coffeeintotheorems

newms: I split the separate discussion into a new thread.

Split from previous thread I personally think you're overthinking this. I, for one, never worry about ethics when I take drugs; my sole concern is potential long-term effects, and the evidence I've seen on this is mixed (i.e. some potentially bad long-term effects, though mainly from abuse of the drugs, and some good.) We're not talking about NZT and Limitless here. If that were a reality then I would be willing to consider ethics, since Eddie Morra was so far ahead of the rest of the human race that he became superhuman, and he used his abilities to gain power over others. That story was an extreme thought experiment, though, and so it's off my philosophical radar for the present. I would avoid the normative "should" here. But it may not be a bad idea to do so anyway: http://www.npp.wisc....yTheHealthy.pdf

Hello, OP! Sorry for jacking your thread here. As a matter of sincere apology, I'll help you out a little more. The consensus on the general GRE is that it's a hoop you need to jump through, even though the content of the vapid math portion is middle-school level mathematics. Basically you need to train for it by taking every single official practice test you can get your hands on and then get as close to an 800 as possible. As for the verbal and AWA, getting a high score won't help much (I'm a case in point on that), but you do want to make a certain minimum to avoid raising any suspicions. Those minima are roughly a 450-500 on Verbal and a 4.0 or 4.5 on AWA. If you're a native English speaker and can throw together a decently-constructed argument, you should be able to make these. If you really do have the brain (whatever that means) for higher mathematics research but have genuine "test anxiety" (whatever the hell that means), then you need to seek help elsewhere, because that's way out of my scope. I can say this, though: the first times I took the general and subject GREs, I was very depressed and did poorly on them because I freaked out and spent too long obsessing over easy questions. My initial scores were only a 720 on the Q general gre and a 600 on the subject test--the 46th percentile. Many years later, I had more purpose and undertook a focused study/training for the tests and got 800Q and then 810 (85th percentile) on the subject test--and those were without drugs!!! In summary, my view is that merely getting off your ass and getting to work can work wonders, although the effort on your part will be non-trivial. You can check out the math subject gre forum http://www.mathematicsgre.com/ for info on the subject test and for data on what kinds of applicants get into what schools: http://www.mathemati...c.php?f=1&t=357 http://www.mathemati...c.php?f=1&t=495 You can also find links to some real practice tests there: http://www.mathemati...c.php?f=1&t=593 If any moderators are listening: is there any way you can make this information a sticky post or something? I've been providing these useful data sets to people on this forum for a while, but I won't be around here forever. (I'll probably duck out of here in a month, once I move and start my grad program.)

Do you mean a parallel in terms of measurable improvements in a mathematician's performance? Or an ethical parallel? Or both, since the two are intimately tied together?

Fair enough . If you're a naturally happy, energetic, focused person, then there's nothing I could say beyond the simple "Get your s--- together this year"--i.e. get A's in all those higher math classes you're taking, train for the GREs (no excuses!), and aim high but with realistic expectations in your apps. You can search the web for data on what kinds of applicants get into what kinds of schools; I'm not going to provide any more info on how to do this because I've done so ad nauseum on this forum. (Just a preemptive message, nothing personal.)

Here's one idea if you feel you need to daydream a little less and focus more: http://amphetamines.com/paul-erdos.html (With more modern drugs and a doctor's guidance, of course.) This also presupposes you have all the other fundamentals down--i.e. good diet, exercise, sleep habits, study plan, (tentative) career/life plan. This is highly controversial, of course, and others may disagree with me. I am open to changing my opinion.

Any mathematically rigorous course like that is going to look good. Getting to the heart of the matter, though, it is no replacement for Analysis. For example, in real analysis you make a deep, close study of integration and all kinds of convergence questions related to series and to sequences of integrable functions. These issues arise naturally in theoretical statistics (e.g. delta method and other asymptotics, high-level probability theory), and that is why Stats departments like to see it on your transcript. If you're mostly interested in an MS and in applied careers then you certainly won't need to have made such a deep study. All I'm saying is that it's academically stronger for some important theory in prob/stats. Linear algebra is also extremely important for Stats--perhaps even more so than real analysis--because it is useful in both the theory and practice of the field (e.g. matrix algebra and matrix representations of vectors of coefficients to be estimated, to name just one example.)

