How well reals are approximated by rationals: equidistribution, discrepancy, the three-gap theorem, and the metric theory.
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Every idea is taught with motivation and a worked example before the drills, and an FSRS spaced-repetition engine schedules each review for the moment just before you'd forget it. A short placement check finds what you already know, so you start Diophantine Approximation exactly where it's useful.