Mathematics Grad. School Application Harvard

[negru]

Depends what you mean by uncommon. If more than 20 students in the US can do it, it will be pretty common when applying to Harvard, that's the problem.

 

[Newtime]

Depends what you mean by uncommon. If more than 20 students in the US can do it, it will be pretty common when applying to Harvard, that's the problem.

It just sounds fishy. He's claiming to only be taking UPPER division graduate courses, and has been doing so since freshman year. Also, he's claiming he wants to (and can) finish his undergrad years with taking nothing other than math courses. What university allows this? And if he was this advanced, surely he wouldn't be wondering about his chances of getting into top grad schools on internet forums. It seems either he is making this up, subtly bragging, or completely oblivious to how exceptionally talented he is.

 

[negru]

I'm not exactly sure what upper division math courses are. Algebraic geometry, number theory? More advanced? If "intro" level grad courses are algebra, real analysis, manifolds, it wouldn't be impossible to get over them in one-two years before/around freshman year.

There are many universities with completely no requirements other than completing a major. In particular, I will be graduating with only one course outside of math/physics.

Also, unless you have a good academic advisor, starting/thinking about research/what it really takes for grad school doesn't come automatically. A few years ago I also thought that the only thing I can do is take as many courses as possible. I didn't even imagine the possibility of doing research before completing most of the graduate courses. Thankfully I started reading forums in time.

 

[Anonymous217]

Depends what you mean by uncommon. If more than 20 students in the US can do it, it will be pretty common when applying to Harvard, that's the problem.

It is doubtful more than 20 students in the US can take graduate courses freshman year and supersede all undergraduate requirements in a top math university (note the top math university condition). I know this is definitely true for UC Berkeley and this seems very unlikely in privates, especially in those that focus on a liberal arts education like Princeton.

 

[Phyisab****]

It seems either he is making this up, subtly bragging, or completely oblivious to how exceptionally talented he is.

This.

 

[negru]

With proper advising and some previous training (eg olympiads) I think most of the top students at each university can do it. Maybe not advanced grad courses, but the intro ones definitely. And with an obvious cost in spare time. I think it's primarily the lack of a competitive spirit within schools which holds back most students, not their own potential. If all the advisors tell you to try some music classes, do some reading, take your time, you obviously won't feel any need to go hardcore.

 

[Anonymous217]

With proper advising and some previous training (eg olympiads) I think most of the top students at each university can do it. Maybe not advanced grad courses, but the intro ones definitely. And with an obvious cost in spare time. I think it's primarily the lack of a competitive spirit within schools which holds back most students, not their own potential. If all the advisors tell you to try some music classes, do some reading, take your time, you obviously won't feel any need to go hardcore.

It's not whether they can succeed in graduate courses early. It's whether they can meet all the requirements to be solely taking graduate courses early.

 

[Annonymous111]

It just sounds fishy. He's claiming to only be taking UPPER division graduate courses, and has been doing so since freshman year. Also, he's claiming he wants to (and can) finish his undergrad years with taking nothing other than math courses. What university allows this? And if he was this advanced, surely he wouldn't be wondering about his chances of getting into top grad schools on internet forums. It seems either he is making this up, subtly bragging, or completely oblivious to how exceptionally talented he is.

The reason I'm wondering about my chances of getting into top grad. schools is that they're top grad. schools. I've also heard of people who get rejected from these grad. schools after publishing papers to high quality math jounrals bc they haven't got good grades. Grad. admissions are a mystery to me as are undergrad. admissions. I was rejected from most top undergrad. schools. I know there're people more talented than me but I didn't see what I'd done wrong to get rejected. I'm trying to turn the tables when I apply for grad. schools.

I never said I was talented and nor do I think I'm talented. I wholeheartedly agree with DeRham. I haven't done serious research. I've only got good grades in courses with fancy names. Getting into grad. school is one thing and being a successful mathematician is another. Just getting into Harvard doesn't guarantee that you'll become a successful mathematician simply because grades, test scores and rec. letters don't necessarily give a good indication of research potential.

I feel that I should point out though that I'm not making this up. I'm not saying that I'm talented nor am I bragging, but I'm not someone who would lie about these things.

