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Quick Questions: May 18, 2022

87 Answers

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Where do you find the time to do extracurricular reading?

There are so many books I want to study out of, not just maths but other things too, but even on normal days when my sleep disorder doesn't fuck up my schedule (which should be getting fixed before next academic year), I get so exhausted studying by myself that I can only do so much (typically ~2 hrs) at a time, which makes my pace ponderous, and then even after switching topics to keep things fresh my brain overheats and I just have to not think for hours at a time to recover.

And I compare myself to other people, who seem to be able to read tons and tons of stuff, while I'm genuinely wondering if I'll get through my whole reading list (even just as it stands today) before I die, or whether I'll be able to read quickly enough to even do my master's dissertation in general relativity (which is not taught at my uni) two years from now.

What do I do about it?

P.S. I'm immune to caffeine, which I've discovered the hard way, unless your suggestion is to neck *twelve* pills of the stuff in one go instead of six lmao.
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Do the Princeton Lectures in Analysis (Stein and Shakarchi's books) need to be read in order?
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What's the difference between R(i) and C? I saw R(i) in a meme video, but can't find any resources to clarify its definition online.
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Super quick question. I'm looking to derive the x and y units of a FFT. I remember finding a whole book that stepped through the exact formulas of what the discrete units would become. This book was, like, 8 chapters just on the *units* of Fourier transforms. Super instructive. Problem is, I forgot the title and Google has not been helpful. Is anyone out there familiar with this book?
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I have been trying to find good resources for exercises of transfinite induction and recursion but have been coming up flat. Does anyone have any good leads
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Does anyone know if geometric group theory is related to any areas of research in industry? I know topological data analysis is big but I can’t find any uses of geometric group theory outside pure research
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Let there be two functions, say f and g, and both are p-integrable (i.e., in this case they're both in L^(p)(E), E being a measurable set). A few weeks back, I had to prove that f+g was also p-integrable, but I wasn't allowed to invoke Minkowski's or use any norm arguments. I was told to just "use the definitions"

I tried using a finite a.e. argument, but I'm pretty sure a function being finite a.e. doesn't imply integrability. I assume there's some sort of characteristic function counterexample one could make

Is it just a given that this holds since functions in L^(p) space also form a vector space? Some of the trivialities of real analysis/measure theory went over my head
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can we have two functions f and g where lim x->∞ f(x)-g(x) = 0 while lim x->∞ f(x)/g(x) diverges to infinity?
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What are the ways to turn a finite product equation Π , into a regular formula?
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Hi, homeschooling mom here. My son was fascinated by the beautiful pattern of a 3-D paper chain that looks kind of like flowers/snowflakes, how it is folded and how it is made. Could any of you please point me toward key terms to google for to find more info/projects/examples/videos? I can come up with the folded paper snowflake thing but I'm sure there is more depth to attain here. Thanks!

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