Take a look at the applicant profiles in this link: http://www.mathemati...0a5b7bd2e19d5a0 There you will find at least three applicants there with profiles no better than yours (grades and UG institution) who got accepted to top-notch statistics programs including Hopkins, Harvard, Yale, Wharton, Madison, and Michigan. End of discussion.

Ahh, the pervasive sound of desperate people demanding answers on the internet. Getting one C freshman year is not going to wreck your life, mate, especially not if you have an A in graduate analysis to balance that out. If you keep obsessing over this, then you're only going to be fighting against yourself and wearing yourself out. If you really can't let go of this, then no amount of encouragement here is going to change that, and you should seriously consider therapy, anti-anxiety meds, amphetamines, etc. (That is not sarcasm--I mean it.) I would kill to have HYP on my record; as such, you will get no sympathy from me. Your pedigree has opened doors for you and linked you into a network of powerful academic and professional resources that are yours for the taking if you can stop being so fearful. For what it's worth, I had a friend who did his undergrad at Harvard. He doubled-majored in applied math and economics, and got many Bs and even a C on his transcript. Yeah it sucked--especially having been that perfect 4.0 concert-pianist Asian kid in high school--but he chose not to let it get him down and was able to land a job at a bulge-bracket firm on Wall Street. So don't stagnate over this. Keep moving, moving forward, towards the day when you will wake up and realize that you really have nothing to complain or worry about.

If you don't want to take on debt for more coursework, here's what I would recommend instead: in a word, lots of self-study. You need to totally absorb yourself in higher mathematics because, quite frankly, that's what you'll be doing in grad school. In other words, try to simulate the experience. If you can do so successfully (i.e. be happy and productive doing so), then that's a good sign that you'll enjoy "the life." Now, what to study. You definitely need to have a solid foundation in the big two--Real Analysis and Abstract Algebra--because pretty much any department will require you to take quals in at least one of them, if not both. So if you've never taken Algebra (which honestly surprises me a little, since I know UNC is a strong program) then you might want to start there. I recommend Gallian's book for beginners. Here's a further way you could direct your studies: obtain copies of past qualifying exams at schools you're interested in. Look at the types of questions, and--when you know enough--try taking some of them. I have no idea if this will impress adcoms, but right now the crucial thing you're trying to accomplish is developing a sense of mathematical confidence and self-worth, and I think that would be a great way to do so. I never did this, but, logically speaking, this would be the most direct way to convince yourself that you are worthy of a target PhD program. After all, the quals are the first major hoop to jump through...right?

I feel for you, man. I was in a similar boat (only 3.0 gpa when applying to grad programs), and I didn't get in to any schools the first year I applied. Your general GRE is awesome (mine was nearly the same), but I don't think that will be enough to pique the adcoms' interest for very long. Make sure you train for the math subject GRE and try to get at least in the 80th percentile. (If you can get past 90%, you'll look even more desirable.) The GREs are just icing on the cake, though, and won't address the fundamental problem that you've correctly isolated: namely, how do you demonstrate objectively that you have matured and have both the passion and the discipline to succeed in graduate school mathematics? I don't have a hard-and-fast answer for you, but here is my speculation: the best thing to do would be take some graduate-level classes at your current university. You may feel a little uncomfortable doing this. You may have to pay out of pocket or take out a small loan. But it's the most direct thing I can think of to do. If you're really not comfortable with this idea, then I have a few other ideas I could share. But I'd have to warn you, they are pure speculation--it would be good for you to get others' perspectives and advice on your situation. Now, I didn't do this (taking grad classes on my own.) I'm not sure how I managed to get into a few decent programs, although I think my connections to those universities (professors and students I knew who study or studied there) probably played a large role. Have courage; it looks daunting, but you can do it. Before you can convince an adcom that you deserve their acceptance, though, you have to make sure you convince yourself that you deserve it, and only you know deep down how you feel about that. The best way to convince yourself you deserve a second chance would be to make a promise/commitment to yourself and keep it--like the idea I mentioned of taking grad classes on your own. Good luck.

