A degree in computer science isn't required, just a basic understanding of how computers, operating systems, and applications work and interact, logic, binary numbers, a little electronics, and some common sense. The most important traits of a new system administrator are the abilities to find and digest information, solve problems, develop creative strategies, and recognize and work within one's own limits. System administrators who have formal education and a degree tend to be preferred and sometimes required for jobs. However, that's not necessarily because the education is particularly relevant to the job, it's more because it is evidence of follow through and perseverance. Many practicing system administrators hold degrees in technical fields other than computer science, such as physics.
System administrators solve problems daily.
Sysadmins are usually working on production systems, because it is expensive to duplicate a system purely for the system administrator's benefit. There is no widely accepted formal curriculum for system administration. Unfortunately you can't go to the local university and sign up for a degree program in system administration. Nonetheless, universities are starting to develop system-administration curricula. The number of books on system administration increases all the time.