For a very long time I have wanted to derive the class number formula, and recently I was able to wrap my head around the formula in the case of an imaginary quadratic field. Now I want to see if I can wrap my head around the proof for the formula in a general field. The parts of a field I want to understand are:
- Embeddings (real and complex)
- Discriminant of a field
If you were to describe these in the simplest terms possible how would you? (I'm only a junior in high school, so trying to teach myself these concepts is really difficult when the only resources available to me are from colleges/Wikipedia. At the moment, I don't care about how "formal" my understanding is, I just want to be able to understand what these terms "show" about a field. ) Any examples would help a lot too, especially in an imaginary quadratic field as I am most comfortable with that. I would really appreciate any help, thanks.