Undergraduate Research: How to Get Started in Theoretical Physics

[Annonymous111]

Talk about easier said than done!

Sure. But if you want to get into Harvard, Princeton, Stanford etc., what choices do you have?

 

[ephedyn]

As far as I know, 10-12 grad courses is near impossible even if you are a very strong student in Stanford.

http://www.stanford.edu/dept/physics/academics/Sample4yearSchedules.pdf

There's not even half of that factored in here. Anonymous217 is being nice. I will call this a bluff. I believe if you've reached the point where you're doing some graduate courses, you'll have graduated and moved on the grad school rather than take 10-12 grad courses. You make two fundamental flaws in what you're saying, (1) that the number of graduate physics courses you do nearly mirror the number of upper division mathematics courses you will have to do, e.g. differential geometry, abstract algebra, PDEs/BVPs, numerical methods, (2) graduate physics courses are way too specialized, and doing 10 will stretch you very thin.

Harvard, MIT, Stanford, as far as I know, require at least 1 experimental course in the undergraduate level. Some 8 classes will have to go to humanities courses. (Let's assume the guy doesn't do both grad humanities and grad science courses in college.) The core requirements will often require at least 2 courses in calculus, and 2 courses in classical mechanics and electromagnetism. Since it's a physics major we're assuming, 2 courses in at least QM/solid state/thermo/nuclear etc. is not far-fetched. Now, I'm giving you the benefit here - I'm supposing that it only takes 6 classes to finish ALL of general requirements for undergraduate physics and calculus. I'll assume from this point on no other undergraduate physics are taken.

That's 15 classes taken out of the picture. 17 more to go.

I don't think you start college knowing all of upper division partial differential equations, linear algebra, abstract algebra, real analysis, numerical methods etc. - that, VERY surely, you will encounter in graduate classes. Even if you stretch it a little, and assume you need only take 1 of each of the above, which leaves 12, just nice to pull off your 12 graduate course trick, something is very strange about doing 12 specialized courses and 4 general physics courses (we're even assuming that the said person somehow assimilates the intermediate, upper division physics knowledge that is often prerequisite background to the specialized courses from just these 4 general courses).

More realistically, I am in that position myself doing abstract algebra, differential geometry and upper division physics in my first semester, and will be taking my first graduate physics course next semester. I am still considering double majoring, which gives me space for more classes to achieve your grand suggestion: even so, listing all of courses I will take, I will only have done 6 graduate courses. At which point, it doesn't make sense to stay on anymore because I will have satisfied all of my requirements, and I might as well be doing any further grad courses as a grad student, where it's free. It does come across as very strange to me as to why anyone would stay on and do 10-12, being in this position myself.

 

[Annonymous111]

As far as I know, 10-12 grad courses is near impossible even if you are a very strong student in Stanford.

http://www.stanford.edu/dept/physics/academics/Sample4yearSchedules.pdf

There's not even half of that factored in here. Anonymous217 is being nice. I will call this a bluff. I believe if you've reached the point where you're doing some graduate courses, you'll have graduated and moved on the grad school rather than take 10-12 grad courses. You make two fundamental flaws in what you're saying, (1) that the number of graduate physics courses you do nearly mirror the number of upper division mathematics courses you will have to do, e.g. differential geometry, abstract algebra, PDEs/BVPs, numerical methods, (2) graduate physics courses are way too specialized, and doing 10 will stretch you very thin.

Harvard, MIT, Stanford, as far as I know, require at least 1 experimental course in the undergraduate level. Some 8 classes will have to go to humanities courses. (Let's assume the guy doesn't do both grad humanities and grad science courses in college.) The core requirements will often require at least 2 courses in calculus, and 2 courses in classical mechanics and electromagnetism. Since it's a physics major we're assuming, 2 courses in at least QM/solid state/thermo/nuclear etc. is not far-fetched. Now, I'm giving you the benefit here - I'm supposing that it only takes 6 classes to finish ALL of general requirements for undergraduate physics and calculus. I'll assume from this point on no other undergraduate physics are taken.

