My friend Yunzhe Li and I are currently writing a short no-nonsense course starting with essentially no required knowledge and culminating in the rigorous proof of one of the greatest ideas mathematics has ever produced: there cannot be a sensible notion of truth if we allow non-computable/constructive mathematics. The text (under construction), goes through Godel and Chaitin’s incompleteness theorems and shows the decidability/undecidability of theories of arithmetic (among other things).
Notes: Still under construction!
Exercices: