<p>Haha I also came across Calculus with Theory today(though I first heard about ocw some time ago). Indeed, I think I’d prefer a rigorous, theory-oriented rather than problem-oriented approach to calculus, but maybe not as arid as, say, baby Rudin. I’ll check that course and see whether it works for me. Glad to see you also prefer NT to analysis, that’s quite rare, I think(though frankly, I sometimes wish I were the other way around).</p>
<p>Analysis would surely seem more bearable if I knew for sure when I could stop studying it. I know that in order to qualify for a PhD, you typically have to pass an algebra/analysis(and topology, maybe) exam, but after that would I still be required to take analysis courses? Can a math PhD clarify this for me?</p>