<p>I took BC Calculus this past year and thought it went pretty well and am pretty sure I’ll be getting a 5 come July. However, I’ve also read that the BC curriculum is a very superficial way of learning Calculus, and from what I experienced, I think this view makes sense. Thus, since I don’t really have much to do this summer, I thought I’d get a better grip on the fundamentals of Calculus before September 20. So I picked up a copy of Spivak, since I’m <em>guessing</em> I’d be placing into 16100-200-300.</p>
<p>Now I’m having second thoughts about this, mostly since proofs seem rather difficult to self-study, and I’d rather not get used to doing them the wrong way.</p>
<p>Might it be better for me to instead take a look at MIT’s OCW for Multivariable or Differential Equations? I’m interested in being a Physics major, so that might be more helpful, as well as being easier to learn.</p>
<p>Thoughts? For clarification, I’m not doing this because I’m stressed or worried or anything. I’m just bored.</p>
<p>(just FYI, I’m also an incoming freshman so you should probably trust the next guy more xD)</p>
<p>With a 5 on the AP BC, I think Calc IBL is the course you’re looking at (which is a special, purely proof-based section of the 160’s). Unfortunately, however, Spivak doesn’t enter into this: you get ‘scripts’ with definitions and you theorems, and you have to prove the theorems yourselves (as a class; apparently it’s very collaborative).</p>
<p>I’m actually in almost the same position - prospective physics/maths double major who bought Spivak thinking proof-based calculus might be fun. Then I looked into IBL calc and realized that going through Spivak might defeat the point of it (which is to avoid ‘corrupting’ us with hand-me-down proofs - there’s more detail on that on the UChicago website). I’m still not entirely sure about watching OCW lectures on Calculus because of that, though I’m probably going to go through the physics lectures (Walter Lewin from MIT and Leonard Susskind at Stanford both have really good lectures that should keep you occupied for the summer).</p>
<p>If you want to know more about IBL calc though, I can send you a few links - just send me a message.</p>
<p>You really don’t need to be solid on proofs for physics - and you are right that it is hard to self-study them. Physics lectures would be a nice way to go. You might like reading up on modern physics as well - both theory and some of the works on great physics developments/lives of of physicists. If you’ve not read Feynman yet, now is a fine (ouch) time to start.</p>
<p>@estrat1: Calc IBL is a special section of the 160s? Here I was under the impression that IBL and 160s were totally separate things. But from what I’ve heard 160s sounds like a better fit for me, since [for better or for worse] I’m someone who likes having some structure in their learning and the 160s seems more structured. I may be wrong on this, though. I would appreciate the IBL Calc links if you have them.</p>
<p>@nemom: I understand that the Physics department does not much stress rigor/analysis - the Undergrad Research page basically says as much, which is why I thought MV/DE/LA might be a better use of my time. On the other hand, I’ve been talking with my dad and he thinks that working with Spivak, or at least splitting my time with Spivak and one of the aforementioned subjects, might be a good challenge. As for Physics, right now I’ve only been reading some popular books (Feynman’s Six Easy Pieces + Character of Physical Law, Leonard Susskind’s The Cosmic Landscape. I’m thinking Not So Easy Pieces next, since I don’t really want to commit to a textbook but would like some more challenging stuff.)</p>
<p>I was also wondering, it’s been a year since I did Calc (BC). Now, I know it’s against conventional wisdom to study for placement exams, but would it be better for me to refresh myself on what I’ve lost in the mind-numbing past year of Stats? Or would I risk over-placing myself, even if I had at point been ready?</p>
<p>@ Rny2: I would advise against intensive studying, though a general refresher should be fine. Take an hour or two to go over the theorems and broad ideas (on the plane or in the car or on the train or what-have-you). You should pick things up quickly and easily; it’s very much like riding a bike, IMHO. If you place into a class that is too difficult, you can always drop down, and if you think it’s too easy, request to move up. Just don’t go back through the entire Calc BC curriculum and relearn every little detail because that would be defeating the purpose of the placement exam.</p>
<p>cool, cool, thanks for the advice neltharion. I hear it’s pretty much ya-know-it-or-ya-don’t kind of stuff, so I’m not too worried either way. I need to organize all my old high school stuff anyways <em>groan</em> Wayyy too many stacks of loose paper around my romm . . .</p>
