<p>"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 would say no. Every scientific discipline nowadays requires you to be able to take determinants and calculate eigenvalues but if you tested out of Ma1b you can probably do that, and in any case these are the things that you look up in planetmath...
I didn't take Ma1/Ma2a (tested out, mostly by self studying) but from looking at the Ma 1bc anal problem sets the last three years they pretty much give you elementary results found in any linear algebra/mult. calc. text and accompany them with needlessly complicated proofs, the only ones they can since the class doesn't have enough background to understand shorter more sophisticated and elnightening ones (eg the Cayley-Hamilton theorem doesn't look too interesting after you've seen the classification of finite abelian groups). The emphasis is still on <em>what does it mean to prove something</em> rather than actually learning interesting things about matrices. In any case ma 5/ma 108 will cover everything relevant from ma1 independently and in greater generality.
I think almost every math major at Caltech feels (s)he doesn't know enough linear algebra but that's much more likely to be remedied by google/wikipedia/planetmath than ma1b.
About 1/2-1/4 of prospective math majors take ma5 freshman year, some do spectacularly well,some find it hard at the start but see the light midway through the term (pass/fail is nice for that...), some drop it and take it the following year when they are more mature (drop day is only two weeks before finals, so there's plenty of time), and some drop it after gaining the wisdom that they don't want to have anything to do with math- all good things.</p>
<p>What does it actually mean to pass out of a class? You don't have to do the class but you have to do harder ones instead? I don't know too much about the American system as you can tell.</p>
<p>Btw - does anyone know if knowledge from A-levels is actually useful at Caltech? I do maths and further maths and from glancing over the placement papers it seems i'll have to learn a lot of new terminology. Is this something i should read over this summer or do they go over it all again?</p>
There's no consensus - even at Caltech. If you place out of math, you get the full credit - just as if you've taken the class, and the requirement is fulfilled. If you place out of chemistry, you still have to take harder chemistry classes to fulfill core. Physics and CS are like math as well, so maybe the chemistry people should just get with the program.</p>
<p>Other schools can be, of course, completely different.</p>
<p>where do you get a hold of math 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>My schedule for the past three years (a bit heavier than average):
Freshman:
Fall: Ma 2a (Which would be Ma 2b for you...they switched them 2 years ago)
Ma17 (Putnam Prep-ish)
Ma5a
Winter: Ma 5b
Spring: Ma5c
Ma 4
ACM116
Smore: Ma 108 abc , Ma 109abc, Ma120abc, Ma 116c
Jr: Fall:110a, 121a, 117a, 118a (Special Topics in Logic, offered very rarely)
Winter:110b, 121b, 145c, 147b
Spring: Ma 110c, Ma123, Ma147c, Ma 191c (Special Topics Course on Inverse Spectral Theory), SS/Ma214 (Mathematical Finance)</p>
<p>Sr (Projected): Ma 130abc, Ma 151abc, Ma 140abc, Ma 10/11 (written/oral presentation) </p>
<p>happyentropy, how hard was it to really absorb and really learn the material taking so many math classes (Do you still remember most of thestuf you learned from sophomore year, for instance?)? Did you take a lot of courses in other subjects (i.e. how much units did you take each trimester)? How much hours of studying / hours of free time did you have each trimester? I'm </p>
<p>Thanks for the info.</p>
<p>collegefreshman: I think the analytical courses are slightly more rigorous than the practical courses.</p>