That's 15 classes taken out of the picture. 17 more to go.

I don't think you start college knowing all of upper division partial differential equations, linear algebra, abstract algebra, real analysis, numerical methods etc. - that, VERY surely, you will encounter in graduate classes. Even if you stretch it a little, and assume you need only take 1 of each of the above, which leaves 12, just nice to pull off your 12 graduate course trick, something is very strange about doing 12 specialized courses and 4 general physics courses (we're even assuming that the said person somehow assimilates the intermediate, upper division physics knowledge that is often prerequisite background to the specialized courses from just these 4 general courses).

More realistically, I am in that position myself doing abstract algebra, differential geometry and upper division physics in my first semester, and will be taking my first graduate physics course next semester. I am still considering double majoring, which gives me space for more classes to achieve your grand suggestion: even so, listing all of courses I will take, I will only have done 6 graduate courses. At which point, it doesn't make sense to stay on anymore because I will have satisfied all of my requirements, and I might as well be doing any further grad courses as a grad student, where it's free. It does come across as very strange to me as to why anyone would stay on and do 10-12, being in this position myself.

You can surely get special exemption from humanities courses at Harvard, Stanford etc. if you prove that you're so good that they can't ignore exempting you.

 

[Annonymous111]

Nothing makes you a shoe-in when applying to a place like Harvard (unless you are the child of someone important :P)

What if you solve the Riemann hypothesis tomorrow? Even if the rest of your application is full of F's and you've got nothing, you'll be accepted, in fact, offered professorship at Harvard, if you solve the Riemann hypothesis. Ditto for any long unsolved problem in a field of math, but to a lesser extent.

 

[Annonymous111]

You can surely get special exemption from humanities courses at Harvard, Stanford etc. if you prove that you're so good that they can't ignore exempting you.

Also, at Harvard, you can do whatever you like. That's because if you're good enough to get in there, you'll be good enough to make your own decisions in life. No-one needs to force you to do courses you don't want to.

Just a question: Do mathematics grad. schools care about the grades you get in non-math courses, or the breadth and depth of the non-math courses you've taken?

 

[DR13]

What if you solve the Riemann hypothesis tomorrow? Even if the rest of your application is full of F's and you've got nothing, you'll be accepted, in fact, offered professorship at Harvard, if you solve the Riemann hypothesis. Ditto for any long unsolved problem in a field of math, but to a lesser extent.

Oh come on. If you solve the riemann hypothesis (or something of the sort) you will be getting great grades.

 

[DR13]

Also, at Harvard, you can do whatever you like. That's because if you're good enough to get in there, you'll be good enough to make your own decisions in life. No-one needs to force you to do courses you don't want to.

Why are you assuming that we are only talking about Harvard undergrads?

 

[HeLiXe]

There are a couple of ways to get involved. At my university we have a undergrad research program for freshman and sophomores (which I am doing). In the research group that I am in there are seven undergrads. Two of us are in the program, the other five are just doing it (they talked with the head professor). The five are actually majoring in the research area (materials science and engineering). So if your university does not have a specific program I would talk to/email some of the professors in your interest area. But before you start sending off emails you may want to talk with some upperclassmen to see which professors would be open to taking you on.

Thanks DR13. I discovered that there are a lot of opportunities for undergrad research in the school I want to transfer to. The physics department has several professors doing research at the National High Magnetic Field Laboratory, and the chemistry department has a lot of research going on as well. I'll be looking more into everything. Thanks again for pointing me in the right direction :)

 

[Annonymous111]

Oh come on. If you solve the riemann hypothesis (or something of the sort) you will be getting great grades.

That's not necessarily true. You could be a very lazy person, or get bored of easy courses because they're too easy, and simply get bad grades not because you can't get good grades, but because you're intellectual ability is so high that university doesn't challenge you.

Just to prove that this isn't hypothetical, let's take Stephan Smale. He got F grades in university (in both undergrad. AND grad. school). But he went on to prove one of the deepest theorems in differential topology and was awarded the fields medal.

