<p>Yeah I wouldn’t describe the upper division math classes at MIT as algorithmic. Also while creativity is certainly needed for math research isn’t deep knowledge of the relevant area also needed too?</p>
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<p>I’m not sure which schools you’re talking about, but it seems like many schools have just one math degree, whose requirements are stronger than the general math major at MIT, but less strict that the theoretical option.</p>
<p>I agree that math classes at MIT are not really algorithmic, and that math research requires both creativity and deep knowledge. But the general expectation seems to be that math graduate students don’t start to work on serious research until they’ve passed qualifying exams, by which point there’s been enough time to get the knowledge needed. There will always be those few that are very far ahead and are able to do serious research as undergrads, but I don’t think this is something to really worry about.</p>
<p>How far into a graduate program in mathematics do the qualifiers usually take place? In my field, typically that’s spring semester of the second year–giving the students basically a year and a half after starting the Ph.D. program. I know it is different in some other fields.</p>
<p>Caltech’s math major requires the 5 terms of math in the core curriculum, 3 terms of algebra, 3 terms of analysis, 3 terms of geometry/topology, 2 terms of discrete math, and 5 terms of restricted math electives.</p>
<p>I think Harvard’s math major requires more courses but is more flexible about what they are than MIT’s theoretical option. I think I have been somewhat mistaken about previous claim too. I think in terms of number of courses the MIT theoretical math major is on the low end but in terms of prescribed courses it’s on the higher end.</p>
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<p>You are of course right, in that the courses do require legitimate problem solving. There are designed to challenge the students and indeed when I was on campus 18.100B (Analysis I) was the most dropped undergraduate course per-capita at MIT. That being said, the point I was making was that the students knew that there was a solution to find.</p>
<p>I agree that knowing that there is a solution is a big advantage. Skill in problem selection is one of the most important things for a scientist to develop–finding a problem where the solution will be significant, but the problem is solvable, though unsolved so far.</p>
<p>To the OP, please note that many CCer’s may SAY that they have perfect SAT scores and perfect GPAs, but in reality, College Board releases how many perfect SAT scores there are every year… There are not very many. That said, yes, many people do have over a 2300 SAT score, but do not take that as the only factor in acceptances! I suggest you read some decision threads and only look for the acceptances, and you will see that many of the accepted do not have outrageously amazing SAT scores (still above 2100 usually), but there were other qualities of their application that stood out for them to earn the coveted acceptance letter. Whenever I feel demoralized about perfect SAT scores still getting rejected, I look at the acceptance threads and see that SAT scores are not the sole determinant of the decision made. I hope this helps as I frequently feel your pain about this situation.</p>
<p>Don’t know if this has been brought up yet, but I’ve read somewhere that Yale admits 95% of students who have 1600 CR +M and are valedictorians. They only admit however 1/3 of students who are only belong to one of those categories. Just wondering how true this is, has anyone else heard this? Does anyone else know if it’s reliable.</p>
<p>Guys are we forgetting the point of this thread ???<> HOLISTIC ADMISSION PROCESS ANYONE !!!</p>
<h2>Mikayle Quote in post 119:</h2>
<h2>As to math pre-prep, I don’t buy the thesis that academically bound mathematicians struggle to catch up (and I hold an MIT Mathematics degree). The dirty secret of Math is that the advanced prep work does not really help you. The actual job of a research mathematician is to develop the answer to problems where nobody has a clue as to how to approach the problem. It is a highly creative activity, and one that tends to move ahead in leaps, rather than incremental steps (with some specialties excepted). The thing is, most students do not get to do REAL math until late in university or early in graduate school. It may be the only field in which students who have been told since a very young age that they are good at the subject only discover in graduate school that they are not actually good at the subject, what they are actually good at is cranking through complex algorithms that they have learned will solve problems of this type. As such while taking 18.701 freshman or sophomore year might expose you to more complex algorithms and sooner. It is not going to set you away from the pack in the academic sense.</h2>
<p>That is exactly what I am wondering. I didn’t hear about USAMO before, so I pulled up AMC12 past problems and looking at them now. I realized that they are testing the prior knowledge (I totally agree it requires skill to be able to do those), but based on the conversations here on CC, I expected USAMO to include questions that test application of mathematics principles which requires creativity. I only looked at one test for AMC12, so may be I am wrong.</p>
<p>chrysanthMum, the AMC12 is the first step toward qualifying for the USAMO. Students who do sufficiently well on the AMC12 are eligible to take the AIME. I would suggest that you take a look at the questions on the AIME. To me, it is a bit of a stretch to say that the AMC12 tests prior knowledge, and I think that the AIME draws less on prior knowledge. Then, if a student has a sufficiently high combined score on the AMC12 and the AIME, the student qualifies to take the USAMO. It consists of 6 questions, spread over 2 days, 4 1/2 hours each day, all proofs. I don’t think it draws very much on prior knowledge, although it does draw on developed problem solving ability.</p>
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<p>There is one simple answer to this: in at least mathematics, a lot of the initial hurdle is that the same insights are presented in numerous ways, and as a result, it’s much easier to see the interrelations after some level of “mathematical maturity” is developed. </p>
<p>I don’t think volume of coursework coming in is so important as the fact that one has thought about serious mathematics, perhaps written some proofs, etc over time. It’s perfectly possible to learn quickly, as you did, in this field too, but here are some facts:</p>
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<li><p>success in graduate admissions in mathematics is very GPA-dependent, although there’s a lot more to it than that of course</p></li>
