Reddit reviews How to Solve It: A New Aspect of Mathematical Method
We found 5 Reddit comments about How to Solve It: A New Aspect of Mathematical Method. Here are the top ones, ranked by their Reddit score.
What you're probably looking for is a book on foundations, like logic or set theory. The thing is though that such books often do assume a certain level of mathematical maturity and experience with proofs. In addition, while the main results should be self-contained, the examples and exercises may make use of things that are supposed to be familiar but which you haven't learned due to your background (or lack thereof).
My advice is to be patient and focus on really learning the elementary topics, up to and including the standard calculus sequence. After that things really start to open up and you can usually find quality undergraduate-level books on just about anything that interests you.
But it probably isn't too soon to pick up a book on writing proofs and proof techniques. The one I used when I was younger was Peter Eccles' An Introduction to Mathematical Reasoning. I often hear Polya's How to Solve It recommended as well. I'm not sure how similar these are to the AoPS series though.
Anyway, good luck! Stick with it, mathematics is very worth it.
Here's my radical idea that might feel over-the-top and some here might disagree but I feel strongly about it:
In order to be a grad student in any 'mathematical science', it's highly recommended (by me) that you have the mathematical maturity of a graduated math major. That also means you have to think of yourself as two people, a mathematician, and a mathematical-scientist (machine-learner in your case).
AFAICT, your weekends, winter break and next summer are jam-packed if you prefer self-study. Or if you prefer classes then you get things done in fall, and spring.
Step 0 (prereqs): You should be comfortable with high-school math, plus calculus. Keep a calculus text handy (Stewart, old edition okay, or Thomas-Finney 9th edition) and read it, and solve some problem sets, if you need to review.
Step 0b: when you're doing this, forget about machine learning, and don't rush through this stuff. If you get stuck, seek help/discussion instead of moving on (I mean move on, attempt other problems, but don't forget to get unstuck). As a reminder, math is learnt by doing, not just reading. Resources:
math on irc.freenode.net
Here are two possible routes, one minimal, one less-minimal:
Minimal
Less-minimal:
NOTE: this is pure math. I'm not aware of what additional material you'd need for machine-learning/statistical math. Therefore I'd suggest to skip the less-minimal route.
You will likely get a lot out of How to Solve It. It teaches you how to break down problems and how to structure your thinking.
For the math itself, your examples are all covered by pre-algebra and algebra 1 (algebra is a pretty broadly defined area of math, but you want the beginner algebra books that most students would start in 8th-10th grade). I don't have specific book recommendations for that level of math, but taking the Khan Academy classes that the other poster linked would likely be a good start.
I'm not sure if you are looking for recommendations regarding more pop-math reading or actual textbooks, so I will try and recommend both.
That's probably a really wide variety of resources, so my recommendation is to pick one and see how you like the material! I'm sure if you are really ambitious, you can try working through a topic with guidance from one of your teachers and maybe even work on some sort of project with them.
It's also worth joining - or starting - a math club at your school. And if you are still looking for other activities, look into local math competitions that you can participate in.
Polya tried to answer your question:
How to Solve it