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How often do you guys feel like you have to “relearn” specific math topics?

34 Answers

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Completely normal. There are several textbooks and papers that live in my back pack because I am constantly referring back to them to recheck previous results. Just consider google and old books as an extension of your brain. You know exactly where to look to find the information and there will never be a time during your research where you wont have access to those resources.
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I'm not sure I ever even learn them the first time.
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Today i relearned covering maps and group actions on sets...

For me it is very depressing that i forget things which i spend a lot of time to learn. I suppose that is how it works
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I read the title to your post and immediately thought, "linear algebra" before reading your text.

I always find myself having to review concepts from linear algebra from time to time. It's such a deep and beautiful field with so many powerful results. Few could hope to retain every piece of information, and revisiting the topic so frequently gives me such an appreciation for it.
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All the time.
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Every time I teach multivariable calculus….
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Thats how human brain works.You cant retain all the information youve learnt.
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3rd year phd in physics here. Do all kinds of calculus every day. Had to look up the leibniz rule yesterday.
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First, the answer. As a hobbyist, I relearn math all the time. It's almost the name of the game. As a high school (engineering) teacher, some of my engagement with mathematical ideas is expressly to find new ways of communicating them, which requires relearning.

  


Second, the metaphor. This reminds me of an idea I came across previously in the comments. What you know in your head is your toolbox — what you carry around with you to solve problems you might encounter. What you've learned but no longer know (perhaps codified in your texts/notes) is your workshop. There's some heavy machinery that's not really feasible to carry around, but there's also tools that don't fit in your toolbox. You know how to use them, but you have to go and get them. Maybe even find them if your workshop is as disorganized as most.

  


Third, the advice. Don't feel shame over needing to revisit an idea or subject — it is not only a natural part of learning but a necessary one. A similar pridefulness hindered me greatly in college. Had I the humility to accept the various types of difficulty that accompany continued study perhaps things would look differently; at the very least my GPA certainly would. To that end, measure yourself by your effort not strictly the outcome. This is something I continue to struggle with, but when I'm able to do so it makes many more things–including relearning**–**worthwhile and enjoyable.
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All. The. Time. Even with an above-average memory, I always need to revisit what I’ve learned to keep it fresh and to apply it to problems I encounter.

I view my role as an (applied) mathematician not as being a “repository of knowledge” but as an experienced trail guide in the “Forest Of Math”. I don’t have it memorized, but I’ve “been there” before and I trust myself to find my way when I need to go back.

Furthermore, it’s more important in my line of work to *know which part of the forest to check for answers* then it is to have specific parts of the forest committed to memory. Real-world problem solving relies a lot on intuitions built layer-by-layer for how to *diagnose what the problem even is.* I spend most of my time trying to help non-math people figure out which sorts of math techniques will help them. Then, I get busy reviewing all the details so I can code up a good solution!

Edit: specifically on linear algebra: I took the basic undergrad version twice, and then an advanced undergrad version, followed by graduate numerical linear algebra. Even in that last class, I felt like I was still learning new things about the basics. Linear algebra is a core piece of my toolkit, and have never stopped learning more about it.

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