I'm a first year PhD student in a CS department at what some would probably consider a mid-tier university. I've been reading from Vershynin's High-Dimensional Probability and been trying to learn about concentration; I like problems relating to probability and geometry (e.g compressed sensing, dimension reduction, matrix recovery, etc.) But I'm wondering, more broadly:

  • If you could go back to grad school, what would you be doing during your first couple of years to learn techniques, etc.?
  • One thing I struggle with is determining which papers to read. There are so many to pick from; is there a better strategy than just reading whatever seems to pique interest/come from authors you know?
  • Are there books/problems/papers you read during grad school that helped you either technically or in forming your research interests/problem taste?


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    $\begingroup$ Terrence Tao has a bunch of advice on his blog for all stages of a math carreer, you might find some of it useful: terrytao.wordpress.com/career-advice $\endgroup$
    – Denis
    Oct 30 '19 at 10:59
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    $\begingroup$ I work in machine learning, and I never got a great foundation in high dimensional probability. I worked through Vershynin's book as a postdoc and wished I had found a resource like that much earlier. It's a great book, and you definitely can't go wrong spending time working problems in the book. If I had a time machine, I would go back and spend more time on high quality textbooks like his and less time on reading random papers. $\endgroup$ Oct 31 '19 at 3:45

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