<p>So I have read a couple threads here on MIT math course planning, but they all seem to be coming from students wondering if there is something like Harvard's Math 55 at MIT. I do not consider myself to be at that level but am planning on majoring in math. Does anyone know of threads for more "average" MIT math students?</p>
<p>If not, some specific course advice on my situation would be appreciated (I was accepted EA). Perhaps other students will also find it helpful.</p>
<p>contests: USAMO qualifier (score 7-14 range)
coursework: Calc BC, Multivariable, Linear Algebra, Diff eq, Intro Analysis from local college (used Gaughan's Intro to Analysis).
misc: -comfortable with LaTeX (in case it's relevant)
-Not much exposure to upper level math but I am leaning towards pure rather than applied.
-I want to be challenged!</p>
<p>What math options could I enter into? Maybe some graduates could give their own background before MIT and their sequence of math courses (that would be awesome!)? </p>
<p>Lastly, I have exhausted my school's offerings after multi/linear so would appreciate any suggestions for independent math study in my last two high school terms that could prepare for potential course sequences.</p>
<p>My suggestion would be 18.701 Abstract Algebra. Other options would be some variant of 18.100 analysis or 18.700 linear algebra [probably at a higher level than what you’ve seen]. I think you have enough background and ability to do well in 18.701 and a lot of freshmen take it so you shouldn’t have trouble finding people to study with. If it turns out to be too hard then there’s always P/NR to fall back upon. If you have AP/ASE credit for other GIR subjects you can take another elective math class your first term as well.</p>
<p>Assuming you got a 5 on Calc BC you’ll get AP credit for 18.01. I would advise you to take the ASEs for 18.02 and 18.03. The 18.02 ASE is pretty straightforward so you should have little trouble with it. The 18.03 ASE requires a decent amount of homework but the homework will teach you any material your ODE class did not cover. The homework is also much less painful than taking the actual class. If you do the homework you should have little trouble passing the 18.03 ASE [the pass rate was 96% this year].</p>
<p>My situation was a bit unusual as I had taken a lot of math classes at the University of Minnesota in high school so I started off with AP credit for 18.01, ASE credit for 18.02 and 18.03, and transfer credit for 18.100B, 18.700, and 18.703 modern algebra. I took 18.112 complex analysis and 18.152 partial differential equations freshmen fall.</p>
<p>For math independent study my advice would be to choose whatever type of math interests you most at the moment and find a book in that subject at your level and work through that. Even if you don’t fully grasp everything when reading it you will still get better at math and it will be easier when you take a class in that subject and need to learn the material more deeply.</p>
<p>Hopefully this helps. MIT is a great place to study math and if you have further questions about math at MIT I’ll try to answer them as well.</p>
<p>Well first off, I think you are definitely well-equipped to take courses that would be recommended to those who would be interested in taking Math 55 at Harvard (these would be some combinations of 18.100B/C (Real Analysis), 18.112 (Complex Analysis), 18.701 (Algebra I), and 18.702 (Algebra II) throughout freshman year). So the advice in those threads apply to you too.</p>
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<p>I would recommend taking 18.701 over 18.700 and 18.100, or you could take both 18.701 and 18.100 at the same time if you have room in your schedule and are interested, and this is not uncommon for some freshman. 18.700+18.701 might be too slow for someone who knows some linear algebra and has extensive experience with proofs, and then 18.701 is only offered in the fall while 18.100 is offered every semester.</p>
<p>For reference, I only had credit for 18.01 and 18.02 coming into MIT, with less experience with proofs (never took a proof based class or qualified for USAMO), and took 18.700 my first semester and 18.100C second semester. In retrospect, I’m not sure if taking 18.700 was such a good decision because I later took 18.701 which reviews everything in 18.700. I do feel like I’m a lot more comfortable with linear algebra having taken 18.700, but then this was also my first linear algebra course.</p>
<p>Other good options for those interested in being math majors but might not have as much experience include 18.014 and 18.022, more theoretical versions of single-variable and multi-variable calculus respectively.</p>
<p>Thanks! I was under the impression that only IMO students or people who had accomplished high level math research were in Math 55, but whatever, thanks :)</p>
<p>18.701 seems like a good recommendation. If I don’t have transfer credit though for 18.700 (I doubt my hs’s linear algebra was the same theoretical depth), is there an ASE offered for it? </p>
<p>I actually live in the Twin Cities also (I go to boarding hs so don’t really have any ties to the area), and took math 4603 from UMN over the summer. UMTYMP student, if you are able, could you compare it to 18.100? Also what’s the differences between 100A, 100B, 100C?</p>
<p>Finally it seems there is a lot of flexibility in the department, in that shravas also mentioned 701 and 100/700 concurrently as a possibility even though 100/700 are the prereqs?</p>
<p>There isn’t an ASE for 18.700 although there is one for 18.06 the easier linear algebra class. However, you don’t credit for 18.700 if you take 18.701. I never took 4603 but it’s probably something like 18.100A although possibly quite a bit easier. It’s possible you could get transfer credit for 18.100A but I wouldn’t recommend it as you will probably be off taking 18.100B or 18.100C. 18.100B uses Rudin and is pretty much like a condescended version of Minnesota’s 5615-6H although it covers slightly less material. 18.100C is the same as 18.100B except it focuses more on proof writing and communication.</p>
<p>18.701 has 18.100 as a prereq but it’s neither necessary nor enforced. Prereqs are typically not enforced and are not always necessary. Conversely, some classes use material from classes not listed as prereqs.</p>
<p>Got it, very helpful. Looks like I should strengthen my analysis background, but I am pretty comfortable with writing proofs at least.</p>
<p>Another question about math at MIT. What is the math club like? I checked out the site and it seems to be a lot of lectures/cool presentations. Is there any directed prep for college math contests or is that something students do on their own?</p>
<p>No, I did not do Minnesota ARML, if that testifies to my lack of roots to the area. When I moved to TC I already went to school out of state and did ARML with my school team. So yeah…but Minnesota is great place though! More states really need programs like UMTYMP/PSEO.</p>
<p>You don’t need to strengthen your analysis background before coming to MIT, it’s just something you’ll want to do as part of being a math major.</p>
<p>The math club has some talks and some other events like what to do during the summer and occasional diners. Some of the talks are vaguely related to the Putnam and there is a 6-credit problem solving seminar class 18.A34.</p>
<p>I agree that more states need stuff like UMTYMP/PSEO though!</p>