Learning

Diophantine Approximation: From Continued Fractions to Roth's Theorem

Real Analysis Foundations → Applications of Roth's Theorem

A systematic graduate-level path through Diophantine approximation, starting with foundational real analysis and building up through continued fractions and metric theory to the Thue-Siegel-Roth theorem and its applications. The path emphasizes rigorous proofs, quantitative bounds, and the deep interplay between number theory and analysis.