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I am a 1st year PhD student. I got a bachelor's degree in CS but I didn't start learning TCS systematically until this year.

This dumb question came to me when I opened an undergrad complexity lecture watchlist after I forgot it for months, and realized that I had already learned the content from an "advanced" textbook. And I found things covered by the course were learned by myself within a much shorter time. That's perhaps a special case. But I noticed that undergraduate-level courses/materials cover more details and examples about the basic concepts than advanced ones, and I don't know if it's necessary to know such a kind of details.

So my real question starts here: should one skip undergraduate-level TCS courses/materials to save time, or do it step by step to reinforce knowledge?

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    $\begingroup$ Depends on your learning style and specific goals. But in general, YES! Even better is to also study undergrad pure math materials! $\endgroup$
    – Mahdi Cheraghchi
    Commented Jun 28, 2020 at 2:44
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    $\begingroup$ Maybe here’s a helpful test that could give a best-of-both-worlds: you can skip material you think you already know, but make sure you look at exercises and feel confident about them. In the interest of time, I don’t think one ought do every problem in a book or anything like that, but a good sign that you might need more “reinforcement” is if there’s many exercises that you really have no idea at all how to approach. But as commented above, you need to find your own routine! $\endgroup$
    – Jason Gaitonde
    Commented Jun 29, 2020 at 1:32
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    $\begingroup$ When you are self-learning, it's very important that you don't get bored. But skipping exercises can be dangerous. Do at least one on each part/chapter, and I mean: really write down your solution. Sometimes I had been confident that I understood something just by thinking out a rough solution, but it later turned out I was wrong. $\endgroup$
    – Hermann Gruber
    Commented Jun 29, 2020 at 8:33
  • $\begingroup$ Thank you so much for the comments! These are very helpful to me and exactly what I was doing this weekend and will continue doing in the future! $\endgroup$
    – raycosine
    Commented Jun 29, 2020 at 8:51

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Yes. From my experience, going back to basics teaches you new things every time. My students tough me the most.

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