'I hope' is a wish. 'I expect' means that you are waiting for it to happen. I'm hoping to learn as much as possible' - you want it to but it might not happen. It is a wish. I'm expecting to learn as much as possible' - you don't see any other result. You are sure it will happen.

"Expect" suggests "I should receive this". "I hope" sounds wishful. :)

EXPECT= anticipate something HOPE= desire something

I hope...to want something to happen, you might be a bit disappointed if it doesn't happen I expect....you believe you deserve ( or you know/suspect) this to happen, you will not only be disappointed but quite irritated, if it does not happen. Hope this helps!!