What classes do you have to take?

You can find this information by looking at any prospective school's webiste. Yes, you do have to take math and chemistry.

As far as science goes, typically nursing programs contain:

2 semesters of anatomy and physiology with lab

1 semester of chemistry with lab

1 semester of microbiology with lab

The math requirement varies by the school/program. Some require stats, some require calculus. If you intend on going on to graduate school stats is a must.

The nursing program itself will involve courses such as Pathophysiology, Pharmacology, Health Assessment, and then your nursing specialities: Med/surg, Psych, Pedi, Maternity, Community health. And on top of all that, you will have to fulfill your school's gen ed requirements. In my school (traditional 4 year university), those included: social sciences, cultural diversity, history, philosophy, theology, English and I'm sure something else that I am forgetting.

I suggest going to an information session at one of the schools you are considering applying to.

Ethics and computer competency here, in addition to those you listed.

State colleges in Florida require that if you did not take 2 years of a foreign language in high school, that you have to take something at the college level. I'm not sure if they include this under cultural diversity or not.

And don't forget all the clinical practicum classes. :)