Ask HN: How to retain core competency in math when your job doesn't require it? - craftyguy
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usgroup
Simple answer is past-times. For example, I have a side interest in ODEs and
PDEs, which I basically never get to apply for work.

So I'm working on 3 problems from orbital mechanics, control theory and
investment science respectively, each which is interesting in itself but each
which flexes my ODE and PDE muscles.

In short, just invent problems you find engaging and then scratch away at them
on planes and trains, and in all those in-between times.

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artwr
It 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](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/](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/](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.

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mindcrime
1\. Khan Academy

2\. Youtube (see: Professor Leonard, 3blue1brown, Gilbert Strang, etc.)

3\. Books like:

[https://www.amazon.com/Humongous-Book-Calculus-Problems-
Book...](https://www.amazon.com/Humongous-Book-Calculus-Problems-
Books/dp/1592575129/ref=sr_1_3?s=books&ie=UTF8&qid=1537278451&sr=1-3&keywords=calculus+problems&dpID=51K61QI-
MPL&preST=_SX218_BO1,204,203,200_QL40_&dpSrc=srch)

[https://www.amazon.com/Calculus-Practice-Problems-Dummies-
On...](https://www.amazon.com/Calculus-Practice-Problems-Dummies-
Online/dp/111849671X/ref=sr_1_4?s=books&ie=UTF8&qid=1537278451&sr=1-4&keywords=calculus+problems&dpID=51nPdaLibEL&preST=_SX218_BO1,204,203,200_QL40_&dpSrc=srch)

[https://www.amazon.com/Schaums-Solved-Problems-Calculus-
Outl...](https://www.amazon.com/Schaums-Solved-Problems-Calculus-
Outlines/dp/0071635343/ref=sr_1_5?s=books&ie=UTF8&qid=1537278451&sr=1-5&keywords=calculus+problems&dpID=51tAGvcE80L&preST=_SY291_BO1,204,203,200_QL40_&dpSrc=srch)

[https://www.amazon.com/gp/slredirect/picassoRedirect.html/re...](https://www.amazon.com/gp/slredirect/picassoRedirect.html/ref=pa_sp_atf_stripbooks_sr_pg1_1?ie=UTF8&adId=A0504778C2N61BSH4IS6&url=https%3A%2F%2Fwww.amazon.com%2FChallenging-
Calculus-Problems-Fully-Solved-
ebook%2Fdp%2FB07H39K6BJ%2Fref%3Dsr_1_1_sspa%3Fs%3Dbooks%26ie%3DUTF8%26qid%3D1537278451%26sr%3D1-1-spons%26keywords%3Dcalculus%2Bproblems%26psc%3D1&qualifier=1537278450&id=7327685849459176&widgetName=sp_atf)

4\. And maybe not as calculus specific, but doing Project Euler problems might
also be useful.

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deytempo
I 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.

~~~
socketnaut
You might be more comfortable with Python syntax than with standard
mathematical syntax, but I wouldn't think of it as being closer to "just a
logical description" or closer to being the "raw idea." You're just choosing
to use different notation.

I would guess that most people comfortable with both representations would
feel that standard mathematical notation is lighter and conveys the "raw idea"
more directly.

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WheelsAtLarge
If 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.

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overinflated
I 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.

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SamReidHughes
It 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.

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shortoncash
I struggle with this so much and am glad you asked it. I reopen the books and
things come back to me slowly, but it is very hard to retain without daily
use.

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craftyguy
You spend a non-trivial amount of time learning calculus, for example, but how
do you maintain that competency?

~~~
HiroshiSan
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)

~~~
geezerjay
> 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.

~~~
mindcrime
Given that the OP has already learned the material and is mainly interested in
retention, that shouldn't be a problem.

In my experience, it's the mechanical stuff that you forget most quickly
without use, as opposed to the conceptual stuff.

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jforjuancho
What about teaching?

