One of the best things I ever did was spend a month learning calculus several months before I started the course. When the course started, I was always on top of things, unlike my compatriots. As a result, I had considerably more free time than they did, at a point when free time was an expensive thing.
I would echo TALewis and Cod in saying "go for it". But don't sweat it if you run into stuff that leaves you reeling. Just move on to the next subject and let that wait till the course starts. At that time you will have had the chance to "grok" the easier stuff, which will make it easier to figure out the harder stuff when the course comes to it.