It just goes to show that grad. schools should stop being shallow and start looking at the broader picture. GPA doesn't mean all that much for everyone. Now I'm not downplaying the importance of GPA out of selfishness. I myself have great grades, I've only gotten A's. But the point is that some people don't, and they shouldn't be disregarded simply because they don't. I'll be one to be admit that I know people more talented than I who've got F grades in courses that I could get A's without virtually lifting a finger. But they're volumes more talented than me. And I'm talking about hard courses here.

For example, doing 4 courses at once means that you can get bad grades simply because you've got so much to do. It's very possible that someone could develop a deeper understanding of material if they did 2 or so courses, rather than 4.

 

[Annonymous111]

Why are you assuming that we are only talking about Harvard undergrads?

I never assumed this.

 

[negru]

Just a question: Do mathematics grad. schools care about the grades you get in non-math courses, or the breadth and depth of the non-math courses you've taken?

Non-math courses count for absolutely zero. Even if they did count for anything at all, doing virtually anything else but math-related would count more.


I think we went over this on some other thread as well, but it is indeed possible in many schools (top and non-top) to take only the courses you want, with zero general requirements outside of finishing a major. However, some math departments do require language classes. But that's just 1-2 classes. Bad/good? I don't know, undergrad is pretty much your last chance of finding other random stuff about the world (in an academic setting), but the competition for grad school is pretty fierce. You don't want to be behind. It's all about how much you're willing to sacrifice. It's always about that.


Regarding ephedyn's countdown: you can always skip the undergrad classes and take the corresponding grad ones instead. There are generally no real prereqs for classical mechanics or quantum mechanics at the grad level (or GR for that matter). Pretty much the same topics are covered (especially in QM. personally I learned what a hamiltonian is from a QM course), the only difference is you'll (possibly) need to work harder.

I don't see why a student who aces (or almost aces) undergrad QM wouldn't be able to at least decently handle grad QM instead. And after you're done with CM and QM, you're practically at the same level of any grad student.

I mean, it's not like some phase-transition occurs once you get to grad school. You don't receive 100 new skill points or smth. The only thing that changes is the mentality (both yours, your peers', and your profs'). I don't see why that change in mentality couldn't happen in one's undergrad years.

 

[Annonymous111]

Non-math courses count for absolutely zero. Even if they did count for anything at all, doing virtually anything else but math-related would count more.


I think we went over this on some other thread as well, but it is indeed possible in many schools (top and non-top) to take only the courses you want, with zero general requirements outside of finishing a major. However, some math departments do require language classes. But that's just 1-2 classes. Bad/good? I don't know, undergrad is pretty much your last chance of finding other random stuff about the world (in an academic setting), but the competition for grad school is pretty fierce. You don't want to be behind. It's all about how much you're willing to sacrifice. It's always about that.


Regarding ephedyn's countdown: you can always skip the undergrad classes and take the corresponding grad ones instead. There are generally no real prereqs for classical mechanics or quantum mechanics at the grad level (or GR for that matter). Pretty much the same topics are covered (especially in QM. personally I learned what a hamiltonian is from a QM course), the only difference is you'll (possibly) need to work harder.

I don't see why a student who aces (or almost aces) undergrad QM wouldn't be able to at least decently handle grad QM instead. And after you're done with CM and QM, you're practically at the same level of any grad student.

I mean, it's not like some phase-transition occurs once you get to grad school. You don't receive 100 new skill points or smth. The only thing that changes is the mentality (both yours, your peers', and your profs'). I don't see why that change in mentality couldn't happen in one's undergrad years.

Definitely agree that it shouldn't count toward anything. But I have heard "rumours" that it hurts your application if you get bad grades in aything, whether math related or not. Does anyone know anything about these rumours?

Yeah, I know what you mean with sacrificing. I really don't see the point in taking something other than math just for the sake of it. I mean, if someone's transcript is just math courses, that's OK. Maths in itself counts for several subjects, and it's quite possible to be good at one aspect of math but not be very nimble with another. So rather than try to learn what the smell of NH3 is in a Chem. lab, it's probably better to try to accumulate as much math as possible.