It's not that hard these days to get enough math background before going to undergrad. Besides hundreds of students learn calc. at an insanely young age. Some of them continue with math enough to have a strong background before even going to undergrad. I'm not saying that I do. But it isn't something that's uncommon.

BTW, the only reason I think I have research potential is because while I've never actually done solid research, they're indicators that suggest I might be good at it - for example ideas come to me if I think long and hard enough and some of them original. But I've never actually published anything. I'm not saying I'm great or anything - just that I do have some potential in research as do many other people - and this has nothing much to do with my grades.

 

[Annonymous111]

With proper advising and some previous training (eg olympiads) I think most of the top students at each university can do it. Maybe not advanced grad courses, but the intro ones definitely. And with an obvious cost in spare time. I think it's primarily the lack of a competitive spirit within schools which holds back most students, not their own potential. If all the advisors tell you to try some music classes, do some reading, take your time, you obviously won't feel any need to go hardcore.

I have to disagree here. They're plenty of students who can take intro grad. classes in Freshman year I don't doubt that. But olympiads don't actually have very much intersection with undergrad. math so acing olympiads doesn't necessarily say that you know undergrad. math. In fact it's quite possible to ace olympiads without even knowing calculus. As a former participant in suh compettions myself you're not even allowed to use calculus in olympiad problems.

 

[Annonymous111]

It's not whether they can succeed in graduate courses early. It's whether they can meet all the requirements to be solely taking graduate courses early.

There are several factors that saw me avoiding the general requiremets. I can't state them here but most were to do with my prior record in math. They gave me special exemption from the general requirements but "strongly encouraged" me to satisfy the general requirements. So I chose the former.

 

[Annonymous111]

I'm not exactly sure what upper division math courses are. Algebraic geometry, number theory? More advanced? If "intro" level grad courses are algebra, real analysis, manifolds, it wouldn't be impossible to get over them in one-two years before/around freshman year.

There are many universities with completely no requirements other than completing a major. In particular, I will be graduating with only one course outside of math/physics.

Also, unless you have a good academic advisor, starting/thinking about research/what it really takes for grad school doesn't come automatically. A few years ago I also thought that the only thing I can do is take as many courses as possible. I didn't even imagine the possibility of doing research before completing most of the graduate courses. Thankfully I started reading forums in time.

I agree. What are "grad. classes" really? I mean there're universities where grad. classes would be first or second year undergrad. classes at a better math university. To say you're taking grad. classes probably doesn't mean anything. E.g. if manifolds are what's covered in a grad. class then that's pretty basic. The point is that to do manifolds you don't need to have much more than a solid background in multivariable calculus and linear algebra (and some basic topology could help). Maybe a course in "morse theory" could be called a grad. class. I'd say a grad class is something that requires more material than what's covered in undergrad in at least one area.

A good indicator of what grad. classes really are is to compare with Harvard's selection of math grad. classes. http://www.math.harvard.edu/courses/index.html . The "primarily for graduates" is the real meaning of "grad class". But it's evident that Harvard is not equally strong in all areas from that list.

 

[Annonymous111]

A quick question. Is GPA measured in terms of your average % mark over all your courses or just your average grade? Does it matter whether you get 90% or 95% as long as you get a A+ or does your GPA take into account the difference. Thanks guys ...

 

[Annonymous111]

I'd also like to know how much it matters what area you have the best background when you apply to grad. school. I mean take an area X with no one in the Harvard math faculty working on anything related to X. SUppose you've published high quality research in X but want to get a PhD in X. Will Harvard (or any grad. school for that matter) reject you simply because your "X" doesn't match the interests of their faculty?

 

[twofish-quant]

There's a lot of hype about Harvard being a great university and all but surely they have some sort of maximum standard and surely there can't be too many people publishing papers to top math journals applying.

There aren't, but Harvard only graduates about a dozen math Ph.D.'s each year.

Surely Harvard doesn't expect people to publish original research before going for a PhD? And math is something that it's really difficult to get some original research done without having a specialized enough background.

They can and do. You are competing here with the best in the world, and there are people that are just absolutely incredible at math.