<li><p>courses don’t reward people for ability! They reward people for getting the proofs correct - so if you’re better equipped for absorbing mathematics, you simply do better, that boosts confidence, and you move on happy and continue the trend</p></li>
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<p>A lot of “difficult” problems become easier with that maturity. And in mathematics, it’s my experience that hard work during a given term actually needn’t get you very far - the work you’ve done prior is often much more important, because it laid the foundations (not even for explicit prerequisites, but just the ability to think in the way the class demands)</p>
<p>While I have been the sort who experimented for years and years and kept learning indefinitely, it’s not really true that those who take advanced courses for years and years are really better off in the end for a career in the field. To be honest, my knowledge has helped my enthusiasm more than I think it’ll help my career directly. Ultimately, everyone who gets through the foundations of a field hits some kind of “wall” where they need to specialize. And then their branches of knowledge split off. </p>
<p>It’s just that the price to pay for not being able to do very well in your classes initially is very, very, very high in mathematics, if further studies is your goal. So some baseline “maturity” coming in is desirable.</p>
<p>One other thing - maturity in a theoretical field might be a bit more directly dependent on knowledge of the interrelationships of the various subfields, because theory builds rather directly on the past insights often. So the barrier to cross to reach “maturity” is just pretty high.</p>
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<p>Often “when you’re good and ready” but as a rule, at the end of 2 years, one should probably have an adviser.</p>
<p>I’m only just reading this thread now and have reached so far, only the fourth page where the topic of SAT scores came up, particularly the difference between a 2200 and a 2400. I plan to finish the thread and comment upon the current discussion but this conversation struck me as curious.</p>
<p>QuantMech wrote a detailed post on his belief that the scores were very different: <a href=“http://talk.collegeconfidential.com/15190057-post56.html[/url]”>http://talk.collegeconfidential.com/15190057-post56.html</a> He concluded that a student with a 2400 would score no less than a 2350 on his or her worst day.</p>
<p>UMTYMP commented that considering them equivalent was “ridiculous.” The OP, llazar said that it was “insulting.”</p>
<p>When I considered this in comparison to my own experience with the SAT (and the ACT) I found this rather strange. Perhaps I’m very odd, but I scored a 2110 on my first* time and a 2300 the second, a mere 10 points off of the 200 point difference being discussed before. </p>
<p>Quant Mech, in his very informative post, said he thought a jump from 2200 to 2400 might be possible if the person were seriously ill or distracted taking the first test or studied for a great deal of time before taking it again. I was neither ill nor distracted taking the test the first time, and I studied for neither test. It was a long time ago, but I have the slight recollection of opening an SAT book the night before the second test and doing one or two math questions, but this certainly wasn’t the protracted period of studying he describes. I never thought of such a jump as unusual. I tried hard on the first test, harder on the second.</p>
<p>My section scores are probably relevant.
CR: 730 M: 670 W: 710 (Essay: 8)
CR: 800 M: 700 W: 800 (Essay: 10, maybe?)</p>
<p>Is it really that ridiculous to think that scores 200 points apart are comparable, or that a student who got one could have gotten the other on a different test? Or, is a 2400 uniquely different and special, making my 2110 to 2300 irrelevant?</p>
<p>*I also took the SAT in 6th and 8th grades. These scores, of course, were irrelevant in my college admissions process. My 6th grade score was even on the old 1600 SAT. I studied for a number of weeks before taking the test in 6th grade. Besides this and the “one or two math questions” described above, I’ve never studied for the SAT. Unless jokingly teasing a friend by defining all the words on her SAT flashcards counts.</p>
<p>Ah, a later post provided the statistics on score variance between testings, problem solved.</p>
<p>Another possibility is that during the period between taking the tests you learned stuff/got smarter. I suspect that accounts for most large jumps. As the statistics described in the thread suggest such jumps are unlikely but not impossible in short periods of time.</p>
<p>To Millancad, #134, my comment was really directed at the thought that someone who scored 2400 the first time around might score a 2250 or so the second time around. While this is not impossible, I concluded that it was rather unlikely, based on my analysis of what it takes to score 2400 in terms of the number of questions missed. </p>
<p>In terms of the person with the 2250 score saying that it is essentially equivalent to a 2400, I suggest that the student see whether he/she can in fact score 2400 before saying that they are really the same.</p>
<p>CB used to include statistical information on the % of students whose scores went up, down, or stayed the same in each section, given the actual score on the current exam. This would be helpful to have, but I haven’t seen it tabulated.</p>
<p>I suppose that some people do score 2400 due to “luck,” but I suspect that the score is more reproducible than many people think.</p>
<p>I think a better reason to ignore score differences is perhaps if the skills required to score that much higher aren’t necessarily terribly relevant to the school at hand. </p>
<p>Personally, I don’t think 2200 and 2400 are remotely the same in terms of the skill at the SAT itself required. I could imagine many years ago having scored 2200 or lower on a bad day, but I have a much harder time imagining someone like me not making enough mistakes to make a 2400 impossible. How I scored pretty well is that I practiced some to get used to the test, and to get used to the kinds of silly little errors one could make on critical reading.</p>
<p>I dunno, QM. My son scored a 67 on CR in October of his junior year and two months later scored 790 on the CR portion of the SAT. That’s a significant difference in two month’s time. I don’t have an explanation as to the jump in score. His W went from 78 on PSAT to 730 on SAT (missed 1 question vs. missing three questions). The 800 in math stayed the same since 8th grade; that’s the easy stuff. </p>
<p>Writing and math seem more clear cut. CR seems more subjective, though verbally gifted kids seem intuitive about such things. I think one can improve CR scores in the way that mathboy did.</p>
<p>It’s worth noting that the PSAT is shorter and has generally easier questions so the random noise is greater.</p>