Markov's Calculus of Probabilities: The Foundational 1900 Text on Probability Theory and Markov Chains — First Complete English Translation (Faithful ... (Russian Math Classics — English Editions)

Andrei Andreyevich Markov completed Calculus of Probabilities in 1900. This is its first complete English translation — and one of the founding texts of modern probability.

The mathematics inside it shaped the century that followed. The stochastic processes Markov formalised in the years around this edition — now called Markov chains — sit beneath Google's PageRank, hidden Markov models in speech recognition, reinforcement learning, and every autoregressive language model. In 1913 Markov turned his methods on language itself, counting the first 20,000 letters of Pushkin's Eugene Onegin by hand and computing the transition probabilities between vowels and consonants — the first statistical model of natural language ever recorded, and a direct ancestor of today's AI.

This Faithful Edition preserves Markov's original structure, section numbering, and notation, with the mathematics reset in clean, modern typography. Eight chapters build the calculus of probabilities as Markov built it, each result proved from first principles: the fundamental concepts and theorems; the addition and multiplication of probabilities; mathematical expectation; the law of large numbers; the method of least squares; and the classical limit theorems.

A rigorous, historically faithful edition of a landmark in the history of mathematics — and, through Markov chains, an intellectual cornerstone of modern machine learning. For historians of science, probabilists, students of stochastic processes, and collectors of the classics of Russian mathematics.

Part of Russian Math Classics — English Editions. Translated by Valery Manokhin, PhD (Royal Holloway, University of London). Published by Northern Star Academic Press. Full catalogue at russianmathbooks.com.