Back to Basics

This is a little embarrassing to admit, but I don’t feel like I learned mathematics well enough in graduate school. In particular, I do not know algebra—my specialty—well enough.

My solution? Go back and work through the textbooks and problems that I worked on (or should have worked on) in graduate school. This is how I have been spending my research time this semester. In the short term, this is foolish. This will not yield any new results. But I am hoping for long term gains in productivity.

I wish I would have learned the material better the first time, but this is thenext best thing.

6 Responses to “Back to Basics”

  1. Andy "SuperFly" Rundquist Says:

    This is really interesting. Can you give an example of the type of thing you wish you had learned better?

    • bretbenesh Says:

      Some examples are that I know nothing about “transfer” or “character theory.”. The larger problem is one of fluency. I learned Spanish pretty well in school—I was definitely proficient. But I never pushed past that to become fluent.

      The same thing is true of mathematics (although I am much closer to fluency in algebra than i was in Spanish). I think my research would be better if more of my thinking were automatic.

  2. Hitchman Says:

    I sometimes feel the same way… In particular, i have been a bit if a magpie, moving from one shiny object to the next, rather than a dwarf, delving deep into a subject in search of new treasure.

    But take heart! Terry Tao’s explicit advice for young mathematicians includes “learn and relearn you subject.” So, really, you are doing as the master says.

  3. Kate Owens (@katemath) Says:

    I have thought this same thing. Now I feel like I could get so much more out of those grad classes than I got the first time.

    • bretbenesh Says:

      I have thought the same thing at various points about every level of my education. This scares me, since I was (as I am sure you were) an excellent student by most measures.

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