Ok, I found the inverse using row-reduction of the non-augmented juxtaposed with I3. It took me three pages, and the only conditions needed to avoid dividing by zero are c != 0 , b+c != -1, and a+b+c != -2. I promise you this will work and is probably the easiest way. (Crack open your linear algebra text if you've forgotten the process.) I recommend doing the following three things to keep your work as organized as possible: 1) Turn your paper sideways to get maximum lateral space (i.e. so you can keep long equations on a single line without going off the page) 2) In between row-equivalent representations of your matrix, make sure you explicitly write down every row operation you're performing 3) Simplify your algebra at every step whenever possible. Good luck. Let me know if you get it to work.

With all due respect, I think you're making a fundamental error somewhere in the GE (Gaussian elimination) process. For example, maybe you're forgetting about the variables x, y, and z implicitly being "behind the scenes," and then you're, say, subtracting b1 from all sides of an equation. When all else fails, you can always solve the system the old-fashioned way--by writing out all variables (x, y, and z), eliminating them one at a time, then substituting. In fact, I started doing this because I was curious. I've got to say, the algebra is pretty ugly; I stopped after I solved for z (and I didn't even solve it completely; just got close.) Here are a few ideas: 1) Instead of b1, b2, and b3, I would use three variables without subscripts, to avoid confusion. Maybe just a, b, c? 2) One practical problem with GE is that when you're writing everything within the confines of a matrix, you limit your space and end up having to cram stuff in. Unless you have really big paper or turn it sideways. 3) Another option you might try that would require you to write a little less of the b variables would be to actually find the inverse of the matrix and express your final solution in terms of that. Recall: if you're starting from the matrix-vector equation Ax=b and the inverse A' exists, then your solution is x = A'b -- in other words, express your final solutions as dot products, if that would be acceptable to your audience. Remember, to find the inverse you juxtapose the non-augmented matrix A with I3 (the 3x3 identity) and row-reduce (A | I3 ). Another important question: do you absolutely need an explicit final solution, or do you just need to demonstrate that it has certain properties? If your thesis audience does not need to see the final solution, then maybe you could just declare that "given b1, b2, and b3, x in terms of these coefficients is the first entry in the vector given by performing GE on the augmented matrix."

That's interesting. The first thing I would do would be to substitute some values for b1, b2, and b3 -- say 2, 3, and 5 -- and then check two things: 1) Make sure the determinant isn't zero for those values. If it is, then funny things might happen... 2) If the determinant is nonzero (or even if it is zero), solve the system for those values and see what happens. 3) If 1 and 2 check out, try other values for the b's, such as all zeros, all 1's, etc. This is just a little tinkering to make sure something weird isn't going on. After that, just solve algebraically with Gaussian elimination (or any ad-hoc technique that might be faster), and see what you get. If you're getting "1=1" then I'm guessing your scratch work isn't very organized and maybe your substitutions are sending you in circles. (Hey, we've all been there.) Out of curiosity, what's the application in which this equation has shown up?

Abbas, What are your research interests? Please see the PM I sent you. In summary, to get a competitive edge over other applicants, you are going to have to clarify your research interests and find good target departments with faculty interested in the same. Aside from taking more advanced courses somewhere or getting relevant work experience, I can't think of anything else to tell you.

Berkeley--your UG institution--has one of the best Stats programs in the world. Have you tried asking any of the professors there how competitive your application is? I'm not qualified to evaluate your chances, since I didn't get into a single one of the seven Stats programs I applied to. You seem to have a strong profile, however, so I would guess you could get in with funding at least at a second-tier school. The main thing I see lacking in your academic background is a course in Real Analysis. I hear that's pretty important for a competitive application at the top schools.

Dude, I'd love to help you, but you have a much better profile than I do (did!) and, as such, can and should aim at better schools than I did. (Although schools I applied to like IU and Purdue might be great fits for you as well. They're not top 20, but they do have solid if not strong programs in Analysis, which seems to be an area of interest for you.) I see you applied to many top schools last year. Were you able to glean any information as to why they didn't accept you? You mentioned something cryptic about "mistakes in the process" -- can you be more specific?

