<p>So, I'm planning to major in physics. I was wondering what level math will be most useful for me to study further? I can either study for AMC/AIME math or Calculus. Would you guys recommend I study Calculus in depth since it was pretty much discovered for applications in physics or should I get really good at the basic contest prep material? Thank you.</p>
<p>Calculus. It will help you more in the future.</p>
<p>Can you explain your question further? Why can you not do both? What does it mean to study calculus “in depth”? Do you already know calculus?</p>
<p>^Well I’ll already be studying for them chem and bio olympiads and don’t want to stretch myself out too far by adding another one unless it will be helpful. I hear studying for math contests takes a long time too. </p>
<p>When I say studying in-dept: My calc teacher has a 100% pass rate(everything 5’s, maybe 1 4 out of a class of 40) and she presents these “Calculus Contests” every Tuesday. I do not know the name of the organization who sponsors them, but supposedly if you do well on theme, you get invited to the next level. Typically there are like 5-8 questions or something and the average score is about 2 because these contests are so complex. I would be studying to do very well on these contests.</p>
<p>To put it simply, Bio and Chem olympiad difficulty is nothing compared to Math olympiad…it’s just the cold hard truth. Personally i would suggest you do what you WANT, not based on some contest. If you like contest math (not for the sake of winning, but out of pure joy) then go ahead and do that.</p>
<p>I would strongly suggest taking Calculus. I would guess that 95%+ of the students starting at MIT have had at least a year of calculus. Many will be much further along. You don’t need calculus to be admitted (as far as I know), but the profs are going to assume that you have at least a passing acquaintance with calculus and–with a very small number of exceptions–will be put off if you do not. I sometimes teach a freshman honors course at a large, public university, and I expect the students to have completed single-variable calculus before they start. Virtually all of them have. It sounds as though you have a reasonably good calculus teacher at your high school–all the more reason to take it. The ideas that you learn preparing for AMC/AIME/USAMO would be interesting, and a few of them might wind up being applicable in physics, but they aren’t central in the way that calculus is.</p>
<p>^I will be taking Calc B.C as a junior either way. When I say learn Calc further I mean learn it well enough to score high on Calculus contests.</p>
<p>Do you have a link to the Calculus contest web site? I am not familiar with it, so it is hard to say. Glad to hear that you will be taking Calc BC as a junior. So are you trying to make decisions for your senior year, or to make decisions about devoting extra effort during your junior year? </p>
<p>For a physics major, I think the most important thing (toward the beginning) is to learn how to “think in calculus.” By that, I mean that algebra probably comes intuitively to you, so that given a problem in words, you have no difficulty constructing an algebraic equation to solve it (assuming that’s possible). Many smart people do not have similar intuition about problems that are naturally expressed in calculus terms–maybe so for differential calculus, but it takes a time or two (or three) of constructing your own integrals to solve physical problems, to get the hang of it. This is likely to be separate from the calculus contest math, however.</p>
<p>Given the clarification in post #7, I’d say, just go with what interests you the most, in terms of the contests, and have fun.</p>
<p>I’m not sure but this might be the calc website [Continental</a> Mathematics League](<a href=“http://www.continentalmathematicsleague.com/cml.html]Continental”>http://www.continentalmathematicsleague.com/cml.html)</p>
<p>Nascent, I took a look at the sample calculus test on the web site, which is from 1999. If essentially your whole class is scoring 5’s on the AP exam, and you are one of the top students, you wouldn’t have to study too much for the 1999-type exam. However, the difficulty level could well have changed since then–can’t tell from the site itself.</p>
<p>Do you have access to last year’s calculus questions? My off-hand feeling is that the AMC/AIME/USAMO questions are more intrinsically interesting than the 1999 calculus questions. But I think the best advice is to just go with what interests you–you could go ahead and try the calc exams without overly investing time in them, but focus on contests up to USAMO.</p>