Grad. school is important, but one thing I've learned recently is that there's no point thinking about it all the time. At the end of the day, if you stick to doing the best you can and persevere for 4 years, and you have some talent, you'll be as prepared as you can be for grad. school. Trying to do things just to get grad. schools attention is pretty pointless unless you really want to do it for your own sake. Grad. school should be because you want to do research. So I hate people taking baby classes to get a high GPA just for the sake of grad. school. I mean what's the point in life if you're going to do that?

Anyway grad. school isn't the end of the world even if you don't get in a top one. For example, Dennis Gaitsgory, who is now a full professor at Harvard, did his PhD at Tel Aviv University, which isn't necessarily the best, but it isn't bad either.

Fully agree with you. There're certain top schools that don't have requirements but sometimes these have to be negotiated. You only have one chance in life to do some random course, certainly true, but on the other hand, you only live once. There's no point in being jack-of-all-trades and master-of-none.

Anyway, enough of my babbling.

 

[hadsed]

In a perfect world, Anon111, you would be right. But we don't live in a perfect world, so there will always be those people who will try to beat you out by beating the system. It just so happens now that there are so many people doing this that it's beginning to have a real effect on who gets what places in the top schools. Admissions has to do something, and the easiest thing to do is to say, 'Everyone who we think is smart enough should get amazing grades effortlessly anyway'. That way they can try and fish out the really special people from the average.

That's what I think anyway.

 

[ephedyn]

Getting back on topic, I don't think bad GPA + research vs good GPA + no research requires comparison.

Personally, I've never met a person involved in research who isn't already doing well in school. I don't think someone who doesn't have enough to get through his classes, at least by talent or focus and effort, has what it takes to spend time outside the class doing any kind of research, be it experimental "grunt" work or computational "number-crunching" work even if it is true that these require less intellectual ability.

In the case of Stephen Smale, the story is very much incomplete. He did have some bad grades, but those were the exception, not the rule. Moreover, his biography does mention that he started working hard before he reaped the results. My favorite story involvess the Nobel laureate chemist Robert Woodward, who was expelled from his school because he was too absorbed in his own endeavors in the lab after school than his classes per se, but went back, did 16-17 courses in in a semester and eventually made it to grad school.

But one has to take these with a grain of salt - Smalt was born in 1930. In his time, you could attend the first day of college, decide you didn't like it that much, pack up, and drive down to another part of the country and attend another college. It wasn't as difficult to get in undergrad/grad school, because the world population was still recovering from the Great Depression. Today, a little less than 7 out of 100 students who apply to Harvard are accepted - and the number of "valedictorians" in the college market outnumber the total applicant pool you had in those days. Similarly, there weren't 'established standards' to look at for grad school applicants - research, Putnam/IMC, scholarships (Goldwater, Churchill etc.), fellowships whatnot. You could really get in grad school nearly just because you applied, and had a close enough relationships to faculty staff who had connections.**************off-topic*************

Anon111: I agree with you that one's grad school might not matter that much. There are people who have graduated from ETH, the grand Ecoles etc. but went on to do a lot. We don't have to look very far - Geim and Novoselov, who won the 2010 Nobel prize in Physics.

negru: Surely. Most of the time we can either test out of classes, or we already have humanities credits from high school. Moreover, if you are in a top school, it's likely that you already have many credits transferred over from high school. But that doesn't happen very often - not enough for there to have enough undergrads-who-had-done-ten-grad-courses to fill whole grad school departments! The people I know who have gone to grad school in Cambridge, Oxford, MIT, Imperial etc. were every bit human: they attended introductory courses in calculus, linear algebra and differential equations like almost everyone else and by no means managed to exempt themselves from humanities (many of them hated these as much). As a matter of fact, the Putnam fellows I know at some of these top grad schools did 4 years in college like everyone else, because they had to stay back and slowly finish off their humanities courses, like everyone else.

In fact even in a school like MIT where students have gone through a lot of high school preparation in university calculus and establish themselves as talented science students, most of the people actually start out with calculus or at most differential equations, introduction to classical mechanics and like everyone else among them, did their load of humanities stipulated in their university requirements.

