Manifolds
About 6 months ago, I got an e-mail from Zev, now a senior at Lawrenceville (my High School). He had finished the math courses that L'ville could offer, and was wondering what he should do for an independent study. I recommended working through Rudin or Herstein, but he said that he'd already finished Rudin and done basic group/ring/field theory. Um... ok, try complex analysis! Or topology!
Well, I just got another e-mail from him. He seems to now be done with Alfohrs and Munkres too, and has no clue what to do next. I suggested Manifolds or Algebraic Topology, but I realized that I don't know of any good manifolds texts. Munkres manifolds text is used for the course at UChicago, but the text has gotten terrible reviews. Thus, I ask... does anyone know of a good manifolds text appropriate for self-study. Alternately, does anyone know of a better topic than manifolds for a ridiculously strong high school math student?
Well, I just got another e-mail from him. He seems to now be done with Alfohrs and Munkres too, and has no clue what to do next. I suggested Manifolds or Algebraic Topology, but I realized that I don't know of any good manifolds texts. Munkres manifolds text is used for the course at UChicago, but the text has gotten terrible reviews. Thus, I ask... does anyone know of a good manifolds text appropriate for self-study. Alternately, does anyone know of a better topic than manifolds for a ridiculously strong high school math student?