I teach at an American research 1 university. I am planning a course on combinatorial topology for undergraduates whose background is:
- multivariable calculus
- linear algebra
- at least one proof course
In particular, I can't assume they have taken a class on analysis. I would like the course to carefully prove the classification of piecewise-linear surfaces with boundary. Can anyone recommend a textbook that accomplishes this?
Edit: "Topology Now!" is close to what I am looking for, but I would prefer something that builds surfaces out of triangles, in part to avoid having to talk about what it means to be locally euclidean.