<p>Some delta-epsilon limit/continuity stuff, possibly. You shouldn’t be expected to know more than that to test into honors calculus.</p>
<p>How hard is Spivak to go through by yourself? Provided you get the answer book, of course. There’s also a website I know where you can post math questions on the board and they get back to you–with good responses!–within a day. Would that be enough to try some self-study?</p>
<p>As long as you’re a disciplined and independent student, Spivak shouldn’t be too tough to go through. The inherent problem with independent study is that you’re not coerced into thinking too hard about any problems, especially if you already have the answer key. This breeds poor problem solving skills, and it won’t help you much in the future.</p>
<p>So what I suggest is that you go through Spivak and do every single one of the exercises, and don’t ask anyone any questions (or look in the Answer Book, which I don’t suggest you buy) until you’ve thought hard about it for a good three days or so. The double- and triple- star problems are a great way to prepare for Honors Analysis.</p>
<p>There’s no need to “prepare” for the placement test. Don’t spend the summer of your senior year (which should be the best summer of your life) reading through Spivak or Rudin or Komolgorov and Fomin. I guess you could if you wanted to, but it seems like a monstrous waste of time, if your only goal is to prepare for Honors Analysis. Your placement score will probably be inflated, and you might get into Honors Analysis, but once the pace accelerates, and the class moves beyond Spivak or w/e, you’re going to be lost, if you don’t have the ability to place into the class without preparation. That’s just my opinion. </p>
<p>Besides, Sally’s pretty lenient about letting people in, provided that they don’t do too badly on the test. If you don’t place into 160 or above, then you shouldn’t be thinking about 207-209. Just don’t worry about it; if you have the ability to do well in the class, you will find a way to get in;)</p>
<p>p.s. Well, I guess it actually depends on the instructor. I don’t know who’s teaching next year, but if it’s someone like Peter Constantin, then a little preparation might be necessary. If it’s Sally, I wouldn’t, but that’s just me..
I don’t know about Ryzhik; we had him last year for a few lectures while Constantin was gone, and he didn’t seem to go too fast</p>
<p>This year, Ryzhik made the completion of the reals a prerequisite for the class. So you might want to look into that a bit. We also had a bit of a different pace from last year’s class, covering all of measure theory in the first half of the class (up through Radon measures and Fubini-Tonelli) and then moved on to contraction mappings/topology/etc. in Kolmogorov/Fomin. The preparation you’ll need will depend upon your instructor.</p>
<p>You really don’t need to worry about placing into honors calc if you’re in BC (and doing reasonably well). I didn’t know a thing beyond the BC material, which I reviewed for about an hour a couple days before the test, and I placed into 199 (Intro to Analysis). I had only the faintest idea of what a delta-epsilon proof was, let alone how to do one.</p>
<p>how are you doing in math now though? that’s the question…</p>
<p>Me? I’m doing fine. I’m not at the top of the curve or anything, since there are a lot of math major types who took crazy math classes in HS or took 160s last year (I’m in 203, real analysis 1, now), but I’m getting about the class average. It’s hard, but I’m enjoying it.</p>