Top schools are in fact more familiar with the genius kid who wants to get out of his humanities classes, and so have higher standards for people who want to do the same. Like Anonymous217, I would love to know who are these real people (enough to fill a whole department) who have done 10-12 courses in grad school level, not because I don't want to believe it, but because I want to believe it - it really interests me if I can have a credible source about them.

Lastly, to me, it sounds that my argument has sealed enough of a proof that most people who get in these top grad schools don't actually do 10-12 grad school courses in college, because the counterarguments that one can come up with against it require an immense suspense of belief: "you have to work very hard" and "you can become so good that you convince them to let you do whatever you want". This sounds more like Hermione from Harry Potter, or some other book than reality.

 

[Annonymous111]

Getting back on topic, I don't think bad GPA + research vs good GPA + no research requires comparison.

Personally, I've never met a person involved in research who isn't already doing well in school. I don't think someone who doesn't have enough to get through his classes, at least by talent or focus and effort, has what it takes to spend time outside the class doing any kind of research, be it experimental "grunt" work or computational "number-crunching" work even if it is true that these require less intellectual ability.

In the case of Stephen Smale, the story is very much incomplete. He did have some bad grades, but those were the exception, not the rule. Moreover, his biography does mention that he started working hard before he reaped the results. My favorite story involvess the Nobel laureate chemist Robert Woodward, who was expelled from his school because he was too absorbed in his own endeavors in the lab after school than his classes per se, but went back, did 16-17 courses in in a semester and eventually made it to grad school.

But one has to take these with a grain of salt - Smalt was born in 1930. In his time, you could attend the first day of college, decide you didn't like it that much, pack up, and drive down to another part of the country and attend another college. It wasn't as difficult to get in undergrad/grad school, because the world population was still recovering from the Great Depression. Today, a little less than 7 out of 100 students who apply to Harvard are accepted - and the number of "valedictorians" in the college market outnumber the total applicant pool you had in those days. Similarly, there weren't 'established standards' to look at for grad school applicants - research, Putnam/IMC, scholarships (Goldwater, Churchill etc.), fellowships whatnot. You could really get in grad school nearly just because you applied, and had a close enough relationships to faculty staff who had connections.


**************off-topic*************

Anon111: I agree with you that one's grad school might not matter that much. There are people who have graduated from ETH, the grand Ecoles etc. but went on to do a lot. We don't have to look very far - Geim and Novoselov, who won the 2010 Nobel prize in Physics.

negru: Surely. Most of the time we can either test out of classes, or we already have humanities credits from high school. Moreover, if you are in a top school, it's likely that you already have many credits transferred over from high school. But that doesn't happen very often - not enough for there to have enough undergrads-who-had-done-ten-grad-courses to fill whole grad school departments! The people I know who have gone to grad school in Cambridge, Oxford, MIT, Imperial etc. were every bit human: they attended introductory courses in calculus, linear algebra and differential equations like almost everyone else and by no means managed to exempt themselves from humanities (many of them hated these as much). As a matter of fact, the Putnam fellows I know at some of these top grad schools did 4 years in college like everyone else, because they had to stay back and slowly finish off their humanities courses, like everyone else.

In fact even in a school like MIT where students have gone through a lot of high school preparation in university calculus and establish themselves as talented science students, most of the people actually start out with calculus or at most differential equations, introduction to classical mechanics and like everyone else among them, did their load of humanities stipulated in their university requirements.

Top schools are in fact more familiar with the genius kid who wants to get out of his humanities classes, and so have higher standards for people who want to do the same. Like Anonymous217, I would love to know who are these real people (enough to fill a whole department) who have done 10-12 courses in grad school level, not because I don't want to believe it, but because I want to believe it - it really interests me if I can have a credible source about them.

Lastly, to me, it sounds that my argument has sealed enough of a proof that most people who get in these top grad schools don't actually do 10-12 grad school courses in college, because the counterarguments that one can come up with against it require an immense suspense of belief: "you have to work very hard" and "you can become so good that you convince them to let you do whatever you want". This sounds more like Hermione from Harry Potter, or some other book than reality.

