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Getting into Princeton Grad School for Math?

  1. Mar 6, 2010 #1
    I am a current freshman at NYU, and I want to make it into Princeton's graduate program in math.

    My Reasons for Wanting to Do This

    I'll be frank: this is a very immature goal for me to have. Aspiring for the "top" graduate program reeks of a misplaced notion of achievement. Love of math is clearly far more important than prestige.

    I have tried to think through my future, and although it's mostly uncertainty, I am completely sure that I want to be thinking about and discussing both math and philosophy until I die. The ideal profession for me, then, is to be a professor. I would be surrounded by intelligent people to discuss things with, and I wouldn't have to waste time doing work I wasn't really passionate about.

    Here's where the unreasonable want of prestige comes in: I want to eventually be professor at one of the top 10 universities. Why? Because I want prestige! Or rather, I want to not ever have to worry about anyone looking down on me. Or rather, I am insecure about the fact that my current undergrad university is not as prestigious as I would like it to be, and I want to prove myself by over-compensating. It's kind of non-sense, but I have unrealistic standards for my own academic achievement which I must uphold.

    However, the only chance I would have at getting one of these positions is if I were to go to one of the top 10 grad schools. If I aim to get into Princeton for grad school and miss, hopefully I would still get into one of the top 10 (and if not, I'd try various escape routes). So... I am aiming to get into Princeton for grad school, fully aware that my chances are bad to begin with, simply because I can't bring myself to aim any lower than that.

    In high school, I did awfully! I just didn't know what I was doing, and the reality of the situation didn't kick in until senior year. Fortunately, I still got into NYU, which has one of the best math departments and the best philosophy department. I could have done better, however, if I had just cared the slightest bit about grades. This is why I want so much to turn things around.​

    My Current Academic Situation

    11th Grade of HS:
    • Calculus 3 (A)
    • Linear Algebra (A-)

    Freshman Year of NYU:
    First Semester:
    • Analysis I (A)
    • Computer Simulation (A)
    Second Semester:
    • Analysis II
    • Vector Analysis

    My overall GPA is a 3.925 right now, but I can assure you it is only going to go down. I am confident, however, I can keep it above a 3.8.

    My GPA in math is a 4.0 right now (...only Analysis I is counted so far). I will probably get an A in Vector Analysis, because I understand the material very well. I fear I might get an A- or a B+ in Analysis II, because I got off to a bit of a bad start. I fathom I can reasonably keep my GPA in math above a 3.85... perhaps?​

    My Academic Plan

    I am going to pursue an honors major in math. I have placed out of a lot of requirements, but I still need to take 12 courses total in math. I am going to have to start taking graduate-level courses at some point (of course I want to!). Even after that, I will have roughly 14 free courses to do with what I please. I plan to use this time to possibly have a second major in philosophy, although that could potentially prove disastrous (if I try to double major, I may get distracted, and my schedule would be tight).

    I am planning on taking either 3 or 4 math courses this next fall semester and another 3-4 math courses the spring after that. The higher concentration of math will allow me to focus my attention entirely on the subject. The downside is that the homework will all be coinciding, piling up and destructively interfering with my sleep schedule! I am going to meet with my advisor soon to try to work out details.

    I have applied for a couple REU math programs. I'm not hopeful (seeing as I am a freshman), but I'd really like to do math over the summer. If I don't get in, I will have more time to get a head start on my reading for next year (this should make straight-As not so difficult).​

    What Advice I Need

    Just tell me anything I might want to know to help me achieve my dream. I am asking far enough in advance that any advice you give has the potential to steer me in right direction early enough to avoid seemingly inevitable failure.

    • Tell me what kind of grades I need not only to be competitive, but to be wanted.
    • Tell me whether I should forget about the philosophy double major and just take 20+ courses in math.
    • Tell me whether I should keep drinking heavily every once in a while, or whether the acute damage is enough to hurt me academically.
    • Tell me whether I should worry about the fact that I, for once in my life, find myself lying in bed awake, feeling a choke in my throat, and dreading a midterm for which I am less prepared than the other half of the class.
    • Tell me what I should do now that I would otherwise figure out way too late.
    • Tell me whether I should just go into something that makes money and forget about all of this.
    • Tell me how slim my chances actually are.
    • Tell me what the applicant pool is like for Princeton, or UChicago, or MIT, and whether the ~5% acceptance rates mean I have no chance of standing out.
    • Tell me whether I should try to transfer to UChicago as an undergraduate and face a bunch of core requirements, but immerse myself in a far more academic environment than I can find here.

