How to prepare for first year university after college diploma? This will be my first year attending university after obtaining an advanced diploma from a local college. I will be going into first year Computer Science in September and graduated this year with a diploma for Computer Systems Technology.

I am concerned about the first year courses however. First year Computer Science requires Chemistry 1, Algebra 1, Calculus 1, Discrete Mathematics 1 as well as the comp sci courses. It's been 3 years since I've had to do any higher level math and chemistry and I'm not sure how I'll adapt to the different learning style and intensity of university.

How can I prepare myself for these courses and university over the summer?
It would be a good idea to Contact the professors of the courses.  Usually they are already assigned to the course before it is offered and something you can look up prior to the course starting.  They could give you a list of recommended reading/sites to visit or they may simply say you have nothing to worry about.

I too have switched between community colleges, public and private universities and I do understand your worry.  While the experience is subject to change based on the individual, I found there to be little I needed to do to change my study habits and achieve the desired grades between all 3 experiences.

Remember it is school where you LEARN.  You aren't expected to go in already being a calculus expert or a mad scientist.  These are the freshman/sophomore level courses where it is generally assumed little prior knowledge outside of the pre-req basics.  Of course some classes also go hard early to weed out students as well and force drop out.

The only other suggestion outside of contacting the school/teacher for materials 
 is seeing if you have the text book for the classes listed already.  From my days in college, usually the online forum for the class had a home page that listed off basic syllabus info such as teacher name and course materials needed. 
 If not you can always contact the school/call the uni book store to find out what the names of the books are for those specific classes.  You will generally be able to find text books on Amazon and will be significantly cheaper than the uni book store anyways.  Thumb through the chapters on your own leisure.  That way you can go through the book and write notes down on things that seem to be a struggle topic and do your own focused preparation.  Or you may go through all the books and see that you really were worrying for nothing!