Eric Larson and Akhil Mathew are two examples of students who are likely to do 10-12 grad. courses in math during their undergrad. I hope I am not giving personal information since I'm only naming their names, and not linking to any of their information, and naming their names seems to be OK. If it isn't would a pf mentor please delete this. This is not my intention to delibrately give out personal information.

It's simple. The people who do 10-12 grad. classes are the ones who finish all of undergrad. math during high school. It's rare, but it happens more frequently these days. Take the two examples I gave. In fact, they've published research in high school and done grad. math in high school.

 

[ephedyn]

Well, I don't think it's unacceptable to state their names if they can be googled, so thanks. However, after taking a look, I know people who showed more talent in high school but nevertheless did not take 10-12 grad courses in college. I personally thought you knew people who had actually done it. So I feel that your estimation is off the mark. And even if they do, 3-4 years from now, actually finish 10-12 grad courses in college, it does go to show that it will be very, very rare - not every year do you get only a few of them.

And P.S., case in point: Not even Terence Tao finished all of his undergrad math during high school.

 

[Annonymous111]

Well, I don't think it's unacceptable to state their names if they can be googled, so thanks. However, after taking a look, I know people who showed more talent in high school but nevertheless did not take 10-12 grad courses in college. I personally thought you knew people who had actually done it. So I feel that your estimation is off the mark. And even if they do, 3-4 years from now, actually finish 10-12 grad courses in college, it does go to show that it will be very, very rare - not every year do you get only a few of them.

And P.S., case in point: Not even Terence Tao finished all of his undergrad math during high school.

Well according to some pf mentors it is unacceptable. I have been warned against it. It could be that they're just picking on me but I don't want to take chances.

I'd say that in the current era, many, many people have more knowledge than Terence Tao had when he was 18. THe point is that when you accelerate in math, you're not necessarily doing yourself any favors. If you learn calculus and go to university immediately, you will have the same knowledge as a first year student. THe only advantage you have is age. But age doesn't matter when it comes to grad. school applications. I'm sure a grad. school wouldn't accept a 2 year-old who knew calculus, if that's all he knew.

For example see this: http://www.math.princeton.edu/graduate/generals/tao_terence .

Even I know more harmonic analysis than that in undergraduate. But that doesn't mean that I'm better than Terence Tao since for one thing I don't even want to become a specialist in harmonic analysis. The standards are much higher these days. People need to know many areas of math at a high level in grad. school. I'm only speculating but I wonder whether Terence Tao applied to Harvard for grad. school. If he couldn't get in there, it just goes to show that luck is the most important factor in grad. school applicants.

Anyway, enough of my babbling.

 

[ephedyn]

Well, there have been more controversial conflicts between users and admins on this site

Wow, that's a very interesting site. I ended up spending the past hour reading.

I don't think you're babbling. Most of it was worth thinking. I don't agree with some of your points, though.

 

[Annonymous111]

Well, there have been more controversial conflicts between users and admins on this site

Wow, that's a very interesting site. I ended up spending the past hour reading.

I don't think you're babbling. Most of it was worth thinking. I don't agree with some of your points, though.

Which points do you not agree with me?

Anyway, I think that he was accepted at Princeton's math grad. school simply because they saw potential in him because of his age. It's not normal for someone to go through a not-so-good (to say the least) university like Flinder's and get accepted at a top school. The main reason is that you won't be exposed to serious math before grad. school. I don't even think Tao had publications before grad. school. So it's a bit of a mystery why he was accepted over the other fierce competition. I'm pretty sure grad. schools don't give weight to gold medals at olympiads.

 

[Annonymous111]

See also http://www.claymath.org/interviews/tao.php

Terence Tao seems to claim that he applied to about a dozen places for grad. school but was only accepted at MIT and Princeton.