    And most importantly: Tell me what questions I don't even know to ask!

    Thank you, preemptively!
     
  2. jcsd
  3. Mar 6, 2010 #2
    An Ivy League school will not help you get a handle on your personal insecurities. That has to be healed from within. Approval from society, your peers, or achieving "prestige" won't help.

    I sincerely hope you realize this sooner than later.
     
  4. Mar 6, 2010 #3
    union68, I understand this. Why else would I myself call my own aspirations "unreasonable" and "unrealistic"?

    I already know how to be happy, but I have decided I'd rather be stubborn and miserable.

    Or, perhaps I just want to get an idea of how much unreasonable misery I would have to endure. After all, there ARE people who do get into Princeton's graduate math program. What qualities do those people have? Certainly they were not all of such absolute genius that I could never hope to compete! With so much time left in my undergraduate education, certainly I do not have no hope of becoming competitive!

    I mean, are you trying to advocate that I don't even attempt to get into Princeton for grad school simply because one of my motivations stems from personal insecurity? Are you advocating instead that I hope only to get into some grad school?

    All I know is that in the past, not clearly thinking through what I have to do has had bad consequences. At some point, I'm going to have to make a decision about how much I want to put myself through. Before I make that decision, though, I want to make sure I am not deceiving myself about what I need to put myself through.
     
  5. Mar 6, 2010 #4
    If you are taking 3-4 math classes per semester, where are you going to fit the good ol' generals? Unless you've already taken care of those?

    And I'll also echo what union said. Even if you were to succeed in your almost impossible scenario, there is always going to be someone better than you. If you did get there, you will just be disappointed as there will be someone at the school with more prestige than you. It's a tough pill to swallow, I know as I used to be like you until I realized that is a hopeless goal that only ends with disappointment unfortunately. :(
     
  6. Mar 6, 2010 #5
    Just do your best in the present that's all you can ask of yourself. It's not the end of the world if you don't become a professor of math at a prestigious ivy league. That is a great mission statement: "I want the prestige of being a professor first and foremost"

    You seem like a very narcissistic individual. The truth is is that there will always be someone better than you, get over it. That doesn't make you a failure. You're a failure if you cannot seek happiness without the approval of others.
     
  7. Mar 6, 2010 #6

    chiro

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    If you want to get a feel of what the generals are like you can read them on princetons website.

    I should point out that you should be more focused on becoming the best on a personal level and not be the best so that you get showered with praise or so that you can boast. Also most people find out that prestige doesn't count for much once you get real life experience. In most jobs in my experience be it blue collar or white collar most want to hire people that are good team players, hard workers, have a somewhat decent personality, and are able to learn and contribute to the company. Also if you were to go into university you would have to do some teaching in most circumstances (granted there are "researchers" but even then they will more than likely have to teach something).

    I'm pretty sure twofish-quant mentioned in another thread the difficulties faced in getting an academic position let alone an academic position at a "prestigous" university and you can probably search for it to get some really good advice.

    My advice to you is to get some experience in "real world" situations so that you can realize that no matter how smart, quick thinking, or whatever you are, that people out there will be smarter at some things, not so smart at other things, and require you to forget your achievements, your abilities, and remember that in most environments we are all on the same page when it comes to attitude and personal perception of other people.
     
  8. Mar 6, 2010 #7
    I don't think I "advocated" anything of that. I merely addressed what was apparent to me: a lack of self-respect and a misplaced sense of worth and value. Perhaps you should reread my post and actually think about it before you get defensive.

    What if you don't get into Princeton? What if you don't get into any school in the top 50? Since you seem so invested and wrapped up in "prestige," can your self-confidence take that sort of blow? If we said, "No, you have absolutely no chance of getting in," would you still study math?

