Don't get excited, I'm not looking for answers to my homework. I am a simple plebeian with a humble request.

What specific search should I do to figure out how to learn about these problems?

i know this is the most ass-backwards way of doing things, but I simply do not currently have the luxury of other paths.

If I knew the name/subtree of Algebra for these specific problems, then I can learn it them and solve them on my own.

Much appreciated for any direction.