, however, say in absolute terms that your lack of the basic classes- even if you have shown skills in the more advanced topics- will be a big problem.

 

So you know here is what my school says are basic requirements, and this is a fairly standard statement on most math grad programs.

 

Applicants for admission to either PhD program are expected to have preparation comparable to the undergraduate major at MY SCHOOL in Mathematics or in Applied Mathematics. These majors consist of 2 full years of lower-division work (covering calculus, linear algebra, differential equations, and multivariable calculus), followed by 8 one-semester courses including real analysis, complex analysis, abstract algebra, and linear algebra. These eight courses may include some mathematically based courses in other departments, e.g., physics, engineering, computer science, or economics.

 You have covered some of the advanced topics which is good.  However, I don't know in other fields, but in mathematics it is difficult to substitute the foundation classes. Not having the calc sequence is going to be a deal breaker especially if you do not have research experience to beef up that part of the application.

There are very few non-math majors that apply to do pure math.  We have too much background required. It will

 

 

 

 

But I like maths. There is no ways it's going to be boring for me. Very different from those classes which I clearly don't like at all. I means, part of why I don't care is also that I did not thought it would come back to bite me now. If people can forgive criminal after merely 2 years (statute of limitation expire), surely adcoms would not dwell on something happen long ago and I can do nothing about right? As for the recent fails, well I thought that doesn't matter either since I think I'm going to grad school.

 

This is the most important point: adcoms in top schools (really any school) DO NOT HAVE to forgive you for performing poorly in undergrad because there are many other applicants who do not have the problems you do.  Does that mean everyone with a blemish on their record is rejected?  Of course not, but it makes it much harder to find acceptance and darn near impossible to get into a top university. 

Recent failures are even worse because it shows you haven't changed your habits.  Why should a grad school give you resources for 5+ years if you haven't shown them that you can excel?  Remember they don't owe you a graduate education, they will take the candidate with the lowest risk.  Let me say again, you are severely underestimating the quality of your competition at the top schools.

 

 

 

-Would my application be guaranteed if I had connections? Specially, one of my distance relative was once PhD student of a professor in tier-1 school. Is there anyway I could exploit that?

Honestly unless you are of similar ability, probably not.

 

 

 

Well for most of my rejections that is indeed the only fact. But for this particular latest one, I find certain encouraging thing about it: (a) I was reminded (through email, and it appears to be a rather personal letter since it addressed exactly whose LOR is missing and contains typos) that I am still missing a LOR well into early Feb, which means that I already got throw enough hoop and it come down to the point where everything is needed for tie breaker; (  there are already rejections posted up on the result page long before mine, but after some acceptance; and © the rejection letter mentioned "difficult decision", something which is not seen in any rejection emails I have seen so far.

You really should explicitly email some of the programs you were rejected from and ask what they wanted to see.  That information would be illuminating for us all.  Maybe they are just being nice, or they may say we would love to have you if you filled in x,y,z gaps.  You wont know unless you ask.





The reason I keep suggesting a post-bac is to get the basics out of the way- or at least take the basics somewhere.  There are some masters which let you take some undergrad classes, but these are for filling in gaps at the 400 level (think algebra/analysis) absolutely not for 100 level calc classes.  I know how frustrating this process can be, and I wish you success, but you need to be realistic about your background and how you will appear to an adcom. 

 

 

Edited March 30, 2014 by pazuzu

[victorydance]

Think of it this way: you are competing with the best mathematics students in the entire country (and in fact, the world) for a few spots. These are students who have great applications across the board; they have research experience, they have mathematics degrees with great grades, good recommendations, great test scores, and clear intentions and signals for what makes a successful graduate student. 

 

If you think there are easy ways into top 15 grad schools, there aren't.