    What's worse is that I think you're the type of individual who -- if you did get into a big Ivy -- would look down on all the rest of us mere state-university common folk.
     
  9. Mar 7, 2010 #8
    When i was a kid i always had this idealistic idea that it would be 'ME' who would do wonders in the world mathwise. Unfortunately, for quite some time, even during my first years of high school it was this idea that kept me going, that motivated me to do math each and every day. However, later on, upon realizing that no matter how much i would try to exel at math there will always (as people have been mentioning here) be tons of smarter people than me, i came to a point that i wanted to totally quit doing math. Having been feeding myself with illusions, i no longer saw the point of doing math. What's the point if i will not be amongst the best of the best?!
    On the other hand, math brought me joy as well, and now i love math not because i want to be the best, or i want to show others how good i am, i do math simply because it brings me joy like nothing else would ever do. This is what you have to ask yourself, 'why do i want to get into an IVY league university? Is it to tell the others that i belong to the elite, or what? By all means, you should do your best to get in...you said it yourself, people DO get into MIT, Princeton, Harvard etc., and you might be one of them soon too. However, the source of the motivation should lie within you and nowhere else. It should be intrinsic.

    Although, as human beings, we seem to always be more concerned about the future rather than the present, i think you should try to make the best out of you education right now, the rest (The name of the grad school) will be a mere consequence.
     
    Last edited: Mar 7, 2010
  10. Mar 7, 2010 #9
    Instead of complaining about your academic environment, why don't you try to take advantage of the opportunities? You have probably realized at some point that you attend the school that is particularly exceptional in the realm of mathematical analysis, so why in the hell would you want to transfer? If you haven't already had a class with a Courant Institute professor, I'm pretty sure you have the opportunity to do so. Instead of wondering if your academic environment is perhaps less intense than that of other schools, why don't you try getting to know your profs better? If you can't even take advantages of your current department, what makes you think that transferring to a supposedly more intense environment will benefit you in any way?
     
  11. Mar 7, 2010 #10

    Vanadium 50

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    If someone told us that they wanted to be a professional basketball player with the NBA, and their whole self worth depended on that, would the right thing to do be to give them coaching tips? Or to suggest they develop a more realistic sense of self-worth? Would this advice change if they were a pretty good basketball player in high school?
     
  12. Mar 7, 2010 #11
    First of all, thank you Vanadium 50 for putting things in perspective with the analogy. Having focused on a particular concern of the OP, I did not take each concern into equal and careful consideration, but I had no actual intention of "coaching" the OP through anything. The OP raised concerns about the lack of an intensive enough academic environment, but NYU's math department is certainly prestigious, if the prestige is associated with the accomplishments of the faculty of the Courant Institute. Of course the prestige attached to the faculty of a particular university does not necessarily enhance a student's learning ability. But seeing as how I am fairly certain that reputable professors of the Courant Institute do teach undergraduate courses, the OP is at the very least afforded with unique opportunities. One could argue that the OP cares more about prestige in a strictly brand-name sense, yet judging by the OP's reason for wanting to transfer to UChicago, I'm not sure about his true intention. Regardless of how the OP assigns prestige to schools, it is clear that the he takes his current university for granted, which need not be the case.

    I think those who have read the first post have some sense that the OP does actually want to do math, but completely reject the OP's ultimate "goal" of becoming a professor at a top 10 university. Judging by the OP's first three paragraphs, this is ultimate conclusion is anything but a well-defined goal. While I agree that the OP should get over the need for seeking the approval of others, there is no particularly good reason to take his immediate arrogance -- which should not be condoned -- to be stronger than it actually is. Just because someone is worried about the opinion and approval of others and holds himself to high standards doesn't mean that person is boastful or contemptuous. The OP never intimated that he wanted to get ahead of everyone, but rather he only wanted to be among the top, which again seems arrogant but it's not exactly an unfathomable standard.

    My only challenge to the OP is to separate daydreams from actual goals. If all of this potential effort was predicated upon some perception that personal recognition is the ultimate end, it's probably not going to work out too well. As mentioned by others in this thread, it always comes back to how you feel about math, and how committed you are to the subject.
     
