Tips for learning advanced math (or CS, physics etc.) while in HS? | Hacker News Reader

Tips for learning advanced math (or CS, physics etc.) while in HS?

10 pointsoctatoan5 comments

Someone on another thread said this:

>On the other hand, if you treat each page, each statement as something you have to completely internalize before moving onto the next page—including looking up all the prerequisite topics recursively on Wikipedia or in other texts—you might just end up teaching yourself up to college-level math while still in high school.

What other things would you recommend? And what things would you have made it a point to learn in HS if you could go back? What are some good sources for "the usual subjects"?

(Also, I'm okay with spending a lot of time on this. I already do math for a few hours every day, so it's not a problem.)

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If I were in high school, I would start studying sophomore level math: linear algebra, differential equations, probability, statistics. When you get to college and actually have to take these classes you can spend more time concentrate on more graduate level texts of these subjects or on upper level subjects like analysis or algebra. Graduate school math will rehash these same subjects more formally. The thing about internalizing every page is true for some subjects. For analysis you will be doing well to get through 100 pages in four months. Textbooks just introduce the theorems and corollaries. It takes a long time to understand the wide spread implications and applications of those theorems.

I would just get a few college level linear algebra, diff-eq, and probability textbooks and start reading/working through the content. If these are already subjects at your high school, get some books on real and complex analysis, abstract algebra, and PDE's.

(1) Be sure to ace your HS math!

(2) I found that Linear Algebra was really intuitive and very fun to actually learn.

(3) Probability and statistics is actually quite fun as well ..

Be sure to practice. There are NO stupid questions, only stupid people. If someone belittles you for asking a question, how stupid it may sound, he is a fucking dick. Put aside your ego and simply ask it - people are often more than willing to help you.

Definitely agree with recursive lookups. Just use mathworld.wolfram.com instead of Wikipedia, much more succinct and technical than Wikipedia tends to be. Even better if you can get access to Mathematica as they will occasionally cross reference articles with Mathematica features.

MOOCs arranged in a course catalog format. Gives you idea of order and which courses cover similar material https://www.coursebuffet.com/sub/math

Khan Academy for everything before calculus, and MIT Opencourseware for everything Above Calculus

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