I don't know much when it comes to computers,
But If I wanted to learn how to programm algorithms that perform symbolic calculations and other techniques used to solve or aid mathematical problems, and to be able to classify the efficiency of different types of algorithms in terms of different factors, what sub field of computer science should I study, and how would I start studying it?
So that I can gain these techniques. In addition, I would like to start studying some enumerative combinatorics, is there some way I could study them together or at the same time? In terms of my educational background, I am familiar with parts of elementary number theory, and know about arithmetic functions, I also have about a thorough high school education in calculus, and all proceeding k-12 math courses, but other then that, I don't have any technical skills, and have no experience when it comes to using computers.
I hope this is an appropriate question for this site, and I would greatly appreciate any advice.