FIT2.3.2. Cardinality and Transcendentals

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Field Theory: We show that the set of algebraic numbers is countable and that any extension of a countable field F by a transcendental is countable. We then give an overview of known results on transcendental numbers.
  1. MathDoctorBob
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Автор

This is quite advanced stuff.. In my graduate algebra course these topics were not covered. Awesome!

cpaniaguam
Автор

Could you please tell me some references which might contain proofs of those results in your video and some other basic stuffs in field theory? I am using the "Abstract Algebra" by Dummit and Foote but that one does not contain that much content in field theory.

tianyizhou
Автор

Thanks! Of course, I'm not doing many proofs in this part.

MathDoctorBob