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How do I prepare for abstract/proof-based math courses?

So ummm... long story short, I'm going into my second year at uni and have declared a joint major in neuroscience and mathematics. My first year was fairly doable, mostly general sciences and the most 'difficult' math I've had so far was calc 3. That being said, I have a whopping five math courses next year, including some pretty proof-y courses (namely analysis 1-2). I don't mind a bit of a challenge but I have been warned(repeatedly) about the upper-year math courses at my uni and I want to know whether my study methods will need to change? Until now, solving lots and lots of problems has been sufficient; will I need to start memorizing theorems, find people to work with etc? Most of my friends are pure bio students who genuinely think I am torturing myself for no reason, so any advice from other math students would be much appreciated :)

submitted by /u/msg2000
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from math http://bit.ly/2KeysWf
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