MIT vs Trinity College, Cambridge for maths (revisited question)

Colleges and Universities A-Z Massachusetts Institute of Technology
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<p>…as for the previous topic, I am in full support of “maths.” I think it’s kind of awesome.</p>

<p>I remember my very first math recitation at MIT. I had done my reading and attended lecture…and then, all of the sudden, the instructor started talking about “zed.” I freaked out a little because I thought I had missed something! (I got used to “missing something” later. It’s pretty common and there’s no shame in it…but this was my very first week). Thankfully, a minute or so later, I finally said to myself, “OH! He’s just talking about Z!” What a relief.</p>

<p>“Zed” is also awesome. I’d say it myself if I thought I could get away with it.</p>

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<p>Very nice posts. I think I have just one comment/clarification. </p>

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<p>I would say that if you’re anywhere close to the type of student who has the right to say (s)he has a very good idea MIT’s math program would be the best fit for graduate study, it is clear that you can go there for undergrad and you’ll probably be encouraged to continue your research in graduate school. Further, getting admitted to MIT’s math program is an unlikely event as is, even for rather strong students. It is not good to count on. I think you should choose solely based on which school sounds like the kind of undergraduate experience you want.</p>

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<p>^Agreed, to the greatest degree possible.</p>

<p>It alarms me a little when I see people around here saying they want to go to MIT (or wherever else) for grad school. Look, you shouldn’t know where you want to go to grad school when you’re a senior in high school. Grad school isn’t about the program, it’s about the specific sub-sub-subfield of research you want to dedicate several years of your life to pursuing in depth. Vanishingly few people have mature research interests as seniors in high school, and the people who do can generally write their own tickets into any graduate program that interests them.</p>

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<p>Sound scary? Then listen to Mollie.</p>

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<p>@mathboy98</p>

<p>I think my thought was not well articulated in my post. I agree with molliebatmit. College is when most people <em>really</em> begin to define their interests, and there is a lot of fluctuation in the interim. I went to MIT to be an Aerospace Engineer.</p>

<p>That said, I agree with you. If a student knows that they want to focus on subfield X, and that dedication does not change between ages 17 and 22, then (maybe) they should attend MIT UG with the goal of pursuing MIT’s strong Ph.D. program in subfield X. However, as molliebatmit points out, this scenario is extremely unlikely.</p>

<p>On the other hand, say you think you’ll want to study (and actually end up studying) one of a set of subfields Y_i in grad school (a far more likely scenario). If you spend your time exploring these various fields to different degrees, as most students do, then you will likely not have entrenched research relationships (to the degree I’m talking about) by the time you graduate, regardless of your mathematical promise. In that case, most things equal, you will have a better chance getting into MIT to study one of those subfields if you did <em>not</em> attend MIT for undergrad. Simply because, if you <em>did</em> do undergrad at MIT, your mentors will be looking for a good enough reason to send you elsewhere (for the reasons described in my previous post).</p>

<p>Maybe to put my perspective more plainly by example: I would wager that the average Princeton student has a better chance of getting into MIT’s Ph.D. program in any particular subfield than the average MIT student…and for reasons that have nothing to do with their level of talent or preparation. A significant portion of MIT math undergraduates who want to pursue Ph.D.s end up at the usual suspects: Princeton, Harvard, Stanford, etc.</p>

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<p>Admit it. You probably just like the accent. </p>

<p>That’s what’s called a confounding variable, folks…</p>

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<p>^ Sure, I like the accent too. But I’d become very sad if British people started saying “math”.</p>

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<p>@GeraldM: Princeton is a good school and I might be considering it for grad. school. Btw, why did you say it’s mostly known as an undergrad school?
@molliebatmit: thanks for the link - it was something rather useful
@collegealum314: I think I would go with PiperXP with that. If I say maths everyone will understand what I am talking about - I am curius though, why does this difference exist in the first place?
@PiperXP: I agree with the comment. (Btw, I have really enjoyed your blog at mit.edu :D)</p>

