<p>This question is directed toward all the current students and recent graduates.</p>
<p>I'm an incoming freshman at Caltech this academic year and I want to ask a question about Math Advanced Placement Exam. I have no clue what I want to major in at the moment but one that I'm strongly leaning toward is ACM. So, I decided to take the Math1ab placement test to place out of those classes and take more "interesting" classes early on. But what I found out soon after I stared at the exam was that I was only able to answer half the questions on both exams. And the other half, well, I struggled without getting anywhere. I had expected to do better so it was quite frustrating to perform poorly. My question is, would four years, with Math1ab, be still enough to take all the interesting classes? I understand this is a very open-ended question and it depends on a person's determination but in general, is it possible?</p>
<p>You can never take "all the interesting classes", but it's definitely fine to take Ma1 freshman year - even as a math or ACM major. In particular, a couple of my friends are ACM majors who took all of ma1, and they're doing just fine. The key is, of course, to still take ACM 95 sophomore year (concurrently with Ma2), which is certainly doable.</p>
<p>edit: though I guess you'll still have to take math 5 sophomore year as an ACM major...so that could get a little hairy with all of those, but I definitely know people who have done that sophomore year.</p>
<p>Most people don't test out of Ma 1 and the one's who do aren't necessarily Ma/ACM majors. There's plenty of time for an ACM major to take Ma 1 and still take interesting classes.</p>
<p>I missed 1 question (out of 6?) on the Math 1a placement test, and I think I got a 5.5/7 on the Math 1b placement test.</p>
<p>Will those be enough to pass? Even though I haven't mastered the material 100% yet, I feel pretty comfortable with it (in addition, I plan to go over the Math 1a and Math 1b Analytical notes+HW this summer to solidify my knowledge). I'd hate to retake courses in which I know nearly all the material but have a few weak points.</p>
<p>I'm not sure that anyone knows the passing marks on the tests. You just get an e-mail a couple weeks before school starts telling you whether you passed. I think that after taking the tests I felt that I had gotten everything on Ma 1a and missed one on Ma 1b and I passed out of both.</p>
<p>rspa100. did you already get a hold of lectures notes and HW? I went to the math website but it wouldn't let me access them; it keeps saying the page cannot be found. also, can someone please explain to me the difference between the analytical and practical track for math? and is the difference same for physics?</p>
<p>Essentially I think they want people to pass out of both together, not that you need 1b for 1a. I think this is just so that not that many people will be skipping 1a.</p>
<p>I am in the same situation as rspa100. i missed 1-1.5 questions on each test (at least i think). I've been studying this summer, and I would hate to have to take the class. Speaking of that...I hope this isn't an honor code violation but, did you notice that the 1b class notes cover more material than the test itself?</p>
<p>^ which I always thought was sort of strange, to be perfectly honest. I tested out of math 1, but that doesn't mean I could have easily done the Ma 1a problem sets without some significant thought or effort.</p>
<p>In general, I think the advanced placement procedures at Caltech are a little out of whack. For example, in addition to things like not being able to test of math 1a and math 1b separately, and that the tests don't really cover the course material, I sort of think it ridiculous that there is no way to skip some of the humanities/social science requirements. It's as if they think all students enter with equal backgrounds in non-science subjects (beyond passing the WAFT, of course).</p>
<p>Perhaps I'm just confused of Caltech's intent for these exams/policies, though.</p>
<p>since I studied this material on my own (mostly 1b), will I fall behind my fellow classmates? Also, since I never did proofs in class, I still do not feel comfortable with proving anything out. To what extent could this affect me if I were awarded credit? Should I continue to read ahead?</p>
**disclaimer: there is some minor specific information pertaining to the math placement exams, so anyone reading this who hasn't taken them, should probably skip this post. honor code! **</p>
<p>My experience looks somewhat similar to the situation you're in, so I'll definitely elaborate. </p>
<p>In high school I ended up taking a few extra math classes: calculus (obviously), multivariable calculus, differential equations, partial differential equations, and a class on linear systems and matrices (sort of like applied linear algebra in retrospect). My background was one pretty lacking in proofs. I mean I knew how to do induction and other various, simple techniques, but I definitely didn't take any "advanced calculus" course that would be equivalent to ma 1a here. </p>
