> For graph colouring I think the right WP link
> is Ramsey theory.
That turns out not to be the case: Ramsey theory is an area of Graph Theory that overlaps with, but neither subsumes, nor is subsumed by, questions related to coloring graphs.
> Also not sure graphs are a "branch" of mathematics, ...
It may be the case that you are unsure, but my PhD is in Graph Theory, specifically, and I can assume you that it is a recognized area of mathematics.
> I see graphs as just a common object that relates
> to a variety of mathematical areas.
Similarly groups, topological spaces, sets, etc. Math is built on abstraction - the idea is to find commonality, extract it, then study it in its own right. Then anything you prove there applies to everything it came from. Graph Theory is like that, and it is its own subject within math.
Hmmm... Sets, Groups, Topology, Algebraic Structures... Sounds alot like the Bourbaki "Mother Structure's".
Sets and Algebra, I can teach as a homeschool dad. Group theory, topology, and abstract algebra are to difficult for me.
I don't think this is intrinsic. Lots of Rosen is hard for me.I suspect Smaullyan's math logic book coming out this Summer will be transparent(Euler diagrams alone make it clearer). Likewise, lots of Stewarts Calc is obscure. Yet, strangely Spivak's Calc is clear and simple. I suspect there are similar resources for abstract algebra and topology.. I assume that I will have worked through baby Rudin before DS finishes highschool... however, there must be a more direct, less abstract path.