  13. Mar 7, 2010 #12
    @erok81: I'm almost done with the core requirements. APs and a proficiency exam allowed me to place out of foreign language and science.

    @Feldoh: That's good advice. I am not naturally narcissistic (and there are very few people who are). I do not feel I am better than everyone else, but sometimes I have to force myself to think I am. Why? Well, because for some reason, it has always greatly affected me what other people think about me.

    I am a victim to my inherent emotional response to how people see me, and the only way I know now to avoid being so is to recognize that most of the people who I come in contact with aren't trying to do what I am doing. Most people I see every day aren't interested in math, or they don't want to go to grad school, or they do silly things like get high and giggle while listening to their obscure music. Unless I separate myself from the majority of NYU students who are living lives so radically different from myself, all I feel is excluded for not being more like them.

    (Note: the above sounds like I am being an antisocial prick, but this is not the case.)

    @chiro: I want to teach! I am not aiming just to be a research professor. I love to explain things to people, and I feel I have a natural knack for getting people to understand things. The most rewarding thing in the world for me is to share ideas with people.

    @union68: I am not sure what I would do if I didn't get into any school in the top 50. I haven't figured out my plan yet. All I know is that at the time of application, I want to have already figured out a few alternate life plans. If there is a significant chance I won't get into any top 50 university, I may try to get a job in the government or something. I haven't thought that through yet, though. I haven't committed to preparing for any plan B yet. Would I still study math though? Of course! I study math because I love math.

    Sorry for the harsh initial response...

    @Sutupid math: Brilliant advice!

    snipez90: I do realize how great the math department here is. The professors here are all very intelligent. I have taken classes with Fred Greenleaf, Percy Deift, and Charles Peskin, all of whom are absolute geniuses! I have resolved to spend more time talking to them. I just have to get over a bit of initial fear that I am bothering them. I also have to spend a bit more time reading, so I don't ask stupid questions.

    NYU is one of the places I would be very happy ending up as a professor. My problem is not with the NYU math department, but with the environment overall. At UChicago, everyone is really dedicated to their academics, and that kind of environment tends to make me happier. NYU has an (un)characteristically un-academic environment among its undergraduates. It just means I have to work harder to find people who actually care about thinking more than they care about the newest album coming out, or what's going on at some club in Brooklyn. I have made it my own responsibility to make sure I stay friends with the few people here who will have a philosophical discussion with me. This is something I have to continually work for, however. This is the reason I don't like NYU so much, but I am not using this as an excuse.

    Basically, you can't exactly be drawn into an academic discussion here. I have the impression that it's almost hard not to be be drawn into an academic discussion at UChicago. I am going to decide if I still want to attempt to transfer next year. It's really difficult to transfer though, and even if I got in, I would be confronted with a slew of new requirements, and I would feel guilty leaving NYU.

    I actually know a math major who is applying to transfer to both UChicago and Columbia next semester. He is really intelligent, but he has almost stopped caring about his academics since he applied to transfer! I had been thinking about applying to transfer this year, and even wrote one of the essays, but I realized I was better off not worrying about it for now. I applied to a couple REUs instead, because those could make much more of a difference in my academic development than transferring after freshman year could.

    Well, writing all this out has certainly made me realize how important it is to set aside time to visit my professors. I have been neglecting that opportunity, and honestly, developing relationships with professors is going to be much more influential in my math education than taking a bunch of classes.
     
  14. Mar 7, 2010 #13
    Definitely the latter. The problem is that people that have unrealistic beliefs about their prospects tend to have no fall back plans and to make horrible life decisions because of that.

    No, because even if you are the best basketball player in the world, you could get hit by a car and that would derail your basketball career.
     
  15. Mar 7, 2010 #14
    Let me tell you right now, that it is extremely unlikely that you will be a research professor, so your goal right now should be to think of ways of getting to your real goal assuming that nothing that you plan for doesn't turn out to work. The process of getting into Princeton and then getting a professorship is pretty standard. What you really need to start thinking deeply about (since it's more relevant problem) is what to do with your life if you *DON'T* make it into Princeton.

