<p>I think most students would be behind 1-2 years at most. Even most excellent math students only start out with about 4 semesters [probably something like 18.01, 18.02, 18.03, 18.100] and a lot of students start at with at least one. Another problem with QuantMech’s proposal is how to identify promising math candidates from disadvantaged backgrounds. Many people find they neither like nor are good at proof based mathematics but there is no way of determining that before people see proofs.</p>
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<p>Nominally 18.701/2 may be junior/senior classes but I don’t think most of the students in those classes are juniors and seniors. It is definitely possible to do well with taking 18.701/2 sophomore year though. Isn’t it the case that graduate math classes are essentially required to get into good math grad schools though? I’m also under the impression that MIT’s math classes aren’t particularly difficult compared to other elite schools. Some of the most advanced undergrad classes [functional analysis, representation theory, and differential forms] might be graduate classes at most universities but I think that is exception rather than the rule. Some posters have claimed that Chicago’s undergrad math classes are somewhat more advanced than MIT’s but MIT math majors take many more grad classes. From looking at syllabi that seems reasonable.</p>
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[Disclaimer: I haven’t taken either course but I took a course that followed 18.701 pretty closely] I think that may largely be because they cover much of the same material. My comment may have been less true for 18.700 than the other courses.</p>
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<p>Well often times mathematical/spatial intelligence is considered somewhat distinct from verbal intelligence. I also suspect at MIT that non-native English speakers with great technical skills but poor English skills will mess up any attempt to measure this.</p>
<p>EDIT: I cross-posted this with the last three posts</p>
<p>If students are only 1 year behind, that is better, and they could have a single year of foundation funding, to take a 5 year B.S. If you observe undergrads, I think you will see that a large number face considerable financial pressure to finish in 4 years–so they need to select a major that they can finish in that amount of time.</p>
<p>While UMTYMP student raises a good point that it is difficult to identify the students who will take to proof-based mathematics before they encounter proofs, I think that my suggestion would open the major to students to whom it is not open now, in reality. One might learn from observation over the first few years how to identify promising, but underprepared students more accurately.</p>
<p>The requirements for a general math major are reasonable enough that someone who comes to MIT with no credit in math can finish on time. This is even true for the requirements for a math major with the applied and theoretical options. The issue with being “behind” is not whether or not someone can finish a math major in 4 years, but whether or not someone can graduate with 12 graduate level courses, or maybe just 2 or 3.</p>
<p>I don’t think it was ever in dispute that entering MIT students with decent amounts of mathematical aptitude would be unable to finish the requirements of a math major. The issue with being behind it that is very difficult/impossible to catch up to a large group of math majors. Among others things this would make getting into good grad schools quite difficult.</p>
<p>UMTYMP student makes the point that I would have made–the question is not so much meeting the technical requirements for the degree as being well positioned for the next step, if one wants to continue with education. While I realize that a creative person can do a lot with a B.S. in mathematics (or less, e.g., Bill Gates), most of the really interesting jobs for a mathematician probably require a Ph.D.</p>
<p>It is possible that in grad school admissions, the committee may take a “chance” on an apparently strong student with a weaker record on paper. At the level of hiring post-docs, to say nothing of hiring a faculty member, the person has to be “caught up,” and in fact has to emerge as the top candidate (or at least #2 behind a person who gets a job offer from a better place) in order to be hired.</p>
<p>In my opinion, spending a bit more time pre-bachelor’s degree would be the least disruptive way to accomplish that. One could take a longer time to complete the Ph.D. instead, but at least locally, the hiring committees tend to take a negative view of long Ph.D.'s (while ignoring the pre-grad-school record).</p>
<p>Some of the students from wealthy families take advantage of the extra year in various ways (though mostly not to promote mathematical growth). The east-coast prep schools offer post-hs years to students who want to improve their academic credentials or extra-curriculars, to gain admission to better schools than they could otherwise attend. In our area, over time a few people have gone to the local public school for hs, graduated, and then gone out to the east coast for another pre-college year, and it’s worked out very well for them. Students who might major in a language often spend a gap year in the country where that language is spoken.</p>
<p>The military academies do the same sort of thing–they run a one-year, post-high-school prep program for students they would like to admit, when they want to make sure that the student is up to speed for the regular curriculum.</p>
<p>I am not saying that students would have to take longer if they entered without multi-variable calculus, or even without any decent course in single-variable calculus. Just that I think the option should be open.</p>
<p>I guess it just puzzles me why some fields seem to have these implicit requirements for significant pre-college work.</p>
<p>I had never done research before coming to MIT, and in fact hadn’t even taken AP Biology. I started a biology major in 7.013, introductory biology. By the time I graduated, I had “caught up” – had done three years of research in an HHMI lab on campus, had authorship on a paper under review, and taken several grad classes. Actually, having done significant pre-college research did not seem to enable people in my PhD cohort to finish faster. (I don’t know if this is because of the heavy labwork component.) My pre-grad school work was of very little interest to the PI who has hired me for a postdoc. </p>
<p>From another angle, my husband came to MIT to major in aerospace engineering. Although nobody comes to the aero/astro program with any sort of useful class background, he was somewhat advantaged by having built model airplanes and rockets as a hobby since he was little – he had building skills that were very useful, but not explicitly taught in class. Still, his pre-existing skills didn’t allow him to graduate earlier, and he was admitted to the MIT graduate program along with the majority of his undergraduate class.</p>
