Ask HN: How or where to begin learning mathematics from first principles?
As I've become more skilled with programming and electronics I have felt myself begin to near a wall. My knowledge of and skills in math is relatively poor and all the interesting things that make up the more advanced programming and electronics pursuits seem to be heavily based on math.
When I butt heads with these more advanced topics I find I resort to scouring the internet to cobble together pieces of various tutorials and guides. While it does feel good in a way to hack together limited understandings to make satisfactory solutions I'm beginning to feel less like a hacker and more like a hack. The knowledge I gain is shallow and I don't think my tactics will get me much further.
Instead of working backwards from implementation I would like to start from the beginning and learn math the proper way. Unfortunately most of the resources I find online seem to more focused on teaching me how to solve math problems. I have no interest in solving specific math problems on a test, I'm not going to school and I doubt I will ever take a math test again in my life. I want to work up from first principles and gain the tools to reason about the world mathematically and understand the cool things that are currently out of my reach like antenna design, machine learning, electromagnetism, cryptography etc.
Unfortunately I so know so little I have no idea how where to start. What websites are helpful, what books I should buy, etc. I was hoping someone here could share. Thank you.