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Ask HN: How to retain core competency in math when your job doesn't require it?
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Re: Ask HN: How to retain core competency in math when your job doesn't require it?
#2You spend a non-trivial amount of time learning calculus, for example, but how do you maintain that competency?
Re: Ask HN: How to retain core competency in math when your job doesn't require it?
#3If you're good enough then volunteer or hire yourself as a tutor or night college teacher.
Also, there are a number of people that produce calculus tutoring youtube videos. Maybe you can try that.
Unfortunately, a large percent of what we learn will eventually be forgotten due to lack of use. Most of what we learn will not be used at work. I remember spending tons of time studying calculus yet I've yet to use any of it. If ever I need to use it I will need to review it to refresh my mind but most likely I won't remember most of it.
Re: Ask HN: How to retain core competency in math when your job doesn't require it?
#4I am not very good at classical mathematics. I am quite confident that there are better more intuitive ways of describing the same ideas, so until one such system emerges I tend to learn the concepts that are being expressed in mathematics and convert them away from mathematics to just a logical description of the operation. I haven’t run across anything in calculus for instance that I can’t describe in python with loops and arrays. One might argue that it is all math ultimately but that’s fine so long as I can deal with the raw idea and not the idea expressed in terms of math operations.
Re: Ask HN: How to retain core competency in math when your job doesn't require it?
#5I believe the place of calc (just like trig) is overinflated in pre-real- analysis education. As far as I am concerned, sin is just a function defined a certain way and I ain't worried about SOH-CAH-TOA or anything to that effect. I don't think one requires 1000 page book to learn a few core calc concepts either. Derivative is a slope. That's it. It's the same value along the length of a line. The only problem is non-linear functions where slope changes along every point. In which case we bring in the machinery of tangent/secant lines and take a limit for a very intuitive reason, but the underlying concept remains the same. This informs the definition of derivative. From this point on derivative is just a function defined a certain way and in this regard is no different from any other function like indicator function or whatever. The rest of the talk about derivatives is often just a padding and general interest. Have you ever seen a 500 page book written about the step function?
When you take a bit more advanced class, the symbols for partial derivatives and integrals will be interspersed with other symbology and flash before your eyes like elements in a humongous matrix. You won't have time to think about stuff you learned from 1000+ page doorstop. You have to learn to think more nimbly and abstractly like a mathematician. To that end, check out "intro to math proofs" textbooks.
If by calculus you meant modern math analysis, then simply disregard the stuff above.
Re: Ask HN: How to retain core competency in math when your job doesn't require it?
#6It might depend on the person, but I've retaught myself some math stuff, and I think you relearn it a lot faster the second time. The real problem is not getting bored. It was a bit slow-going at first because I was out of practice, but after a little bit of settling in, it was alright. YMMV, it depends how well your long term memory works.
Re: Ask HN: How to retain core competency in math when your job doesn't require it?
#7You spend a non-trivial amount of time learning calculus, for example, but how do you maintain that competency?
maybe you could compile a list of problems and use anki to regularly train yourself?
There's also Schaums outline for Calculus
You can also try going through Art of Problem Solving Calculus (though it's much more difficult than the typical calculus text)
Re: Ask HN: How to retain core competency in math when your job doesn't require it?
#8It depends what the OP call core math competency.
If you mean the ability to solve and think critically about problems, I like a combination of "How to solve it" by Pólya (https://en.wikipedia.org/wiki/How_to_Solve_It) for more general ideas and regularly finding puzzles onm different topics such as the ones proposed here (https://fivethirtyeight.com/tag/the-riddler/).
For deeper mathematics, I feel like that's hard. I come back to my notes from Grad School once in a while, or try to follow proofs for topics of interests. But to be honest, most of them are a little beyond me at times. Maybe Fermat's library (https://fermatslibrary.com/) can offer some annotated reading which would be helpful?
Regardless, I wish you good luck. Please do share if you have any more good ideas.
Re: Ask HN: How to retain core competency in math when your job doesn't require it?
#9You spend a non-trivial amount of time learning calculus, for example, but how do you maintain that competency?
maybe you could compile a list of problems and use anki to regularly train yourself? There's also Schaums outline for Calculus You can also try going through Art of Problem Solving Calculus (though it's much more difficult than the typical calculus text)
> maybe you could compile a list of problems and use anki to regularly train yourself?
That seems to favour rote learning instead of actually developing or keeping core competences.
Re: Ask HN: How to retain core competency in math when your job doesn't require it?
#10What about teaching?