Axline Scholarship

Colleges and Universities A-Z California Institute of Technology
41

<p>yeah, Terry is a decent backup.</p>

<p>happyentropy and neapol1s have given a really superb summary of everything. The undergrads at Caltech are probably better than many of the grad students in math, which helps get attention from faculty. It's much easier to get research opportunities early than at H, P, or Chicago, (i.e. get money and advising) -- and needless to say about two orders of magnitude easier than at Berkeley. Caltech undergrads are on average somewhat smarter than Chicago undergrads, so your peers will be better at Caltech, but Chicago has a somewhat better faculty. A committed student can get more resources out of Caltech than pretty much at any other top university.</p>

<p>In both students and faculty, Caltech math falls a little below the critical mass of what is needed to have a really superb department. There are individuals who can absolutely beat the pants off anybody in the world -- both on the student and faculty side -- but Harvard, Princeton or MIT have math communities that seem more vibrant. If you want to be a professional mathematician, those places are probably better purely on that dimension.</p>

<p>Caltech has turned out some great pure mathematicians over the years, but it has tended to be better at producing very strongly trained pure math undergraduates (and even grad students, c.f. Don Knuth) who go on to be big in related mathematical fields -- applied mathematics, control and dynamical systems, computer science, theoretical economics, theoretical physics, finance (academic and applied) and the like. One reason is that profs in other departments eagerly grab math undergrads for theoretical projects, and then people get interested and go off and do other things. Especially because other departments seem to have a more active culture than math.</p>

<p>In any case, one thing to observe apropos of the discussion is that an academic mathematician (in general) is a pretty unpleasant thing to be. The job market is very slow, people have to hang around in postdocs longer and longer due to inability to find a good assistant professorship (5+ years is not uncommon). Salaries and stipends are among the lowest of the non-humanities and the specialization is so extreme that the audience for the average paper is miniscule even compared to other balkanized fields. So the question of why you are sufficiently nutty to want to be a professional mathematician in the first place is one you should be asking yourself.</p>

<p>Incidentally, I chose Caltech over Harvard and Princeton to study math (full disclosure: money was one factor) and haven't regretted it. The training is very strong and the opportunities for the committed student are vast. The top few Caltech undergrads who choose to stay in math virtually always get into the very top graduate programs. The best publish research before they graduate at a rate comparable or higher than that of MIT or Harvard or Princeton. </p>

<p>So that's that... obviously, strength of math is not the sole dimension you should be considering. Hopefully the above praise/quibbles have given you some idea of where Caltech fits in and you can factor that one dimension in appropriately as you consider others.</p>

42

<p>I didn't get an Axline, and I accidentally turned in my FAFSA and Profile two weeks late. I don't think I'll be able to afford Caltech. If I have to pay even 20,000 of the 46,000 then I won't be able to go. Ugh, I'm still waiting in anticipation even after all that waiting for the acceptance.</p>

43

<p>More good info and advice, thanks!</p>

<p>The undergraduate research aspect is interesing, and I'd like to ask a question about that : Krantz's book "A Mathematician's Survival Guide" says that undergrad research has some value as an introduction to working on unsolved problems, but that it isn't that important for future mathematicians, and that it is more important to just learn a lot of math. He says "I am friends with a good many Fields medalists, and none of them engaged in undergraduate research." But Krantz's PhD was 1974, so I wonder if this has changed? I know that undergrad research experience is now expected by grad programs in many sciences, is this now true of math as well?</p>

<p>And I do know that the academic market in math is a lot tougher than in related fields, so I'd be happy if my son developed some other interests. Right now he's in love with math, and physics is the only other field he sees as conceivably interesting. (He has had AP classes in chem and econ, and a CTY class on the theory of computation, and none of those grabbed him.)</p>

44

<p>My child also was admitted to Caltech and received an Axline. She is primarily interested in physics/math, so thank you to all of the Caltech people who have posted information about those departments.</p>

45

<p>Aedar,
The most important component of the grad school application are the faculty recommendations, where the faculty are asked to compare you to other students they've worked with in the past. Since lots of math undergrads nowadays get A+'s the only way to stand out is by doing undergraduate research- especially since with the abundance of REU's and such everyone does it. A lot more people apply to grad school now than did in 1970, and smaller top programs have <10% acceptance rate- so (successful) undergraduate research becomes essential to getting in. Moreover the contents of basic undergraduate/graduate courses haven't changed much in the last 40 years-but math has, so the best way to familiarize yourself with problems you may want to work on down the line is often by doing undergraduate research. A lot of such reseach projects consist mostly in reading the literature and trying to apply its methods so you're learning MORE math by doing undergraduate research-not less. Of the 5 people from last year from last year's graduating class who went to top math programs 3 had solved important 50+ year old open problems as undergrads- a fourth one had no research experience and is going to berkeley, so it is possible to get into grad school without research experience.
(I'm not applying to grad school until the coming fall- so all the above is advice I've received from professors-and it is possible that different people have different perespectives on these things).</p>

<p>BTW the academic market in math while very bad- is better than in theoretical physics since colleges need more math than physics teachers.</p>