<p>Perhaps I am too strong an advocate for the kinds of fresh-faced, gee-whiz Midwestern kids with whom I belonged ten years ago. But not everybody knows what he wants to be in high school, and I think that’s okay, and that lack of awareness shouldn’t close off career trajectories, even very competitive ones.</p>
<p>I don’t know exactly why the de facto requirement for pre-college work exists in mathematics, but I would guess that it is a combination of the fairly sequential nature of the course work at the lower levels and the relative accessibility of the “tools,” i.e., pencil and paper, computer connections + some exposure to challenging problems. Your point, molliebatmit, that “lack of awareness shouldn’t close off career trajectories” is why I suggest a lengthened B.S. with external support.</p>
<p>In the biological sciences, very few students have access to the kind of laboratory resources needed to do significant experimental research pre-college. A few of the Intel/Siemens participants maybe do, but not most prospective majors in a biological science.</p>
<p>I also think there is considerably more sorting pre-college in mathematics. It’s much easier to identify mathematical talent from a young age than say biological talent. There are also considerably more opportunities for gifted middle and high school students in mathematics than other disciplines.</p>
<p>More opportunities, depending on the student’s location, background, and how knowledgeable the parents, neighbors, and teachers are. It seems wrong to me that an entering college student would be best advised to consider other options based on factors that are largely beyond the student’s control.</p>
<p>Many people (I bet most, actually) decide to not be math majors, or at least decide not to apply to math grad schools after taking 18.701/2 so this group is actually not that large. This group is also unique to schools like MIT and Harvard, and maybe a few others.</p>
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<p>Someone who has fulfilled the requirements for the mathematics degree theoretical option at MIT is, I think, well positioned to be a graduate student anywhere. Again, it’s not unreasonable for graduate students to take graduate courses.</p>
<p>Could you please convert MIT’s numbers to English course descriptors, shravas? I can’t tell whether I agree or disagree. Where are you thinking that the person who does not have any grad courses, but fulfills the requirements for the theoretical option of the math degree starts, in terms of course content? What grad programs admit them?</p>
<p>Lower down the academic totem pole, we are not necessarily looking for students who have already taken graduate courses as undergrads, just for entering grad students who are prepared to take our grad courses.</p>
<p>Here’s a rough guide to the math classes mentioned here
18.01 Calc I <a href=“18.014%20is%20a%20theoretical%20variant%20of%2018.01”>probably equivalent to calc I and II at most schools</a>
18.02 Calc II <a href=“18.022%20and%2018.024%20are%20theoretical%20variants%20of%2018.02”>multivariable calculus</a>
18.03 ODE (18.034 is a theoretical variant of 18.03)
18.06 linear algebra (mainly for scientists and engineers)
18.100 analysis (covers chapters 1-7 of Rudin)
18.700 linear algebra (more theoretical than 18.06)
18.701/2 abstract algebra (uses Artin).</p>
<p>The theoretical math major requirements are actually pretty light compared to peer institutions. The only requirements are calc I and II, ode, 2 semester of abstract algebra, 2 semesters of real analysis, topology (at the level of Munkres), a math seminar, and two restricted electives in math.</p>
<p>Concerning QM’s extended B.S. idea, actually my impression is that this sort of goes on in the current system. Unlike in the sciences, you typically spend years in grad school taking math classes. And you are expected to take it seriously, which tends not to be the case in the lab sciences where your research is the priority even while taking classes. </p>
<p>So hypothetically, there is time to catch up for a student who is not super-advanced.</p>
<p>Thanks, UMTYMP, your post #112 will save me some time!</p>
<p>collegealum314, I think the idea of accomplishing the “catch up” during the Ph.D. would work fine, as long as the student could be admitted to the type of university to which he/she could have been admitted with the benefit of an extended B.S. instead. As an additional consideration for someone planning an academic career: in mathematics, do the faculty hiring committees look at the length of time the Ph.D. took? In my department, the hiring committees tend to do that–but perhaps that is a difference between math and physical sciences. No one would think twice about the difference between a 5 year Ph.D. and a 6 year Ph.D., but if the Ph.D. stretched to 8 years, it would probably cause some hesitation.</p>
<p>It looks like Falcon never reposted and I have yet to read this whole thread, but here is a updated link to Brown’s admissions stats which gives acceptance percentages for ACT 36’s, individual 800 SAT subscores and val and sal rankings. This is about as detailed a breakdown as any I have seen for a top-20 college:</p>
<p>No single element gives you more than a 29% chance of success and it’s extremely likely that the ones that do get in qualify in more than one category.</p>
<p>Why are we wasting our time arguing about a stupid test? I think we can all agree that the SAT/ACT is misguided, which is why it is not the only factor in admissions. Can we move on now?</p>
<p>clearly, holistic approach is just nothing more than an excuse that allows admissions to walk away from the quantifiable component of an application to a wishy-washy EC, leadership and such BS… It’s unbeatable. You can’t sue and you can’t win. Any kind of minority/necessity qualification (race, musical instrument, sport team) at that given moment will have an advantage. Your grades/scores matter big time to get you into a smaller, more selective group. But once there, it is up to some real iffy logic of admissions thinking.</p>
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I am aware that MIT admissions says that students’ success is not correlated with SAT scores once you get above 700.
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That isn’t actually what MIT says. They say that they have correlated scores compared with future MIT success and see that there is a very strong correlation up to about 700, thereafter, while there is still some correlation, it is much weaker.</p>
<p>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.</p>
<p>I can’t really believe that the lower level MIT math courses lend themselves to an algorithmic approach. The honors versions of the basic calculus courses at the university where I teach cannot be handled in that way. </p>
<p>I also don’t believe that someone who can score points on the USAMO in high school is not good at coming up with creative approaches to problems. Those don’t seem to be solvable with learned algorithms, either (although in a few cases, knowing a rather abstruse theorem could be of help).</p>