 

[axeae]

A quick question. Is GPA measured in terms of your average % mark over all your courses or just your average grade? Does it matter whether you get 90% or 95% as long as you get a A+ or does your GPA take into account the difference. Thanks guys ...

you took graduate courses as a freshmen, but you don't know how GPAs are calculated? kind of getting a troll vibe here

 

[Annonymous111]

you took graduate courses as a freshmen, but you don't know how GPAs are calculated? kind of getting a troll vibe here

Sigh ... I'm not a troll. If I wanted to be a troll I'd do other more subtle trollish things. I've realized from this thread that "don't post something so unbelievable that people will start thinking you're a troll" just be the "normal guy who gets B's and A's and has taken the odd math grad. class." Besides I've not insulted anyone here anyway.

 

[Newtime]

Sigh ... I'm not a troll. If I wanted to be a troll I'd do other more subtle trollish things. I've realized from this thread that "don't post something so unbelievable that people will start thinking you're a troll" just be the "normal guy who gets B's and A's and has taken the odd math grad. class." Besides I've not insulted anyone here anyway.

Look back at what I said. Personally, I don't think you're making this up. But I DO think you're either bragging but trying to seem like you aren't, or you really have no idea how ridiculously far ahead you are. Your question was answered in the first few posts but you asked it again twice, and then you asked about GPA and what not...so I could see where the troll accusations are coming from.

 

[qspeechc]

For what it counts, I think Annonymous111's story is credible. What really do you need to start doing graduate courses in math? Real and complex analysis (including measure theory), topology, algebra, differential geometry. Consider how many untalented people do calculus in high school and it is not beyond belief that a very hard-working and bright student can complete the above topics in high school.

Anyway, that's not what I want to write about. Have you thought that Harvard may not be the school for you? It is better to find a mathematician who does research in an area you are interested in then simply go to a school because of its name. Also, a school might not be as prestigious as Harvard, and yet have many top researchers in the field you are interested in, they may indeed be stronger than Harvard in that field. There are so many great mathematicians that they are not all at Harvard or other fancy-pants universities. You should know what field you are interested in, then go to someone in the department who works in a closely allied field-- say if you're interested in algebraic number theory then speak then an algebraist, if there is no one working in number theory itself-- and ask him what good grad schools or what good researchers he recommends. He would probably know if you have a chance of getting into that school from your academic record so far, or what you need to do if not. Even if he doesn't know what school is good for you, he probably has colleague (perhaps at another university) that does. By all means apply to Harvard, but don't kill yourself if you don't get in. As others have said, to get into Harvard you have to be one of the top math students in the world.

 

[jtbell]

A quick question. Is GPA measured in terms of your average % mark over all your courses or just your average grade? Does it matter whether you get 90% or 95% as long as you get a A+ or does your GPA take into account the difference. Thanks guys ...

Look up the rules at your school, or ask someone in the registrar's office, to be sure.

Where I teach, course instructors report only the letter grades (A, A-, B+, etc.). These are converted to numeric values for calculating GPAs. Something like A = 4.0, A- = 3.7, B+ = 3.3, B = 3.0, etc.

Some colleges and universities may report grades on a 0-100 scale, but I don't know any examples myself. It's not like in high school where this is fairly common.

 

[deRham]

But I DO think you're either bragging but trying to seem like you aren't, or you really have no idea how ridiculously far ahead you are.

My humble input? I don't think it's bragging, after all it's legitimately Harvard math we're talking about, and it's insane to get into, and wondering what exactly people did to get is something that is worth asking.

Sure, there are other researchers elsewhere, but there are a ton of very great ones at Harvard concentrated in certain fields. For instance, if you want to do number theory, it can be a dream to study there, not just because of the professors but because of your peers!

 

[Annonymous111]

For what it counts, I think Annonymous111's story is credible. What really do you need to start doing graduate courses in math? Real and complex analysis (including measure theory), topology, algebra, differential geometry. Consider how many untalented people do calculus in high school and it is not beyond belief that a very hard-working and bright student can complete the above topics in high school.