<p>Heinochus, IBL Honors Calc is also numbered 16100-200-300. IBL is one section of the 160s that is offered (maybe more, if there is sufficient interest). It is intense, no doubt, but can be thrilling for folks who like the inquiry-based approach. Are you looking at majoring in math or physics? </p>
<p>S1 is a rising third year math major who took IBL Analysis as a first-year (and chose it over Honors Analysis). Absolutely LOVED it. Wishes all his math courses were taught that way!! I will tell you that they don’t really teach you how to do proofs so much as turn you loose on them. You will find study groups an essential part of the learning process. S’s IBL Analysis class used to meet in the Reg in the wee hours and brought pizza and brownies.</p>
<p>There is not a formal Lin Alg course – it is subsumed into the 160s. If you want to spend any time on looking at math this summer, that’s where I’d focus, based on what S1 said about what areas his housemates struggled with when they were taking 160s.</p>
<p>Estrat, can you post those 160s links here? This discussion comes up pretty often on these threads. </p>
<p>The math department advisors are VERY helpful in offering advice on placement, whether to go the IBL route, etc. In any event, DO NOT try to study for the math placement test. The results are not binding, and you will find that college-level math, whether you wind up in 130s, IBL or Honors Analysis, will give you a good workout, no matter how good your HS preparation. </p>
<p>Agree that Feynman is a good read for the summer, or whenever you want your mind expanded!</p>
<p>I’m consciously trying not to study for the placement test while actually learning some math, so I think I’m just going to try the MIT OCW Multivariable course. Maybe physics later (I am, at the moment, hoping to be a Physics major).</p>
<p>I’m trying to study for all my placement tests… mostly because I’ve taken a year off from math and physics, and I need to review anyway. I also want to try to place highly so I can double major AND study abroad. High hopes, I know.</p>
<p>As far as the math placement test goes, I’ve taken 2 years of college math (Calc 2, 3, Lin Alg, and Dif EQ), most of which was proof based. I’m hoping to study up and place into analysis or 199 or something above the 160s sequence, just because I feel like I’d be repeating stuff otherwise. Especially as the math classes I took were in an excellent department (almost as good as Chicago’s) and I learned a lot (and paid tuition). </p>
<p>It would be nice to have some pointers as to what to expect of the placement exam. Like, what’s the format? What is the scope? I understand that there is a multiple choice and a free response, but I truly have no idea past that. It feels strange to try to review and study without knowing on what I’ll be tested.</p>
<p>As for the other exams, I am trying to get some physics under my belt for accreditation exams (yes, I took college physics as well in an amazing physics department that has several nobel prize winners and great educational research). I feel like that’s a bit easier to study for because there are clearly defined syllabi, etc. Same goes with Chem and OChem.</p>
<p>From my perspective, I’m trying to get my money out of the tuition I paid for these college classes. If that means studying over the summer, I’m down with that. I just don’t like people telling me not to study and just let the chips fall, because not everyone took Calc BC and AP Physics. Some people went a different route and have a different situation. I’m not trying to learn new material. Just trying to review so I can place well, despite taking time away from math/physics. I feel I could forget how to do a line integral or something. very easily. It would suck to just forget this stuff and be placed lower because of my summer-brain. And, I don’t really know what I want to major in… just that I want a hard science double major with a humanities subject. Otherwise, I don’t know what it will be… and the more credits I have in a hard science major, the easier it will be to complete a double major (and study abroad…).</p>
<p>kitkatkatie,
S1 actually placed into the 160s based on the exam, which shocked the heck out of him (though he had finished MV and DiffEq1 junior year, so he was a little rusty), but had a lot of other high level math courses taught at his HS, including proofs. Take the test, see what happens, but talk to Diane Hermann or John Boller in the math dept about your background. S talked to them and they felt he’d be fine in Analysis, and told him to go sit in on various sections (regular, IBL and Honors) to see what felt right. They both teach Honors sections of Calc, Anaylsis and Alg, so they have an excellent sense of where folks will fit.</p>
<p>I don’t know how the physics dept. works in that regard. S had a physics class senior year of HS which was taken directly from an intro sequence for physics majors w/pre-reqs of MV/DiffEq. Got him the AP scores to get credit for his entire physics sequence at Chicago.</p>