<p>I came in intending to be (and still am) a physics major (now a senior).</p>
<p>With all of that, and not having explicitly taken linear algebra, I was pretty disappointed in that I could not test out of ma 1a, ma 1c, and ma 2a, without passing out of linear algebra. So I basically spent a couple weeks learning more proof-based linear algebra, figuring that if I could teach myself to a level of the placement exam, that would be sufficient. I reviewed the other subjects a little, but nothing extensive (less than ~2-3 hours for each of the other subjects).</p>
<p>So I took the exams, and I was pretty happy with my performance on them. They were largely non-proof based, which helped a lot. The linear algebra, exam, in particular, was significantly more similar to the prac track of ma 1b, which I was previously pretty familiar with (finding eigenvalues, eigenvectors, and things of that genre). I probably thought that I got most of the problems right or very nearly right with a couple questions in doubt here and there. There was at least one problem on the diff eq. exam I couldn't get at all, but for the others, I think I got at least generous partial credit on all of them. For all of the proof based problems, (something like 1-2 of them per exam), while I did not have a completely rigorous solution, I at least followed a generally logical progression to the right result.</p>
<p>So I ended up passing out of Ma 1abc (no Ma 2a, but that definitely was okay), and I proceeded to take Ma 2ab frosh year. </p>
<p>Those classes don't really build off of ma 1abc in terms of content. Ma 2b is probability/statistics so there are few to no proofs (not to say you can't have proofs in those, so much as the class is very practical). I did take Ma 2a anal, but really, the proofs for that class are on a much simpler level than Ma 1, so it was no problem. By this I mean, you're showing things like existence and uniqueness for differential equations which basically comes down to making sure the pre-requisites for some theorem are met :P.</p>
<p>So after that, I was done with core math, and as a physics major, rarely did I have to write formal proofs. I took ACM 95 instead of Math 108 (basically applied and analytical versions of complex analysis, PDEs, diff eqs, and real analysis for 108), which had a rare proof from time to time, and they were a little more complicated, but they weren't grading on rigor so much as knowing the material, so that wasn't really a problem. Same goes for the mathematical physics class I took (ph 129).</p>
<p>Hence, I seem to have gone through Caltech without really ever having a formal introduction to proofs. Is that a disadvantage? Maybe, but I doubt more so than the advantage of taking other, more physics related, classes in the place of Ma 1. I mean I don't mean to imply I can't do proofs, but I definitely wouldn't be totally comfortable taking ma 108 or ma 109 even though the material is perfectly understandable (in my mind).</p>
<p>As for the content of Ma 1. That's never been an issue, and if you're smart enough to figure it out for the placement exam, you're probably smart enough to re-figure it out when you need it. It might come a little more slowly than others, of course, who actually did take ma 1a, but that's not such a big deal. I mean I have definitely had to use all of linear algebra (e.g. in quantum mechanics), and I haven't personally really noticed any problems there. The professors do assume that you actually know all of core math, though, which is really nice and efficient!</p>
<p>Hence I would say that unless you're a math major or really value rigorous proofs, it's probably fine to test out of math 1 (if you can). Heck, even if you do want to be a math major, you could just try to dive into the deep end and learn rigorous proofs in math 5 frosh year while testing out of ma 1 - that's what pass/fail is for.</p>
<p>I think I also tested out of 1a and 1b (maybe 1c, we'll see how that goes...). However, my calculus and linear algebra knowledge is very unrigorous (i.e: I basically prepared for the exams by going through books and remembering formulas), so I'm scared I might forget stuff I need in other courses if I get out of 1a/1b. How much will a lack of rigor in these courses hurt me in math/physics/economics courses? Does the material in later math courses (I want to be a math major) build up on the into courses?</p>
<p>I'm not too concerned about proofs, though, as I've done a lot of math competitions and taken proof-based number theory at my local college (it's just that I've never learned calculus and linear algebra rigorously). Is it fine to take Ma5 freshman year?</p>