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<p>@mathboy98: Honestly I had never thought that the Cambridge math programme was narrow at all.
@MITMathAlum2006: This was a very enlightening post. I have a better understanding of how grad departments work now.
Overall, I get the point and I believe you are right. I am by no means absolutely sure where I want to do my research in at grad school. Mit’s programme is very huge and has all kinds of courses. [I have checked Cambridge’s undergraduate programme and it does not include such a variety of courses by any means.] Also, having read your posts, I have figured out at the moment I should probably care more about my BSC and not my PhD. When time comes I guess I will have figured out the area that is most interesting to me and the grad school that fits me most, if it is MIT, and if I am strong enough, MIT has no reason not to accept my app, right? Thanks for letting me realise that. (your posts have really been helpful)
To return to the Cambridge vs MIT question, I said that from my research I saw the difference in the number of courses and the range of courses one can take at MIT and one can take at Cambridge and the difference is significant to eyes. I have seen that at mit you can take courses involving applicable mathematics, courses related to the domain of chaotical math, computational math etc, which is not true for an undergrad education at Cambridge. What do you think?
Also, another point that concerns me is the system of supervisions at Cambridge. Essentially, at Cambridge you have your own supervisor that is there to explain to you all the concepts you haven’t grasped from the lecture and solve all your queries and make sure you are not found in a stalemate in terms of being left behind the material of the class (which is quite important). I have read that at MIT there is the system of TAs, but I am not really sure how it works. Are TAs accessible? Do they have time for all the undergraduates?
(Thanks again for the discussion :slight_smile: )</p>

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<p>I meant that in 3 years you have less time to explore, and are more prone to sticking to a specialty.</p>

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<p>I will say though that those very interested in pursuing research mathematics would likely do the Part III of Cambridge (meaning a total of 4 years pre-PhD). However, by that year people would likely want to know their specialties, as it tends to be the case that the classes of Part III move faster than is digestible. So one would truly pursue it best after knowing to an extent what areas are interesting, and having gotten a good foundation in those (as many of us know, the difficult to digest becomes much easier if there is basic familiarity.</p>

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<p>@confused314 - Thanks! :D</p>

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<p>@confused314:</p>

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<p>I don’t get this impression at all. Do bear in mind that</p>

<p>[MIT</a> Mathematics | Classes](<a href=“http://math.mit.edu/academics/classes.php]MIT”>Course List)</p>

<p>lists graduate classes as well as undergrad classes. (The graduate ones are where the third digit after the ‘18.’ is 5 or higher.)</p>

<p>If you take this into account, I think the range of courses offered is similar at the two institutions, but I guess with slightly different slants.</p>

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<p>oops, I did not know that - I thought that most of them were undergraduate classes
thanks for that. btw, how many math courses can a typical math major take by the end of the four years at mit? I know that there are the GIRs and that usually students would take 4-6 subjects per semester but I would like to know a realistic number. thanks.</p>

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<p>It depends on the class. Many of the math classes do not have (or need) TA’s. In a large math class, take for example 18.06 linear algebra. When I did it, it met twice per week in lecture of around 150 students, led by a full professor (Gilbert Strang taught it when I was an undergrad, and teaches it still) and then twice per week in a recitation section of about 20 students led by a professor. There were no TA’s in that class, but since there were 20 students per faculty in the recitation, you did get a chance to to interact with faculty, in a class smaller than most high school math classes. Correction: I have just checked the spring calendar [MIT</a> Mathematics | Classes](<a href=“http://www-math.mit.edu/academics/classes.php]MIT”>Course List) and discovered a change from my undergraduate time, it’s now 3 lectures and 1 recitation per week. They may have introduced TA’s as a result.</p>

<p>Whereas 18.100 when I did it, had 40 students, 2 lectures with all 40, 2 recitations with 20, and a session with the TA once per week which was optional, in groups of about 6-8 students. I certainly felt well supported.</p>

<p>Isthmus suggests that

That is simply and comprehensively wrong, and misstates the numbering used by the MIT Mathematics department. Keep in mind that departments can, and do, use their own numbering system. </p>

<p>In MIT math, the first digit after the 18 indicates the branch of mathematics. So all algebra and number theory classes are 18.7xx, all geometry and topology classes are 18.9xx, all logic classes are 18.5xx, all analysis is 18.1xx, all applied math for physics 18.3xx, and for computer science 18.4xx (the one weird exception is that 18.440-18.499 is Probability, Statistics and Stochastic Processes).</p>