46

<p>I agree with entropy that it's hard to stand out without some research or at least indication that you can have original ideas. But math is very "deep" almost everywhere (compared to, say, biology, which is very broad but not so deep in many places). That is, it takes a long time of digging (reading/learning) in most subfields, except maybe combinatorics, before you can really have a chance with an unsolved problem. So it's not necessary to solve a huge open problem (one guy last year who went to MIT for grad school had a publication which was not overwhelmingly original, just showed understanding of an important set of techniques).</p>

<p>So it's important to strive to do something good, but not to be too disappointed if it doesn't turn into an Annals publication. The main use of research is that it lets you get to know profs as they see you in the process of thinking and pressing through challenges. Then they can speak informatively about your mathematical abilities beyond problem sets.</p>

<p>Without research experience, if you want to have a good chance at (say) Princeton or Harvard for grad school, you had better have straight A+'s and beat up the Putnam.</p>

47

<p>ouch, "beat up the Putnam" is a tall order.</p>

48

<p>Aedar,</p>

<p>Do you mind posting your son's stats and awards? I want to know the kind of qualifications that is required to get Caltech scholarship. Thanks.</p>

49

<p>Let me try to help a little, since people may be anxious about posting their or their kids' stats. Background: I was on the Caltech admissions committee as a student member for two years and participated in both the selection and scholarship processes.</p>

<p>To be in the running for an Axline, you need to be in the top few percent in your class (most are #1 or #2) and have SAT scores around Caltech's 75% mark -- so 800-ish SAT I Math and 780+ on the subject tests. There are exceptions but it gets iffy there. Teachers should generally regard the student as among the top in 10+ years or so, unless it's a supergood school (Exeter or TJ or similar) in which a smaller number of years will suffice.</p>

<p>With this done, there are basically three ways to get an Axline, which are not mutually exclusive. </p>

<p>One is to show clear signs of intellectual orginality beyond normal schoolwork. This is usually done by accomplishing some research or at least something that resembles research enough to show your talent for it. It doesn't need to win big prizes, though Intel and Westinghouse help. Many Axlines spent a summer working in a lab or on their own, and submitted a paper (typically about 20 pages) summarizing the results of their work. Professors and students serve on the committees, so they like to look at what a student actually did. If you can get into a program like RSI the summer of junior year, that's great. If you can get into a university lab and/or find a professor willing to mentor a project, that's great. Make sure that there is going to be a chance to do something semi-indepenent as opposed to washing test tubes. Letters from professors matter a lot.</p>

<p>Otherwise, there is the olympiad route. Contest math and science can show you are smarter and know science better than most kids your age, and that's a good signal. Axlines for whom this is the main thing tend to at least go to the national camp and often the international competition. If you are not in this box already, it's probably too late junior year.</p>

<p>The third way is college courses, though that's best supplemented with one of the other two. If you are near a good university (top 50 nationally or so) taking several hard courses there (meaning math about the level of honors linear algebra or analysis, or physics at the first and second year college level, etc.) and impressing the professors can be a good signal. It is unfair that it matters how good the nearby university is, but it's very hard to know what to make of courses at a place nobody has heard of. So that's that.</p>

<p>Generally, few Axlines feel that they were meant to get the award. A few do, like the IMO medalists, but I am more typical in that I was very surprised by the letter. I didn't really think a mediocre summer project and some classes at Princeton would be enough to impress Caltech. So work hard -- you might have a better shot than you think.</p>

<p>Let me know if there is something I didn't cover.</p>

50

<p>Ben - thank you for that post, it was really helpful. I think that what you said applies to most other top-notch colleges, too, in their admissions process. It's too late for me, but I'll make sure my younger brother knows about those three paths you talked about.</p>

51

<p>I think it's unfair to expect your child to receive an Axline, regardless of how much he/she deserves it.</p>

52

<p>Remember how much of a crap shot college admissions is, and think about how just 25 people get it, out of almost 600 acceptances and 3600 applications. Heck, I'm ecstatic just to get in!</p>

53

<p>Thanks, Ben. Much more information there than in the stats of 1 or 2 students. And my son is definitely in the "surprised" category, very pleasantly so :)</p>

54

<p>I was happy just to get in, as well. My scores are probably in the bottom 25% for Tech, especially for math. I probably should have taken the SAT more than once, but I wasn't eager to give Collegeboard any more money. ;)</p>

<p>Congrats to all of you scholarship winners!</p>

55

<p>Ben,</p>

<p>Thanks for sharing the info. It helps a lot!</p>

56

<p>Ben, your post is wonderful!
I suppose those information can also apply to someone applying to a competitive engineering school like MIT, Stanford and Caltech? (for those competitive pools like international students and asians)</p>

57

<p>Yes. Although Stanford and MIT don't give merit scholarships, if you follow the advice, you are likely to do very well in the admissions process.</p>

58

<p>I'll probably be doing research at a university lab this summer.
Should I ask my mentor to write the supplement recommendation for college app next year?</p>

59

<p>MIT actually has a few back-door merit scholarships (this is hearsay, I know, but I know a guy who I consider reliable who was offered one, as well as an Axline, and ended up going to MIT). They're not given by the school itself but rather by "separate" alumni groups so that MIT can continue to claim that they don't offer any merit aid (although admissions "recommends" the winners to these outside groups, and the scholarships are only good at MIT).</p>

60

<p>kenny - yes, that would be a good idea.</p>