What level of mathematical understanding do I need in order to contribute or to understand the crypto behind bitcoin? My mathematical knowledge is up to CALC II (college level.) Is this enough mathematical maturity in order to understand the crypto in bitcoin or do I need more knowledge? If I do indeed need more knowledge than please point me to good books/resources to learn them. Thanks!
I'm no expert, but hopefully this answer helps a bit. In my opinion you only need about year 11 calculus and algebra to understand the basics of elliptic curves and modular arithmetic. You can learn everything you need to know by googling and watching youtube videos. Here are some resources:


a layman's guide to elliptic curves
a visual guide to secp256k1 i started (incomplete but still useful)
an introduction to modular math by the khan academy


and if you are familiar with python or keen to learn then pybitcointools has a native implementation of all elliptic curve functions used by bitcoin. once you are familiar with the math then this code will be very useful for verifying your results.