<p>I've got a pesky decision coming up, and maybe some of you (especially those studying math) can help me. Sorry this is so long, but it's best to throw all possible questions out there, in case someone else is wondering about the same things.</p>
<p>I'm just finishing up my multivariable calc class in high school. It's been a weird "classroom" dynamic because it's just the teacher and me sitting in the library working through the textbook together...he's an old school guy, and his idea of learning the material is doing every problem in the book. So we've done a couple of thousand problems (60-100 or so for every section), and have gotten quite proficient in the nuts and bolts of multiple integration, etc etc. The only proofs we've done (I should say "I've done," because he tends to skip them) are the basic, intuitive ones in the books...properties of cross and dot products, div and curl, etc...nothing intense or requiring much mathematical maturity.</p>
<p>Anyway, we're about done, and it's up to me to decide what to do next. I sadly don't have the option of using it as another study hall for the rest of the year, and as long as I have to be doing something, I want it to be useful. I've got a few options:</p>
<p>1) Do some basic differential equation stuff.
2) Do some basic linear algebra stuff.
3) Go over infinite series again (I self-studied BC calc last year, and I'm not overly confident in my abilities with these).
4) Go through a textbook called "A Bridge to Abstract Mathematics," or something like that. Basically, do an intro to proofs class.</p>
<p>Both (1) and (2) would fill up the rest of the year and would make the 50 series next year even easier. Also, (3) wouldn't take very long, and I'd have time to do something else as well. However, I have some questions about them. Just for background, I'm a high school senior intending to major in physics (with either a minor or second major in math). </p>
<p>--Are infinite series stressed in the intro math series? I mean, are you expected to know them? I read that a 5 on the AB exam (which doesn't cover them) lets you start right in Math 51, so would it be a waste of time to go over them? For physics classes, how often are they used, and would it be easy enough to simply brush up on them when they show up?</p>
<p>--I have no experience with proofs, but I'm a logical, mathematical kind of guy. If I went through an intro to proofs book this year, audited a summer class (intro real analysis, or intro to abstract math, if i'm still unsure about proofs) at the university in my town, would it be feasible to take the 50H series next year?</p>
<p>--If I don't take the 50H series, I still want to transition into the upper level math courses at some time. Would it be extremely repetitive to take the 50 series, Math 115, Math 171, and then Math 174, sometime throughout the four years? Would I really miss a lot if I tried to condense my initial exposure to proofs into a few months, rather than going through Math 131 (I've heard it gives an ok intro to proofs) and 115 before hitting the more challenging classes?</p>
<p>--Will the normal 50 series drive me absolutely insane? I hate doing so many repetitive integrals this year, and would love to avoid any unnecessary review. Especially if I spend the rest of this year doing diff eqs or linear algebra, I worry that the class will be boring, and I'll think of it as a waste of time.</p>
<p>--Does the 50H series cover all the same topics as the 50 series (plus a lot extra and with a different approach), or do the two diverge significantly? Practically speaking, will the 50H series teach me the math I need for physics?</p>
<p>Also, if any of you current students have updates on your current classes, fill us in!</p>
<p>Thanks so much for answering whatever you can/have time to/want to. I really appreciate it.</p>