There's also the question of opportunity. Taking upper-level courses can cost (a lot) of money. Competitions such as the AMC and AIME may be easier to do for a good number of applicants.
I took Calc 3 first semester my sophomore year and could have gone a lot further had my parents been able to afford the cost of the local university (the local community college later offered Differential Equations my junior year, at a much lower cost, and I took Linear Algebra online after that).
True, relatively speaking. Although they had more top 25 and top 100 placements than any other school, it is the first time in many years they failed to get a Putnam Fellow (top 5). They had averaged two per year in the past decade.
You bring up a great point. We could not afford the univ route. My son did all the community college classes through Dif. Equ. and then worked with an online tutor who gave us a great rate. We also had financial help from an outside source. My son was also able to audit 19 units of college physics at two different univ. for free. We feel very fortunate for all the relatively inexpensive opportunities.
Art of Problem Solving, of course, has outstanding courses. They're not cheap but they're not as expensive as some online entities such as EPGY.
At least in my opinion, taking the upper division math classes seems like a better use of time than learning whatever exotic inequalities and esoteric Euclidean geometry theorems
In a sense though, they are both kind of arbitrary things. What is to say that an introductory analysis course really will be more useful? In practice, most of the results in such a course are taken for granted anyway.
However, I do agree that for quite a few people, the first option might appeal more, and in that case, it makes sense to pursue it. I think either of these two candidates will learn whatever it takes for them to succeed. Just because someone takes some college math classes doesn't mean he/she will eventually even have much interest in mathematics, in which case it was just a way to develop sharp reasoning skills and pursue a challenge.
I hope cellardweller is making a distinction between superstar and star, having used both words. I'm thinking a superstar has like an IMO gold medal, and a star might have almost made USAMO. I would say there is bias if someone making the USAMO is considered a superstar, while someone who shows interest and ability in handling challenging mathematics in a somewhat more standard setting is considered academically ordinary. Bias towards competition math, that is.
Academic star is a designation of the MIT admission's office given to applicants with specific academic achievements. My understanding is that it is reserved for applicants who have won special awards or placed in highly selected competitions: Intel and Siemens semi-finalists and above, USAMO qualifiers and above, science olympiad medalists. State, school and local awards do not count as that would probably cover all qualified applicants.
I am not aware that MIT gives the academic star designation to applicants with superior credentials in terms of classes taken or even research accomplishements: that group would probably be too large and the designation may lose its meaning. By definition the star system involves a well-recognized academic award which needs to be rare and highly selective to be counted. There are at most 500 USAMO qualifers while there are potentially ten of thousands of students having taken advanced college math classes while in high school.
Probably well over half of academic star candidates are rejected so it is no guarantee of admission, just a higher chance of admission than candidates who are not academic stars. I have interviewed many successful candidates but none so far were classified as academic stars, even though their qualifications were excellent.
A superstar is not an offical MIT designation but would be Intel winners and IMO medalists and the like which are actively recruited by MIT through emails and letters. While not auto-admit candidates they would probably be offered admission unless there was a major flaw in the application.
Last edited by cellardweller; 03-20-2012 at 04:19 PM.
Thanks, that is very clarifying. I guess the one sticky point in all this is that not everyone who takes some classes past calculus and basic college physics has the same interest, aptitude, etc in those things. I think unfortunately, this is a bit tough to gauge, especially if the candidate is not mature enough to express his or her interest in a distinguishing fashion.
I am interested in all this partially because I did not even know what the USAMO was until well into college, and I know a fair number of enthusiasts who are somewhat the same.
One interesting thing is there are tenured professors at the same (super top) places both with IMO gold medals and no track record whatsoever. Clearly, they have abilities beyond what many others with no IMO/etc track record do, so I imagine letters and other things are pretty crucial to getting the full picture.
I knew a lot of people in advanced classes (like abstract algebra) in high school, and it was generally easier to get an "A" in these classes than it was to make USAMO. In those days there were only 150 USAMO winners per year and no Art of Problem Solving Books existed yet...I don't know if it is any easier today to make USAMO considering that the number of qualified entrants probably has increased.
Still, there are a lot of people who can get A's in high level classes.
I can't really tell you what it takes to make USAMO because I wasn't able to do it myself, even though advanced math came easily to me. If it's like it used to be, knowing some combinatorics and number theory should help. Some people easily picked the so-called "math tricks" necessary to solve these problems just from math team; later I found out much of these "tricks" were based on number theory. As a more verbal person, it was easier for me to learn mathematics when given the entire context. Of course, there are more than number tricks on the test, but the other problems could be typically solved if you had done well in algebra, geometry, and trig. Some of the number tricks problems were kind of, well, you can guess the three letters I'm thinking of--I had NO IDEA where someone could solve this from scratch other than Gauss himself.
MIT is actually very big on math contests as it increasingy wipes the field at the Putnam and it aggressively recruits IMO medalists.
Just to clarify, the Putnam is not really emphasized at MIT. There's a freshman problem solving seminar aimed at preparing for the Putnam, but other than that, most people don't spend very much time, if at all, preparing. Most people who do well on the Putnam did well on math contests in high school, and those abilities seem to stay with them in college. Also, I don't know of any other math contests that MIT participates in, except for possibly the MCM, which is a really different type of contest than the contests most people are familiar with.
Would you guys recommend taking linear algebra or differential equations? It's the end of year for calc right now and we just went over like very elementary differential equations and I kinda like them so far and i feel it's more calculus based as opposed to linear which is basically an entirely new subject so to speak so what would you guys recommend?