A test has sensitivity and specificity ; the disease affects of people. You test positive. What is the chance you have it?
Interactive Explainers
Play with the theorems
Interactive explainers that let you move the mathematics: drag ε and watch δ answer, walk the topologist's sine curve, trap a subsequence by bisection, watch Newton's method fall into a cycle. 15 are free to play right here — the rest come with Trap Analysis.
Video explainers
Narrated walk-throughs of the trickiest ideas, made for this site — no ads, no recommendations pulling you elsewhere. Free to watch whether or not the interactive below is unlocked.
A set with no measure: the Vitali construction
Lebesgue Measure and Integration › Measurable sets and functions
Baire category, and the argument it powers
Unit 4Limit Theorems and Markov Chains › Modes of convergence, WLLN, SLLN, CLT#
Unit 4Hypothesis Testing › Neyman–Pearson lemma and UMP tests#
Unit 4Probability › Axioms, conditional probability, independence, Bayes#
Unit 4Probability › Standard discrete and continuous distributions#
Unlock every visual
Every interactive explainer comes with Trap Analysis — along with the worked solutions, the per-option trap diagnosis and the counterexample objects. The papers, the book and the video map are free without it.
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