<p>student: why must the right hand limit exist opposed to any limit?</p>
<p>prof: uhm so uh the question you're asking is, why is this the hypothesis of the theorem</p>
<p>student: yes</p>
<p>prof: in other words why does this work? in other words, this is a theorem that's true. if you drop this hypothesis, it's total false (<em>big gestures here</em>) and if you don't have this hypothesis you can't use this theorem and you will get the wrong answer (<em>more gesturing</em>)...i mean...uhh it's hard to express it any further than that. so look, in many cases, we tell you formulas. and in many cases, it's so obvious when they're true that we don't have to worry about (<em>wild gesturing</em>) what we say. and indeed, there's something implicit here<---his trademark line/answer</p>
<p>OpenCourseWare is great. I’ve been using it since 2007. I never when to high school, so I used it to learn calculus and to supplement some other things.</p>
<p>It’s the way I first learned about MIT (Good Will Hunting). Had it not been for OCW, I probably would not have considered college as an option.</p>
<p>I practically teach myself AP Calculus BC with 18.01 since all my AB teacher does is flip slides.</p>
<p>But I find Physics and Introduction of Solid State Chemistry the best classes I seen so far. Prof. Sadoway and Prof. Lewin are some of the best teachers I seen in my life. One of the reasons why I’ll apply to MIT amazing educators.</p>
<p>Personally I don’t really like OCW as a primary resource. I use it more like a supplement (for a list of suggested readings and problem sets). I don’t like the lecture notes because they are rather inconsistent. Usually they’re not very well organized or lacking in detail.</p>
<p>e.g. I printed the entire set on quantum physics, and it was kind of hard to read (everything was in scribbles), and it was missing the material needed to do the problem sets (probably that was supposed to be the case, challenging; but just not very convenient as a learning resource). Some are oddly simplified and lacking in info, e.g. statistical mechanics, without referring to the lecture I guess. There’s also those which feel difficult to read, e.g. topology, but that’s maybe more like my fault. Though it’s kinda cool that it is printed in courier and the symbols were filled in pen, just like Nash’s paper on non-cooperative games. Classic, and really cool.</p>
<p>The suggested readings are great. Saff & Snider for complex analysis, Griffiths for quantum mechanics, Sakurai for more advanced QM etc.</p>
<p>Well, I’m a firm believer that a good text can cover more material than a good lecture in the same amount of time. I’m not very good at remembering lectures so I’ve to take notes, and it’s very strange to sit behind a screen with a notepad haha.</p>
<p>None of the schools in my area use Spivak so I couldn’t get ahold of a copy. I mostly used sources on the internet (especially OCW) for Epsilon-Delta proofs. Stewart’s book had a few pages on them - all poorly written. Actually, most of that book was poorly written. I didn’t use it much.</p>
<p>Mmhmm, fair enough. I’ll really recommend it if you get a chance to read it. It doesn’t cover as much as Apostol’s but focuses well on building intuition. That’s why the synopsis says that it’s an ‘introduction to real analysis’.</p>
<p>The other reason I bought Spivak (from India… cheap books there) is because he has a text on differential geometry and a sequel to his calculus textbook (“Calculus on Manifolds” - but there’s missing linear algebra inbetween), and I wanted to get used to the tone in his books first.</p>
amazing educators.</p>