OK, so scientific principles that I do not understand really annoy me. Higher maths (post-calculus), having seemingly little resemblance to any other sort of math, fall into this category for me so I have taken it upon myself to learn more. I have gotten about all I am going to get from the web (which wasn’t much) and am looking for a more detailed look into the subject.
So, first, what broad areas are out there? I need to know what I don’t know. I have a doctorate in engineering, so have a good understanding of everything up through and including calculus. Right now it looks like the next areas to explore would be Number Theory and Set Theory. What else am I missing?
What would be a good basic book[s] on the subject[s]? This looks like a lot of voodoo to me, so I need something that starts from the beginning, but have no fear of lots of equations or things getting technical quickly. I was thinking a college textbook might be good, but I would prefer not to spend a couple hundred dollars on one. My goal is to understand the ideas behind the field, be conversant in the underlying theories, and be capable of reading a current paper in the field without immediately throwing up my hands and giving up.
Also, let me know if my goals are unrealistic. Thanks.