What you'll learn

31 lessons in Diophantine Approximation

Uniform distribution mod 1Weyl's criterionWeyl's equidistribution theoremDiscrepancy: star and extremeKoksma–Hlawka inequalityErdős–Turán inequalityThe three-distance theoremBest approximation & semi-convergentsOstrowski numerationIrrationality measureRoth's theoremKhinchin's theorem (metric)Jarník–Besicovitch theoremSturmian wordsThe large sieveDirichlet's approximation theoremHurwitz's theorem & the golden ratioLiouville numbers & transcendenceContinued fractions & quadratic irrationalsThue's theorem & Thue equationsBadly approximable numbers & the Markov spectrumThe Schmidt subspace theoremTranscendence: Lindemann–Weierstrass & BakerMinkowski's geometry of numbersSimultaneous Diophantine approximationKhintchine's transference principleThe Littlewood conjectureSchmidt games & winning setsMahler's classification of transcendentalsDiophantine approximation on manifoldsGauss–Kuzmin & continued-fraction statistics

How Erudia teaches

Built to be understood — and remembered.

Every idea is taught with motivation and a worked example before the drills, and an FSRS spaced-repetition engine schedules each review for the day its model predicts you would forget it. A short placement check finds what you already know, so you start Diophantine Approximation exactly where it's useful.

Start Diophantine Approximation →

Related Discrete Mathematics subjects

Combinatorics Graph theory Boolean algebra & logic Order Theory Algebraic Number Theory Discrete Math