Ask HN: What is the essential mathematics for tech and best resources for it?

A lot of it depends on what exactly you want to do (in|with) tech. Plenty of developers get by with high-school algebra. At the more extreme end, if you want to write software for weather forecasting or other fields using numerical computation, simulation, etc., then you probably need a background roughly equivalent to a degree in maths. And there's a lot of "in between" those extremes.

For my money though, I'd say a good starting point would be:

1. Calculus through Calc III (as the Calculus sequence is typically structured in American universities)

2. Linear Algebra

3. Differential Equations

4. Probability Theory

5. Statistics

Sidebar: if you specifically want to work with cryptography / cryptanalysis, you probably want to study number theory, abstract algebra, and probably a bunch of other stuff that I don't know anything about. :-)

Resources? Hmm... there's a whole world of stuff out there, and plenty of previous HN threads discussing various books, blogs, courses, videos, etc. But you could do worse than using Khan Academy, and the ProfessorLeonard channel on Youtube. Other good Youtube channels include Michael Penn, 3blue1brown, blackpenredpen, Organic Chemistry Tutor, MathMajor (which is still Michael Penn - he has two channels), NancyPi, and MIT's OCW stuff (Gilbert Strang in particular has great video lectures on Calculus and Linear Algebra).

Also note that if you're self-studying (as opposed to taking a class at university) then it mostly doesn't matter what edition of books you use. And you can find used copies of older editions of maths books for pretty much every topic imaginable for pretty cheap. Search on Alibris and then sort by "Price - Low to High" and you'll usually be able to find a book on your topic for $2.00 - $5.00 or so. If you prefer ebooks there are legitimately available free books on most subjects again, and there's always the pirate e-book sites if you want to go that route.

If you want to learn math, a good place to start would be AOPS curriculum https://artofproblemsolving.com/store/recommendations

Continue with Susan Rigetti curriculum https://www.susanrigetti.com/math

You can get answers to your questions here https://www.reddit.com/r/learnmath/ and here https://math.stackexchange.com/

Outside the "basics", I've seen Newton's method come up again and again in my work. I also work on some map software and geometry (especially trig) has been really useful.

For resources, I love this blog https://www.redblobgames.com/

As another comment points out, plenty get by with high school algebra. (I kind of fall into that category.)

Whatever extra math is required can be considered (sub)domain knowledge.

If you want an efficient way to approach this, you can just start learning/working on whatever tech you're interested in, and learn whatever math you come across.

Which flavor of tech?

The sorts of math that a dev needs to know is extremely dependent on what the project is. With some projects, you don't need much beyond what you learned in high school. With others, you need very advanced mathematics. And there's a whole range in between.

You can find a free eBook of

ISBN-13 978-1-4899-9741-8 Numerical Linear Algebra By Grégoire Allaire and Sidi Mahmoud Kaber

A fun motivated cold water start for some essential basics.