Anyway, that's not what I want to write about. Have you thought that Harvard may not be the school for you? It is better to find a mathematician who does research in an area you are interested in then simply go to a school because of its name. Also, a school might not be as prestigious as Harvard, and yet have many top researchers in the field you are interested in, they may indeed be stronger than Harvard in that field. There are so many great mathematicians that they are not all at Harvard or other fancy-pants universities. You should know what field you are interested in, then go to someone in the department who works in a closely allied field-- say if you're interested in algebraic number theory then speak then an algebraist, if there is no one working in number theory itself-- and ask him what good grad schools or what good researchers he recommends. He would probably know if you have a chance of getting into that school from your academic record so far, or what you need to do if not. Even if he doesn't know what school is good for you, he probably has colleague (perhaps at another university) that does. By all means apply to Harvard, but don't kill yourself if you don't get in. As others have said, to get into Harvard you have to be one of the top math students in the world.

Thanks. I agree with you. There're plenty of great grad. schools. I'm aiming to get into either Princetonn, Chicago or Harvard (but MIT wouldn't be bad either). Hopefully I get into at least one of these.

I've heard that it's hard to get academic jobs in top maths departments unless you're a PhD from Harvard. Is this true? I mean I here that most employers in math just look at your school name of your PhD and if it's Harvard or Princeton you'll increase your shot of getting math jobs. I've aspired to become as a good a mathematician I can be. I really want to increase my chances of jobs and hence I thought getting a high quality PhD from Harvard would look good.

An advisor would be nice but I'm prepared to work on my own if need be. These days, great math books are being published in numerous areas and these have been really helpful. It's becoming more and more friendly to do math when people publish books on the literature who really do know the literature and more or less these books are like advisors if you are independent enough at your work.

 

[twofish-quant]

Thanks. I agree with you. There're plenty of great grad. schools. I'm aiming to get into either Princetonn, Chicago or Harvard (but MIT wouldn't be bad either). Hopefully I get into at least one of these.

What do you do if you can't get in?

I think the problem is that you are treating graduate school like undergraduate admissions, which it isn't.

Instead of admitting about a thousand people the major math departments admit about a dozen. Your likelihood of getting into a big name graduate school is rather low, which means that rather than asking about your chances of getting in, you should set things up so that you are not out of the game, if you *can't* get into the school of your choice.

've aspired to become as a good a mathematician I can be. I really want to increase my chances of jobs and hence I thought getting a high quality PhD from Harvard would look good.

Part of being good means dealing with your limitations. What do you do if you can't get into Harvard because you just aren't good enough? What do you do if you can't get a job in academia because you just aren't that good? You might be good. But do you think that you are one of the ten best mathematicians in the world? You probably aren't, because most people aren't.

There are a limited number of spaces in big name math departments. At some point working hard doesn't help you because everyone else is working hard. At some point, you are just going to hit your limitations.

Do you like math enough so that you are willing to do it even if Harvard rejects you? Do you like it enough so that you will do it even if no one gives you a job doing it?

 

[twofish-quant]

My advice to you is to assume that you aren't going to Harvard. The odds of you getting in are low enough so that you can assume for the purpose of making decisions that they are zero.

Once you've accepted that you aren't getting into Harvard, then you can think more about some of the things that really will matter for your future. Something that you should start thinking about is to make a list of second, third, fourth, fifth, and sixth tier graduate schools that are doing things you find interesting.

 

[Annonymous111]

My advice to you is to assume that you aren't going to Harvard. The odds of you getting in are low enough so that you can assume for the purpose of making decisions that they are zero.

Once you've accepted that you aren't getting into Harvard, then you can think more about some of the things that really will matter for your future. Something that you should start thinking about is to make a list of second, third, fourth, fifth, and sixth tier graduate schools that are doing things you find interesting.

What do you do if you can't get in?

I think the problem is that you are treating graduate school like undergraduate admissions, which it isn't.

Instead of admitting about a thousand people the major math departments admit about a dozen. Your likelihood of getting into a big name graduate school is rather low, which means that rather than asking about your chances of getting in, you should set things up so that you are not out of the game, if you *can't* get into the school of your choice.



Part of being good means dealing with your limitations. What do you do if you can't get into Harvard because you just aren't good enough? What do you do if you can't get a job in academia because you just aren't that good? You might be good. But do you think that you are one of the ten best mathematicians in the world? You probably aren't, because most people aren't.

There are a limited number of spaces in big name math departments. At some point working hard doesn't help you because everyone else is working hard. At some point, you are just going to hit your limitations.

