Learning

Modularity Theorem and Applications to Fermat's Last Theorem

Elliptic Curves over Q → Wiles's Proof of Fermat's Last Theorem

This path provides a systematic graduate-level introduction to the modularity theorem for elliptic curves over the rationals, covering the necessary background in elliptic curves, modular forms, Galois representations, and the proof of Fermat's Last Theorem. It emphasizes the logical dependencies and culminates in the statement and significance of the modularity theorem and its role in FLT.