/sci/ - Science & Math

How do I mature (mathematically)? As a self learner and mathlet.

Code monkey programmer here. I'm a brainlet, but I have started to really enjoy doing math in my freetime and especially basic proofs (worked through Hammack Book of Proof) started from scratch last year and I want to keep going at least until Analysis and Linear Algebra.

Can I go straight to Real Analysis without doing any Calculus first?

Any other tips or advice?

How do i derive the recurrence relation for the sequence a(n) = n! ??

i know a(n) = n*(a(n-1)), but i thought you're supposed to solve for a(n) - a(n-1) and use that result to create your recursive relation.

When i do that i end up with:
= n!-(n-1)!
= n(n-1)! - (n-1)!
= (n-1)*(n-1)!

I dont know how to make this be n*(n-1)!