Why do homeworks ?

The only way to learn in this class (as is the case in general with math) is to

It is like learning to ski. You cannot learn much by just looking at someone do it. The only "fool-proof" way to learn is to try it out yourself, fall a few times and keep going at it. Some things in the course might seem like "magic" at first glance but remember that your instructor and TAs have had more practice than you. So do your homeworks diligently and try and work on problems other the ones assigned (the textbook is a good source for additional problems).