<p>I can absolutely assure you that Algebra I, 18.701 is absolutely an undergraduate class, as is An Introduction to Logic and Set Theory, 18.510 or Introduction to Topology, 18.901. Indeed if you look at the mathematics course catalog ([Spring</a> 2011 Course 18: Mathematics](<a href=“http://student.mit.edu/catalog/m18a.html]Spring”>IAP/Spring 2024 Course 18: Mathematics)) you will see a highly stylized U or G in the first line of each course description to tell you if it is an undergraduate or graduate class. Also keep in mind that it is quite normal for undergraduates at MIT to try graduate level courses. Indeed, to encourage this, Juniors and Seniors are allowed to take a maximum of two elective classes as Pass/Fail subjects. This rule is designed specifically to remove the risk to an upper-class undergraduate who wishes to take a challenging graduate seminar.</p>

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<p>

In addition to Mikalye’s points above, keep in mind that it’s more or less irrelevant whether a course is listed as a graduate course or an undergraduate course – undergrads are free to take them either way. Many courses are joint (the undergrads and grad students are in the same class anyway), and even pure grad classes are easy to take as long as you feel you’re prepared. I took a grad-level course my sophomore year, and there was a student on CC a few years ago who started out freshman year in two or three grad-level math courses. </p>

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A typical student would take 4 courses per semester, so if that student took all GIRs at MIT, that would be 17 GIRs and 15 non-GIRs over the course of eight semesters. If you have credit for some of the GIRs, or if you wish to take more courses per semester, you would be free to take more courses in your major (or outside your major if you wished). </p>

<p>I had to take all of the GIRs at MIT, and I ended up taking 22 classes outside the GIRs. Obviously, having credit for some GIRs would be a good way to free up space in your schedule.</p>

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<p>The mathematics major is one of the very most flexible majors at the institute. See the requirements at [MIT</a> Course Catalog: Course 18](<a href=“Welcome! < MIT”>Welcome! < MIT). It requires some 12 math subjects of which 8 are unrestricted mathematics electives, over four years. Most math majors take more than that.</p>

<p>In the freshman year, most students do many of the GIRs and probably take only one or in rare cases two math subjects per semester. In subsequent years, you will take, as you say, 4-6 subjects (though I had one classmate who did 8, but he was insane). Say you take one HASS subject per term, and possibly one experiment in another department that particularly interests you (for example you become interested in mathematical modelling for economics or heck for urban planning so you take some classes in that department), that still allows for 2-4 subjects per term in the mathematics department over the 6 terms that you are not a freshman. So the correct answer to your question is anywhere from 12 classes to 26 classes, depending on your interests.</p>

<p>Every math major will have a math professor as an academic advisor. Each term at least once, you will sit down with your advisor to discuss your program and your interests and he or she will have to sign your registration form. While I was a math major, I met with my advisor (the wonderful, wonderful Jim Munkres) about once per month to discuss my studies, though most students only met theirs a few times per year. He was extremely helpful when I decided that pure mathematics was not for me, and gave me a lot of extremely valuable advice.</p>

<p>Sometimes students ask “How many courses may I take, per term, after my freshman year?” To which the correct answer is “As many or as few as you can get your advisor to sign off on.” Most of the advisors are quite good at ensuring that you do not take an unreasonable program, and in the math department at least, at ensuring that your classes and research fit together to give you a solid basis for further study if that it your intention. One quick caveat. It is a big faculty. Some take their advisor roles more seriously than others, your mileage may vary.</p>

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<p>@Mikalye:</p>

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<p>Perhaps I was unclear. I meant the third digit after 18, not counting the 18, as in the fifth digit altogether. Then what I said is by and large correct (with the exception of the 18.0xx range), and does not contradict what you say about the first digit following the 18 indicating the sub-area.</p>

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<p>@Mikalye and molliebatmit: Thanks for the posts. They both gave me a better understanding of how things work at MIT.</p>

<p>In terms of the TAs system, as an overall statement, would you say that when you couldn’t understand a concept (let’s say in physics or in math) and you had specific questions about it, was there a TA or even a prof. or another student that was willing to explain it to you?</p>

<p>@Isthmus: Thanks for the clarification.</p>

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<p>So the TA system works differently for the GIRs and 18.03, and 18.06 where there are recitations, than for the upper level math classes where in general there are no recitations, but there may be a TA (18.100C does have recitations, but this is specifically to teach the communication part of the class). The professors and TAs will have office hours, and in my experience, there generally aren’t very many people that attend them, so you should have no problem if you have questions about the material. Like the only time I ever had to compete for attention was when there was a problem set that was due later that day in the class. So I wouldn’t worry at all about getting help as long as you are proactive about it.</p>