[ubavic]

Mathematics.

Of course, mathematics will continue to develop in unimaginable directions, but the “base” notions in math will stay the same. I am talking here about notions of relation, function, group, vector space, tensor, category, measure, integral... Even if some of those are known for a long time, formal definitions that we use today are pretty new. And it seems to me that those will stay fundamental for a long time.

(Seems to me that other sciences (like physics and biology) don’t have that “stability”. In those fields, it wouldn't be too surprising if we discovered some fact that changes a lot we know about it)

Also, as these core notions of math will stay the same, math notation will stay the same also. And that is a good sign that we will continue to use TeX for a loooong time

[71a54xd]

I've effectively forgotten all of the useful math I learned in college, primarily stats and linear algebra along with enough calc to read through mathy CS papers.

Any recommendations for me to properly re-learn this stuff without going to a community college?

[wheelinsupial]

It really depends on what you're trying to do with the knowledge. If you mean learn it to the level of a university undergrad, then you'll need to do exercises and solve a lot of problems.

If you're interested in computational or cookbook type math, then it's best to find some textbooks with lots of exercises and student solution manuals available. You can grab lots of homework problems, solutions, and lecture notes from undergrad material posted freely on the internet. I would also recommend learning about how to use some numerical packages or computer algebra systems, so you can check your work.

If you're interested in proof based math, then it's probably best to find a grad student at a local school that you can pay to review your proofs and provide feedback. You might be able to use some online communities to do this as well.

There are often books that are aimed at a very basic level and others that are aimed at a more rigorous approach for the same material. It can help to review the more basic or less rigorous books to help get some intuition when you're stuck or need an alternate explanation.

There are several online math communities where questions about undergrad math have been asked and answered. A couple of examples for math and stats are: https://math.stackexchange.com/ and https://stats.stackexchange.com/

If you decide to follow an undergrad sequence of problems, you can look at starting with the highest level course you want and determining if there is any discussion on prereqs. You can trace the prereqs (which will typically be a subset of the previous course material) back to the beginning and find the minimal amount of material that you would need to get through.

[ivansavz]

I've written two (nonfree) books that might be useful for re-learning the topics you listed. Links in profile.

Here are the concept maps to give you an idea of the concepts (round boxes) and topics (rect. boxes) covered in the books: https://minireference.com/static/conceptmaps/math_and_physic... https://minireference.com/static/conceptmaps/linear_algebra_...

[aronpye]

Khan academy, it’s free and I’ve always thought the pacing of the lessons to be good.

[the_only_law]

I need similar, but I don’t even remember much of HS math.

[ivansavz]

See my comment, sibling to yours, for first-year university-level books.

For high school math specifically, I have a shorter book that covers only high school topics, with exercises, and applications (and a SymPy tutorial). See book preview here https://minireference.com/static/excerpts/noBSmath_v5_previe... and website is https://nobsmath.com