a) A proof of Gödel’s incompleteness theorem: computability and the theory of recursive functions, proof of the incompleteness theorem with an analysis of its consequences.
b) Mathematical proofs and formal proofs. Introduction to proof-theory. Gentzen’s natural deduction and the sequent calculus. The normalization theorem and the cut-elimination theorem.
c) Foundations revisited and analysis of the relevance for the teaching of mathematics.