<p>As someone that got denied admissions into their dream undergrad school and then got into it for grad school, I have to say it's really not all it's cracked up to be. I'm actually really glad I got denied from Caltech since I really feel I wouldn't have fit in as an undergrad and I loved my undergrad experience at the "lesser" CMU.</p>
<p>Have you found a list of professors you'd like to work with at Harvard yet? I wanted to go to Cornell like nothing else for grad school since I loved Ithaca, it was within driving distance of the rest of my family, they gave a great stipend offer, and I like the cold. I went up, interviewed with a ton of professors, and found absolutely nobody there I wanted to work with. So I had to turn down my own first choice school.</p>
<p>All good points. I would love to get into to Harvard and yes that odds are against me. I have always thrived when the odds were against me. The value of getting in is about as great as the journey to try and get there. Sometimes being rejected is a good thing. If you do not high goals how can you appreciate the other schools when you did not try to reach your dream. Sure I will more than likely get rejected but could I look at myself in mirror and say I did all I could to get in if I never tried?</p>
<p>As for goal. Research and Academia. I teach already and I am enjoying it (When I am not pulling my hair out. Middle School is like nothing else.) I would love the time to just explore ideas further. To slowly work at a project and see it take form. To teach some people who enjoy the subject as much as I do. (That is a rarity to begin with at the college level but possible to find one person once in a while that enjoys math in general. My students right now are not full of joy for math.)</p>
<p>Math 55 at Harvard as little (nothing) to do with theory of sets (?) But to the OP (who sounds like an UG, like me) Number Theory, LA, DE are not advanced math topics. I’d recommend some Introductory Topology, Complex Analysis, PDE, some rigorous treatment of graph theory, and Differential Geometry. Probably an M.Sc publication in math would help.</p>
<p>Edit: a reading course in maths (or some kind of involved senior thesis) I’m sure would help. And naturally, all A’s in your math courses.</p>
<p>To get into Harvard, I would take at least the following graduate courses: analysis, algebra, algebraic topology, differential geometry, algebraic geometry (modulo your interests). You would pretty much need to get As in all of these courses. If you do this, then try to get a high 90% on the GRE subject, a few REUs with good recommendations, hopefully a publication or one in preparation and some impressive awards from your undergrad institution.</p>
<p>Students at Harvard, Princeton etc. usually take nothing but graduate courses after their second year of undergrad. Even at my school ranked around 10th most people have taken only grad courses in their last year or two of undergrad, several have publications, have graduated summa cum laude, and almost all have GPAs in the 3.9+ range. I also know that at least 4 of the 1st and 2nd year students have 800Q/800V on the GRE.</p>
<p>The competition for grad school in math is probably one of the toughest. The reason being that pretty much all applicants are among the very best students in math at their undergrad institution. You really don’t have mediocre people applying for math Ph.D. programs. Another issue is that most schools accept between 10-20 students per year (or even less). Math also doesn’t require language skills in the same fashion as e.g. the humanities and social sciences, so it attracts a significant amount of foreign applicants.</p>
<p>eof, what would you say would be the least Putnam score that would still be meaningful enough to place on an application to, say, Harvard? [Of course, anybody else knowledgeable on the matter may answer as well.]</p>
<p>Interesting subject here…what I wanted to know is can we say the Law school is harder? Any Harvard law class that is more difficult than Math 55 or others? </p>
<p>Obviously we might be comparing apples & oranges but strictly speaking, you know what I mean, heh.</p>
<p>^^ That’s a really subjective question without any meaningful answer. Also, I’m fairly certain that Math 55 is the hardest class to ever exist. So I’m going to say “no”.</p>
<p>Math 55 is not hard because of the material it covers. There are many courses at Harvard (and probably even at most state schools) that cover much harder material. It’s considered hard because it’s intended for freshman, which means that the successful student in that class will need to have taken probably a few years of university level math courses while in high school and will need to have extensive experience with proofs. It’s a good course for former IMO participants, for instance, because most of these people will have had intensive coaching and training throughout high school (and almost always junior high as well).</p>
<p>There are extremely few courses offered that have such bizarre prerequisites because it’s very rare for someone to have figured out what they want to be in life at such an early age and to have dedicated so much time in pursuit of this choice.</p>
<p>If Harvard Law were analogous, then students at Harvard Law would be expected upon entry to have mastered the first few years of material taught at other good law schools. I don’t know if this is the case.</p>
<p>It’s a lot of difficult homework, but lots of advanced math courses would give similar amounts of homework. That looks like a typical first graduate course in algebra at a good university. The part that makes it so hard is that it’s given to freshman, not first year graduate students (for whom there is a huge jungle of very advanced graduate courses offered at Harvard).</p>