Apologies for a soft question. I do not have a lot of time because of my job (programmer) and my wife cannot work so I cannot quit. I also did not graduate from a very prestigious school with good grades. So grad school is out of the question for me.
I am 23 years old, I find that because I did not learn many topics well when I was younger, I have accumulated a lot of half baked knowledge about stuff. For example, I can spell out some theorems, results in fancy notation, but I don't really understand those things. So when I try to restart and re-educate myself I find that I have to unlearn a lot of gibberish that I put in my head just to pass through examinations.
I visited this site and saw some solutions people posted. I was so exhilerated after getting some of them that I wish I had the same understanding as the person who could think of such solutions. So in my private time, I have embarked on a project to learn math from scratch. I do not aspire to make meaningful contributions, because of the late start, but to discover mathematics and get some personal peace.
Before beginning, I decided that I am most interested in stuff like graph theory, and perhaps I would like to explore geometry as well (algebraic, differential)
So I planned a halfway route and here is my question... what is your advise for a person like me to learn mathematics and reach his goal (with literature recommendations possibly online)
- Start from basics, do good problems in pre-calculus algebra (inequalities, permutations, combinations, sequences and series etc?) to get some mathematical thinking
- Calculus from Rudin, to get rid of most of the algorithmic procedures in my minds (is this too tough for me)
- Where do I go from here? Follow some college's standard curriculum? Is there a curriculum for undergrads designed to specialize in graph theory/topology?