<p>So 1a and 1b are basically first year calculus and 21a is multivariable calculus, right? The thing is that I've been qualifying USAMO for years but my school doesn't teach calculus... I only know the most basic things about calc, can I still take 21a?</p>
<p>Only if you’re really good at techniques of integration. I have forgotten a lot of things I learned at Harvard, but I remember that Math 21a was hard.</p>
<p>Take a hard run at it this summer. I suspect you can be prepared for 25, if you <em>really</em> want to be. And I think you’ll find it more rewarding. I recommend Thomas and Finney’s 9th edition.</p>
<p>I am not a harvard student but I would recommend 21a or 25. If you actually enjoy math. Especially hard math then try it. But becareful wtih 25. Ive heard its a “poor man’s version of math 55” which is still pretty dang hard.</p>
<p>There are large quanta between the courses 55 to 25; 25 to 23; 23 to 21</p>
<p>This year in 55b Siu took his problem sets from his grad course on analysis and made them harder for the math 55 students doing the same material. </p>
<p>For 25-- have a good understanding of “proof based” work–that is a very different beast than regular math problems and the students who find themselves in trouble aren’t those for whom the material per se if difficult but rather have a difficult time writing proofs.</p>
<p>Also try if you can to become at least somewhat fluent in LaTeX.</p>
<p>Here us a guide the math department has on its web site-- they don’t endorse the guide but they do publish it-- so go figure (in a matter of speaking…haha)</p>
<p>[Harvard</a> Mathematics Department : 21, 23, 25, or 55?](<a href=“http://www.math.harvard.edu/pamphlets/freshmenguide.html]Harvard”>http://www.math.harvard.edu/pamphlets/freshmenguide.html)</p>
<p>Is everyone overlooking the words, “I only know the most basic things about calculus” in the original post?</p>
<p>My advice: take a hard run at it in the summer if you wish, and then take a placement test in the fall. (You don’t have to decide now, do you? That would be a monumental change from back in the day.)</p>
<p>Sent from my DROIDX using CC</p>
<p>Yes, I saw that, but I also saw the words “qualifying USAMO for years”.</p>
<p>Qualifying for USAMO doesn’t require any calculus though. That said, it sounds like you’ve got a strong math mind. You might be able to teacher yourself enough Calculus to be prepared for Math 21 over the summer. Or you might have better things to do. In any event I believe you can take a placement exam in the fall.</p>
<p>Adjusting to life at Harvard will be hard enough. What’s the rush. Take Math 1a, then Math 1b. You can take 21a at beginning of sophomore year, leaving plenty of time for much harder math classes. I am pretty sure you will have to take a placement test during orientation. This should help you sort it out. Remember, the “below average” math student at Harvard was most likely a valedictorian.</p>
<p>Exactly! Thank you.</p>
<p>A good head for math is an excellent thing. (I wish I had one, really. I mean, I’m a pretty good math teacher, but I know I’ll never truly think like a mathematician.) But a good head for math is not a substitute for having learned two semesters’ worth of content.</p>
<p>Skip introductory calculus. If you’re the type of guy who can qualify for USAMO regularly, you can learn it in a few weeks. Trust me, you’re going to be bored in the lower level no matter how awesome your teachers are.</p>
<p>The nice thing is that there is an expectation that students will jump around a bit during the shopping period in these courses to find the appropriate level. Take the placement exam (actually you have no choice–), that will be a good initial guide and then you can move up or down as you deem appropriate after the classes begin.</p>
<p>I agree with bobtheboy. There is no need to trudge through plug-and-chug calculus (Larson, Stewart, etc) and wait to figure out the machinery behind it afterwards. With your background you can safely skip to the rigorous stuff.</p>
<p>It depends on what you want to do. For many fields, a good working knowledge of calc is really useful. So it seems like a bad idea to recommend that you skip single-variable calc.
On the other hand, I would recommend against 1a and 1b if at all possible. They’re not very good or fun courses - they’re not terrible, but no one (who I know, at least) really likes them.
I took 21a in the fall after a full year (two summers and one academic year, actually) away from any kind of math and after high school BC calc, and it was fine. All you need is basic integration techniques - the most complicated it got was, like, integration by parts.
But like I said, basic calc is useful for a lot of things, especially if you’re going into math (obviously), science or even econ.
My recommendation would be to self-study the BC curriculum over the summer and then to take a look at the 21a textbook, which the course follows pretty closely. (I’m pretty sure it’s the Stewart MV calc book, but this info will be available on the course website before long.)
**Keep in mind that you can’t shop Math 1a, 1b or 21a, since they’re taught in section and don’t start until the second week of classes. You can switch before the add/drop deadline, but that’s often very inconvenient, especially in classes like 1a, 1b and 21a that have a problem set due during every class (THREE a week).
You can shop APPLIED 21a, which might be easier and is another option to consider.
Good luck!</p>
<p>Does anyone happen to have any recommendations when it comes to deciding between 21 and 23? I took multivariable calculus and linear algebra this year, and I’m not sure if I’m comfortable enough to go straight into 23 in the fall - but I’m worried that 21 would be very redundant. (At the moment I’m leaning toward taking 21 to fill in gaps in my knowledge, but I might try doing that over the summer instead…)</p>
<p>Thoughts?</p>
<p>Strangecharm: I only know one person who enjoyed 23, and 7-10 who really did not. 23 seems to be a lot of memorization, rather than actual conceptual understanding of mathematical proofs. Most of my friends who’ve taken it also say that they got very little out of the course other than the ability to say they’d taken it.
You might try filling in some MV/lin alg gaps yourself over the summer like you mentioned and/or looking at some of the course material (homework, exams, etc) from 21a and b. If it looks like you’ve got a good grasp of the material, you might even want to consider something like 25, which my anecdotal evidence suggests is much more rewarding than 23.</p>
<p>Although Math 25a lists BC Calculus as a prerequisite, it is primarily a course in Linear Algebra, which doesn’t use calculus. It is a proof-based course, so the OP’s background with the USAMO could be helpful. </p>
<p>Both Math 23 and Math 25 review single-variable calculus from a more theoretical perspective than that of AP Calculus, and one could fill in the gaps of some practical skills by watching the Khan Academy videos online.</p>