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Also, I don't think you ought to consider "when I was 17, I could do basic calculus in my head" as a sign of more ability than you have today. The problems were
by bmer 5y ago
Also, I don't think you ought to consider "when I was 17, I could do basic calculus in my head" as a sign of more ability than you have today. The problems were likely not that hard, since you were 17.
Do you practice doing long division every day, without pen and paper? If not, then I think you ought to try that before making the judgement "I can't do it". Practice is very important, especially when it comes to memory intensive tasks. The other key bit is coming up with efficient algorithms for doing division in your head that take into account the pros/cons of memory vs. pen and paper (why should we expect algorithms that run well on paper to be effective in our memory-only execution as well?). Over the years, people have developed a wide variety of "mental arithmetic" algorithms.
Finally, doing long division in your head isn't important. No one will judge you by it, when you're applying for a PhD, and so you should not judge yourself by it. There are way bigger fish to fry, even in mathematics.
- silisili 5y agoMan, you guys are very motivational. Thanks for that. The point I was attempting to make was that I could store these carry numbers in bulk at one point, but now am lucky to remember a single one. I only know that as I try to teach my own kid math today. It's frustrating to realize you've 'lost your touch.' But, you're right, it's really not important day to day.
- ghaff 5y agoI would probably have to figure out (or more likely look up) how to do long division these days. I probably haven't done it in decades.