Notes to Future Self

Yesterday I was tidying up a bit and came across the old notebooks I used when I was a research student. As I suppose is the case with everyone else, there’s quite a lot in them that never went anywhere. If you can read the example above, about 3/4 of the way down the right-hand page I left a note saying “This is a pointless task”. I can’t remember if that referred to that particular integral or my research in general!

Some people who have seen this picture remarked on the size of my integral signs. That’s because I had to do quite a lot of integrals with complicated integrands, so I got into the habit of drawing big integral signs as a prelude to writing down what I assumed would be a horrible formula.

The way I worked in those days (1985-88) was to do a lot of rough scribblings on scrap paper. When I got to something I thought was promising I would write up a “neat” version in the notebook and throw away the workings. I know younger folks these days do most of their work on a screen but, as an old fogey, I still write a lot down on paper or on a blackboard. I didn’t have my own blackboard when I was a PhD student, but I did have plenty of notebooks – most of which I have kept. I think that I’ll always find an essential part of the mathematical thought process involves a pen or piece of chalk in my hand, moving around and guiding my brain.

Looking through these books I remember that I also wrote down ideas for follow-up projects. I managed to do very few of these, but some were done by other people elsewhere independently of me, so at least they were reasonable ideas!

3 Responses to “Notes to Future Self”

  1. Anton Garrett's avatar
    Anton Garrett Says:

    I believe that the infinitesemal element dx (or dz or whatever) should be written immediately after the relevant integral sign. This saves a lot of brackets and it is a mystery to me why many textbooks do not do this.

    • telescoper's avatar
      telescoper Says:

      I do that now in my solutions to exams, etc. I found though that doing a numerical integral as a set of nested sums with the integrand in the middle it helps to write the elements dxdydz in the correct order afterwards.

  2. Wyn Evans's avatar
    Wyn Evans Says:

    Wonderful. Grad & Ris is I guess

    “Tables of Integrals, Series, and Products” by I. S. Gradshteyn and I. M. Ryzhik.

    It is a long time since I have looked at my copy, Mathematica being speedier nowadays.

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