    It's really good and refreshing that you are being honest with yourself since this puts you ahead of most of the people in the world. The bad news is that you probably won't be able to get prestige via the academic route. Too many people, too few spots. The good news is that you'll probably be able to get what you want through other means. Start your own company. Join the army. Teach little league football. Have kids.

    Doesn't work that way. One thing that you have to realize is that some people will always look down on you no matter what you do. People that are really interested in football are going to look down on a math professor from Princeton.

    One other thing that you'll find is that once you get into the inner circle, there is an inner, inner circle.

    As I said before, you are three steps ahead of most other people, because at least you are being honest with yourself.

    The first thing (which you've already done) is to figure out what your real dream is. You want people to look up to you. That's not a bad motivation. The question that you *will* have to figure out at some point is how you can do this even if you don't get into Princeton. OK, you didn't get into Princeton, but you got into North Podunk University. At that point, setting yourself the goal of turning North Podunk University into a math department that will rival Princeton will get you serious, serious bragging rights.

    The other thing that you have to realize is that even if you *do* get everything you want, you'll still have problems. Suppose you to get into Princeton University, you become a world renowned professor, and you win the Fields Award. You'll *still* be insecure. You'll be worried about what to do for an encore and worried about people whispering behind your back that you've lost your edge and are over the hill.

    Something that I've found is that people (including myself) that push themselves to achieve often find themselves under *more* stress once they've gotten what they wanted. If you don't have something, you worry about getting it. If you get it, you worry about losing it.

    Let me also point something out to you. You are at NYU. Learn everything you can about the history of NYU. NYU is a hugely interesting university, because until rather recently it was something of a sleepy commuter school, and someone made the decision to turn it into a top-ranked global university, and to a large extent succeeded. One bit of recommended reading is Kirp's "Shakespeare, Einstein, and the Bottom Line: The Marketing of Higher Education" and it has a section on NYU which I think you will find very interesting.

    What I think is happening (since it happened to me as an undergraduate) is that your insecurities and worries are those of your teachers. You are absorbing the world view of your teachers, which isn't necessarily a bad thing, but you have to realize that it's going on. They are brainwashing you, which isn't a bad thing since part of the purpose of going to college is the be brainwashed, but it helps to know how and why your teachers are brainwashing you. My guess is that you want to go to Princeton because you are spending most of your time with professors that secretly (or not so secretly) wish they were at Princeton.

    I think that you have found yourself in a fascinating place at a fascinating time. I really think that you should double major in philosophy/math because philosophy is one of the departments at NYU that has become a prestige department whereas math/science at NYU hasn't got the funding that the law, medical school, and philosophy have. Also it will be interesting to see how the Brooklyn Poly merger goes.
     
  16. Mar 7, 2010 #15
    And there is nothing wrong with being narcisstic.

    Curiously I've found that this isn't the case. It's frighteningly easy to be the world expert of some small obscure topic. One thing that I've noticed is that I sometimes get incredibly depressed when I've found that I have become the best at something. It's like "ok., I'm the smartest physicist in North Podunk (population 5000). Bummer."

    That's one philosophy of life, which works for some people. It doesn't work for me. A lot of my life involves trying to get the approval of other people, but the important thing is to have the freedom to choose *whose* approval you want. You can't please everyone, and part of life is to make decisions on who you choose to please and who you don't.
     
  17. Mar 7, 2010 #16
    People are very social, and so what can happen in these sorts of situations is that you separate yourself from the outside society and then get embedded into your own little society (i.e. we are the math geeks). This can cause interesting things to happen because when you have a small tightly-knit society, then you absorb the rules and aspirations of the society you are in.

    Also it can be really scary to be in this situation since it's easy for the small society to kick you out.

    One thing that you'll find is that if you want to be a professor at a prestige research institution, they aren't going to care much about how well or badly you teach. What happens in a lot of these places, is that teaching is seen as something that the less skilled people do.

