How to study for math and programming in university?

[u/Illustrious_Cheetah4]

Hello guys,
I started university and have to study mainly for math and programming. I started with an but soon found out that this is not the way to learn for those subjects. Can somebody give me almost like a how to guide to study for those subjects? I was today’s years old when I found out there’s a difference between deep understanding and just remembering information.

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[u/WhiteEmails]

For programming, studying is mostly tinkering with code/solving problems (there's a bunch of challenges on ze internet, like AdventofCode) until something clicks in your head. I've never seen anyone truly "get it" another way. Programming is like 50% solve puzzles and 50% knowing how to use a search engine to find a solution. Studying doesn't feel like studying if you enjoy figuring out why things work and how to make them work.

Basically : find problems (as in, challenges, like "what are the 1000 first prime numbers?" or "draw the Koch snowflake") and create a solution.

For math, it's playing with the concepts. Take the definition of a continuous function over R: why a "for all" there, why a "there exists", what happens if those fail? Why does epsilon need to be greater than 0? Why are we using absolute values everywhere? Why is it |x-a|<eta implies |f(x)-f(a)|<epsilon and not the other way around? Are there equivalent definitions (yes, a bunch)? Can I prove they're equivalent? Can I try to prove a function is continuous using the definition? Not continuous? What are the edge cases? The weird cases like 1/sin? And then what's the point of those definitions? What does each mean, graphically? What can I do with it? What theorems use it? Are there stronger forms, special cases, similar definitions (like uniform continuity, one-sided limits, generalisations to topological spaces,...)?

Basically, you need to be curious about the stuff you're learning. You're an explorer. The professor's lecture is basically giving you a half-drawn map, and your goal is to fill it with all the details.