Hi there! I recognize you from the math gre forum. So you've browsed all the profiles and results there in the 2010 and 2011 archives. Before anyone here responds, I'd like to know what your thoughts are. By comparing your profile to others' in that database, what do you think is a likely range (safeties->probables->dreams) for you to apply to? My main advice would be for you to target schools with groups strong in what you want to research and simply design a straightforward SOP around that. The more specific you can be about your interests and profs you'd like to work with, the more likely you'll look like a good fit to them. Add enough strong schools in the middle-high range, and you're likely to get into one of them.

In any given are of higher mathematics there will be an initial tedious hump of abstraction that any new student will have to overcome, even when properly motivated. An unwillingness to force oneself through the difficult, boring, tedious groundwork of subjects like analysis and algebra is a bad sign and correlates very strongly to the tenacity required for graduate studies in pure mathematics. (Out of curiosity, which courses did you take as an undergrad that made you love higher math and want to go more deeply into it? You mentioned logic; what else? I don't know much about ergodic theory--your field--but my understanding is that it requires a great deal of measure theory (analysis) as a prerequisite.) Long story short, my message to the OP and those in a similar position is that you need to take, excel in, and enjoy some course of traditional higher math as a test of your fitness for graduate study. This course could be analysis, algebra, topology, geometry...as long as it is heavy on rigorous proofs. If you don't enjoy any of those subjects--several of which you'll have to pass qualifying exams in--then you're not going to succeed in higher math.

Ah, so that's what "RA" meant . If you're loving that course and understanding it, it sounds like you're well on your way. Congratulations! Also, when I said not to sweat the GRE, I additionally meant that it's the least important part of your graduate applications, at least in the sense that your ability to do middle-school mathematics quickly has little bearing on your success in a graduate mathematics program. It sounds like all you need is speed, which will come with practice. It's like Ben Affleck said about the Series 7 exam: "Don't worry, if you study you'll pass. And then you can start working on becoming a millionaire." (paraphrased very roughly from Boiler Room.) I beg your pardon! And you call yourself a mathematician! I assume what you meant is that the analysis and algebra courses are typically extremely dull, due to a bad choice of text, a bad professor, or both. If that is what you meant, then I concur. What about finite group theory? The Sylow Theorems, the Fundamental Theorem? Those are covered in every first-year sequence, and I find it hard to believe that you didn't find those topics fascinating. If nothing else, the connections to elementary number theory should pique the interest of any new algebra student; a failure to do so would mean he doesn't appreciate some of the more fundamental aesthetic nuances of higher mathematics and should run far, far away.

What proof-based courses did you take? I'm glad you like Calculus; I think everyone here does. However, higher mathematics does not in any way resemble what you did in calc. Before you even think about a degree in higher math, make sure you know and love Real Analysis and Abstract Algebra, two fundamental areas that tend to trip new students up. What do you know of these two subjects? My advice is to worry less about "completion rates" and focus more on making sure you understand what you'll be getting yourself into. Also don't sweat the general GRE; it's middle-school math, you know. Just buy the official ETS practice book, take all of the exams under timed conditions, and work on your weak spots. You should make an 800 after that.

No, it's in a complex (so it's probably not as "nice" as I'd implied), but I did look at some interesting studios at a place on Vine St. There was this old frat house that had been converted into studio and 1BR apartments...somehow they managed to cram 13 units into that building. I almost got one, but they were either too small (~200 ft^2), too expensive ($700-$750), or had their bedroom open right to the outside, where all the dirt, snow, and winter wind could blow directly into one's bedroom. For those who are less...particular than I am about living space, though, some of those places might have been desirable.

This happened to me last year. In fact, this year I got into a place that rejected me last year, probably due to funding issues. Where did you apply this year?

This is such an important skill. In fact, I don't want to even call it a "skill" but, say, a "virtue," in the Aristotelian sense. It's easy to say a tentative "yes" to all things worthwhile you would like to do, but it takes tremendous strength of character to say "no" to some of these.