    Standard thing to do if you end up in a bottom 20 school, is to see what you can do to raise the rankings. This is the interesting thing about NYU is that before 1980, it wasn't a particularly prestigious school, and came close to bankruptcy a few times in the 1970's. One of the great things about going to University of Texas at Austin, is that I got to meet some of the people, that built the astronomy department from nothing. Before 1965, UT Austin had no real astronomy department, and it contracted its observatories out to University of Chicago. Harlan Smith and oil money changed that.

    There is a significant chance that you won't get into any top 50 university. You might start now studying what makes a top 50 university a top 50 university. $$$$$ is a lot of that.

    People are thinking, it's just they are thinking about different things.

    This may not be a good thing. One thing that I've noticed about UChicago, is that their economic theories tend to be heavily mathematical with absolutely no contact with the real world. My guess is that a lot of this is because the economists just talk with mathematicians and don't talk with anyone that would be interested in clubbing in Brooklyn, so they have absolutely no clue about how real people behave under stress.

    Also, I've found that it helps to have a broad definition of what constitutes an "academic discussion". One of the more interesting conversations that I've had was with a fashion designer, and while I was talking to her, I started to realize how much the world of academia resembles fashion.

    Getting to know your teachers is pretty important, because at some point you'll realize that your teachers are human beings, which can be a rather scary realization once you think through the implications of that. There are professors that I respect, and professors that I don't, and one thing that happened to me is that once I got to know some big name professors better, it helped me make some decisions as to who I really want to be, and who I don't want to be.

    I mean, I'd rather be a nice guy than to turn into Professor J. On the other hand, Professor W is freaking amazing. He is close to eighty, so I still have time to turn into him. :-) :-)
     
  18. Mar 7, 2010 #17
    twofish-quant, what you have to say is really enlightening.

    I am sure that by the end of my education, I will probably be better at math than anyone else who has cleared 12 feet in the pole vault. :)

    That being said, I have a friend vaulting 16 feet. He's terrible at math, though, so it balances out. But he's good at cello. He is perhaps the best cello player who can vault 16 feet.
     
  19. Mar 7, 2010 #18
    OK, I'm definitely double majoring in math and philosophy! It turns out that majoring in philosophy would exempt me from an additional core requirement, meaning I would have none left!!!

    So, over the next three years, I have 24 4-credit classes. An honors major in philosophy requires 11 courses total (10 for regular major). I need 9 more courses for the math major (for 12 total). This leaves 4 courses free to dedicate to whatever I wish.

    In addition to this, because we are allowed to take 18 credits each semester before going over the limit (at which point we have to pay more $$$$), I can use the two left-over credits each semester to do formal independent study in math or philosophy.

    Now, this leaves me vulnerable to a whole host of potential schedule conflicts, so I am going to have to work with my advisor to figure out how to safeguard myself against them. The basic plan is to finish my prerequisites and likely conflicts as soon as possible.

    The major problem left after this is that I am supposed to study abroad one semester. Technically, I am required to study abroad to remain in the honors scholar program of the College of Arts and Science. Of course, the experience would be nice, but not if it means sacrificing the ability to take more math or philosophy courses. I need to figure out if it is possible to remain in the program without studying abroad, and if not, whether it is even worth it to remain in the program.

    But first and foremost, I have about 150 pages of literature to read before Tuesday...
     
  20. Apr 1, 2010 #19
    I just have to say this: "THE NYU MATH DEPARTMENT IS AMAZING!"
    Not only did I have no trouble with working out my academic plan, but all of a sudden I'm taking five courses a semester, with three graduate level! Basically, it's absolute freedom! I can take whatever I want! Hooray!

    Here's my more or less finalized plan for next year:
    attachment.php?attachmentid=24806&stc=1&d=1270167772.png

    Differential Geometry I and Real Variables are graduate courses. Because of that, however, they are only 3 credits! [Don't ask me the logic!] This means I can fit in Logic, which is required for philosophy, and still be within 18 credits. Honors I is cross-listed with the graduate course Complex Variables I, so it will by no means be easy. Neither will Algebra I for that matter!

    Now, I just have to be weary about classes filling before registration time. And, of course, I'll have to do a lot of studying over the summer to be adequately prepared for these courses.

    In other news, I am only going to pursue a major in philosophy, not an honors major. It makes no sense to.
     

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