Do you like math enough so that you are willing to do it even if Harvard rejects you? Do you like it enough so that you will do it even if no one gives you a job doing it?

Huh? So you don't even know me and you tell me that the chances of me getting into Harvard are zero?

I've done a lot of research on the kinds of people who get into Harvard after looking at all of the comments in this forum (and the people who advised me to look at their CV's). Virtually none of them have original publications before going to grad. school (in fact, none of them had). Also, most of them had taken at most 5 or 6 grad. classes and only about 2 or 3 of them were "real grad. classes" meaning that only about 2 or 3 of them compared to the grad. classes at Harvard.

Now I'm not trying to say here that I'm better than all these applicants because I've done grad. classes since my Freshman year and stuff like that. I don't even know them after all. For all I know they could be very good but simply hadn't taken many grad. classes for some reason or the other. I'm also not speculating about how their applications look.

But the fact is that I want to achieve the best I can. It's not conceit or anything but I really do believe that if I work hard enough I can be among the best 10 math students in the world. This is me believing not me saying. Yes the world is a big place but none of these applicants who got into Harvard have done anything spectacular that I feel is beyond my reach except for a couple of Putnam awards.

I don't see why I should discourage myself from getting into Harvard. I think I should be trying my best to do so. Thinking that I can't get in just because it's called "Harvard" probably doesn't help me very much and neither does planning that I won't get in from my Freshman year. If everyone thought that they wouldn't get into Harvard for grad. school from their freshman year simply because there's this hypothetical "genius" who they don't even know that supposedly better than them, then what would the world come to?

It's not that I don't know my limitations. I like to think that I don't have any. I like to think that I can surpass any of my limitations to do the best I can. I appreciate the advice of everyone in this forum and I'm not saying here that I don't. But I'm not about to give up just because some people who don't even know what kind of students are accepted at Harvard say that Harvard is impossible for every single person just because of its name.

And to answer your question: Sure I like math enough that I wouldn't stop doing it even if someone gave me a billion dollars to stop. I've been doing it for nearly half my life and that's a pretty big chunk of my life since I'm not very old anyway.

 

[Math Is Hard]

I've been doing it for nearly half my life and that's a pretty big chunk of my life since I'm not very old anyway.

Is that math humor?

 

[G037H3]

Is that math humor?

6 hours a day for 10 years is a lot of time ;)

 

[twofish-quant]

Huh? So you don't even know me and you tell me that the chances of me getting into Harvard are zero?

I'm saying for the purposes of career planning and strategy, you should consider your chances of getting into Harvard math grad school to be zero, and go from there. You end up with better decisions if you do that.

But the fact is that I want to achieve the best I can. It's not conceit or anything but I really do believe that if I work hard enough I can be among the best 10 math students in the world.

And that just not true. If you have a hundred math students, and there are spots for 10 people, then 90 people are just not going to make it, and that is regardless of how hard they work.

Yes the world is a big place but none of these applicants who got into Harvard have done anything spectacular that I feel is beyond my reach except for a couple of Putnam awards.

And if the only thing that is the difference is a Putnam, then that's the difference. If you have a hundred applicants and ten places, and if *everyone* is good, then it's a lottery, and it then boils down to luck, and at that point hard work has nothing to do or little to do with it.

I don't see why I should discourage myself from getting into Harvard.

Because if you keep rolling the dice, then one day it's going to roll against you, and the people that I've seen that manage to make it in science and math tend to be the people that end up with backup plans, so when the dice rolls against them, they are still in the game.

Because, maybe Harvard is all wrong, and you should be prepared to go somewhere else if it doesn't look like its the right school.

Because, if you spend all your day trying to grab onto the impossible or highly improbably, you miss out on other chances.

But I'm not about to give up just because some people who don't even know what kind of students are accepted at Harvard say that Harvard is impossible for every single person just because of its name.

Except some of us know people that have gone to Harvard math, and know the caliber of people that they are looking for. I don't know much about you, but if I assume that you aren't a winner of the Boston marathon, I'm more likely to be right than wrong. Also Harvard undergraduate is very different from graduate math department.

It's not impossible for you to get into Harvard. It's also not impossible that you will win the New York state lottery tomorrow. What I'm saying is that it is foolish to expect that you will get in, and you should be spending a lot more of your time trying to figure out what you do if you don't get in, because you probably won't.

