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Markov Chains Explained Visually

by Victor Powell, Lewis Lehe · Setosa (Explained Visually)

Interactive explainer that animates states hopping between nodes, then builds the transition matrix from those diagrams. Readers can edit the matrix and watch how a chain's long-run behavior changes. It works as a short, intuition-first first exposure before formal treatment.

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probabilitycourse.com

ProbabilityCourse.com is an online learning resource that provides a structured probability course with clear explanations, worked examples, and practice problems covering topics from basics to advanced theory.

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Wolfram MathWorld

MathWorld is an online mathematics encyclopedia from Wolfram Research offering detailed, browsable articles on topics across the math spectrum, including algebra, geometry, calculus, and number theory. Each entry includes definitions, theorems, formulas, diagrams, worked examples, and links to further reading.

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Markov Chains

Rigorous yet compact treatment of discrete- and continuous-time Markov chains: hitting times, recurrence, invariant distributions, ergodic theorem, queues, Poisson processes, and applications to Markov chain Monte Carlo. Standard text for Cambridge's undergraduate course.

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Markov Chains (Cambridge Part IB Course Notes)

Course page for a 12-lecture Cambridge second-year course: full lecture notes, two example sheets, and a lecture blog. It covers hitting probabilities, the strong Markov property, recurrence and transience, invariant distributions, convergence to equilibrium, and time reversal.

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Lecture 31: Markov Chains (Statistics 110)

Harvard Stat 110 lecture that defines the Markov property, transition matrices, and n-step probabilities via matrix powers, then introduces stationary distributions. Lectures 32 and 33 continue with irreducibility, recurrence, reversibility, and random walks on graphs.

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Introduction to Probability Models

Standard applied probability textbook moving from conditional expectation to Markov chains, Poisson processes, continuous-time chains, renewal theory, queueing, reliability and simulation. Its many worked examples and exercises teach readers to build and analyse stochastic models of real systems.

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