 

[Annonymous111]

In a perfect world, Anon111, you would be right. But we don't live in a perfect world, so there will always be those people who will try to beat you out by beating the system. It just so happens now that there are so many people doing this that it's beginning to have a real effect on who gets what places in the top schools. Admissions has to do something, and the easiest thing to do is to say, 'Everyone who we think is smart enough should get amazing grades effortlessly anyway'. That way they can try and fish out the really special people from the average.

That's what I think anyway.

Who views grad. school math applicants applications? Does anyone know? I can't think of a mathematician at Harvard, who is probably super brilliant to just be appointed there, rejecting someone simply because he got a C grade in ancient history. Mathematicians, especially the very good ones, aren't the sort of people to reject applicants for bogus reasons. I can imagine a registrar or something doing that. But the funny thing is that most admitted students don't get great grades outside math anyway, especially if they're good at math.

 

[Anonymous217]

See also http://www.claymath.org/interviews/tao.php

Terence Tao seems to claim that he applied to about a dozen places for grad. school but was only accepted at MIT and Princeton.

I recall applying to a dozen places, and ending up with acceptance offers from both Princeton and MIT.

It sounds more like he applied to a dozen universities and two acceptances he obtained were from MIT and Princeton, noting the strongest schools he got accepted too. You can certainly infer that if he applied to other top schools like Harvard, he wouldn't have gotten in since he would have included that. However, he most likely got accepted into other univerisities as well but just chooses not to mention them because they're not as prestigious as Princeton/MIT.

But the funny thing is that most admitted students don't get great grades outside math anyway, especially if they're good at math.

That might be too broad of a generalization.

 

[Annonymous111]

It sounds more like he applied to a dozen universities and two acceptances he obtained were from MIT and Princeton, noting the strongest schools he got accepted too. You can certainly infer that if he applied to other top schools like Harvard, he wouldn't have gotten in since he would have included that. However, he most likely got accepted into other univerisities as well but just chooses not to mention them because they're not as prestigious as Princeton/MIT.



That might be too broad of a generalization.

I'm sure he would have applied to more than those two prestigious universities. Because Garth Gaudry would've known his talent and urged him to apply to the best places in the US. I don't think he would've applied to a lowly university like Ohio or whatnot.

 

[Anonymous217]

He certainly could have been accepted to other strong math departments in other universities that are within the top 25 or so, but simply chooses not to mention them. You can't infer that he only got accepted into 2 US universities, although that may or may not have occurred.
For example, I got accepted into Yale, Princeton, Caltech, UCLA, Berkeley, etc., but when people ask me for the best schools I get accepted to, I simply mention Yale and Princeton, and I tend to opt out LA and Caltech. And even when I just stated 5 schools that I got accepted to, I already opted out 4 others that are also pretty good universities but not nearly as strong as Yale or Princeton (JHU,SD,SB,Irvine).

 

[Bourbaki1123]

Isn't Berkeley somewhat stronger than Yale in mathematics though? Do you just mention Yale for the name recognition then? Of course, Princeton has an incredibly strong math dept.

 

[eXorikos]

I'm actually wondering what you all mean by research in this situation. Is it actually research where you can publish an article in a journal?

 

[eri]

The research most undergrads do won't get published in a professional journal, but might end up in an undergraduate research journal (many universities have their own) or being a poster presentation at a professional conference. However, some undergrads do manage to get published in a professional journal, and that looks great to grad programs. I've seen everything from last author of 50 for contributing something small to a large collaboration to a first author Nature paper from undergrads.

 

[Anonymous217]

Isn't Berkeley somewhat stronger than Yale in mathematics though? Do you just mention Yale for the name recognition then? Of course, Princeton has an incredibly strong math dept.

Sorry I just noticed this question. Yes, Berkeley is somewhat stronger than Yale in math, and yes I just mention Yale because people tend to view the best schools as the most prestigious and so I would just mention those two (I believe Caltech is also stronger than Yale in math). Yale does currently have a Putnam fellow (who became one freshman year), but I can't attribute that solely to a strong math department since the student placed 1st on the IMO multiple times.
I don't mention Berkeley though because I'm a student there and stating admission would be inherent.