If you are intent on finishing the Boston Marathon, that's a fine goal. If you are intent on *winning* the Boston Marathon, then you may be setting a goal too high.

And to answer your question: Sure I like math enough that I wouldn't stop doing it even if someone gave me a billion dollars to stop. I've been doing it for nearly half my life and that's a pretty big chunk of my life since I'm not very old anyway.

So suppose you can't get into a top ten (or even top thirty) graduate school. What mid-tier, bottom-tier graduate schools are doing research that you find interesting?

 

[Annonymous111]

6 hours a day for 10 years is a lot of time ;)

I'm not 10. ;)

 

[G037H3]

close enough that a small change to the daily study number will change your age to what it is, assuming that the total hours spent on math remain the same

 

[Annonymous111]

I'm saying for the purposes of career planning and strategy, you should consider your chances of getting into Harvard math grad school to be zero, and go from there. You end up with better decisions if you do that.



And that just not true. If you have a hundred math students, and there are spots for 10 people, then 90 people are just not going to make it, and that is regardless of how hard they work.



And if the only thing that is the difference is a Putnam, then that's the difference. If you have a hundred applicants and ten places, and if *everyone* is good, then it's a lottery, and it then boils down to luck, and at that point hard work has nothing to do or little to do with it.



Because if you keep rolling the dice, then one day it's going to roll against you, and the people that I've seen that manage to make it in science and math tend to be the people that end up with backup plans, so when the dice rolls against them, they are still in the game.

Because, maybe Harvard is all wrong, and you should be prepared to go somewhere else if it doesn't look like its the right school.

Because, if you spend all your day trying to grab onto the impossible or highly improbably, you miss out on other chances.



Except some of us know people that have gone to Harvard math, and know the caliber of people that they are looking for. I don't know much about you, but if I assume that you aren't a winner of the Boston marathon, I'm more likely to be right than wrong. Also Harvard undergraduate is very different from graduate math department.

It's not impossible for you to get into Harvard. It's also not impossible that you will win the New York state lottery tomorrow. What I'm saying is that it is foolish to expect that you will get in, and you should be spending a lot more of your time trying to figure out what you do if you don't get in, because you probably won't.

If you are intent on finishing the Boston Marathon, that's a fine goal. If you are intent on *winning* the Boston Marathon, then you may be setting a goal too high.



So suppose you can't get into a top ten (or even top thirty) graduate school. What mid-tier, bottom-tier graduate schools are doing research that you find interesting?

You say "hard work is not everything". What if I work hard enough to publish a math paper in a top math journal? Or what if I take enough math grad. classes that it covers more than what's covered in all the math grad. classes at Harvard? If everyone entering Harvard had covered all the material covered in the math grad. classes at Harvard, Harvard would move higher and have harder math classes wouldn't it? This would be so even if some kind of majority of students had covered that many math grad. classes.

So the fact that Harvard doesn't have those kinds of math grad. classes means that the student who enters there doesn't know most of the math covered there. I've also read in one of Harvard's very own pages about applying for grad. school in math that the most important thing grad. schools look for is that you've been exposed to plenty of serious mathematics and have got mostly good grades. If that's the most important thing, my chances have increased haven't they?

Dude I know PhD math graduates from Harvard and all these top tier grad. schools who really aren't that spectacular. I'm not naming names here but the point is that it's an exxageration to say that Harvard is like the god of math or something like that. Most of thes epeole never took any sort of advanced math classes in their sophomore let alone freshman. So I'm pretty sure I'm going to get into at least one of the top 10 schools. I don't necessarily think that I'll get into Harvard but I'd be pretty surprised if I didn't get into at least one top school like Princeton, Stanford, MIT, Chicago etc.

You ask me What if I don't get into any math grad. school in the top 30?! Your argument is that since the chances of getting into Harvard are nearly zero I should have a back up plan. But the same argument tells me that the chances of NOT getting into a top 30 grad. school is also very nearly zero. That's the absolute worst case scenario that it's not worth preparing for that. If that really happens then not getting into grad. school would be the least of my worries! It's like saying that the US will be bombed tomorow. Ain't going to happen ...