Books

Kiselev's Arithmetic

by A. P. Kiselev

Ages 9–12 · Grades 3–6

The foundational arithmetic textbook used in Russian schools for over a century. 7 parts, 214 sections. Whole numbers through proportional quantities, with mathematical proofs for every operation.

Kiselev's Algebra I

by A. P. Kiselev

Ages 12–15 · Grades 6–8

6 chapters, 126 sections, 239 exercises. From relative numbers and polynomials through first-degree equations, powers, roots, and quadratics.

Kiselev's Algebra II

by A. P. Kiselev

Ages 14–17 · Grades 8–10

12 chapters plus Supplements, 187 sections. Functions, quadratic systems, inequalities, logarithms, progressions, complex numbers, the binomial theorem, and continued fractions.

Kiselev's Algebra Problems

by A. P. Kiselev

Ages 12–17 · Grades 6–10

The companion problem collection to Kiselev's Algebra. Hundreds of carefully sequenced problems and exercises that mirror the chapter structure of Algebra Part I and Part II — the same problem set Russian students worked through alongside Kiselev's algebra textbooks for over a century.

Kiselev's Planimetry

by A. P. Kiselev

Ages 12–16 · Grades 7–10

The first complete English translation of Kiselev's proof-based Euclidean geometry. 269 sections across 6 chapters: basic concepts, triangles, circles, similarity, regular polygons, and areas. PDF, paperback, and hardcover.

Kiselev's Stereometry

by A. P. Kiselev

Ages 14–17 · Grades 9–11

Kiselev's three-dimensional geometry text — the first complete English translation. Polyhedra, the five Platonic solids, cylinders, cones, the ball, and Cavalieri's principle.

Kiselev's Calculus

by A. P. Kiselev

Ages 16+ · Grades 10–12 · University intro

The first complete English translation of Kiselev's calculus — the final volume in his school course. Single-variable differential and integral calculus, proof-based, with classical applications to mechanics and physics. The bridge from Algebra II into the analysis tradition that produced Markov's probability theory.

Rachinsky's 1001 Problems

by S. A. Rachinsky

Mental arithmetic practice · Flexible level

1,001 carefully selected problems from the village schoolteacher whose students were depicted in Bogdanov-Belsky's famous 1895 painting "Mental Arithmetic."

Perelman's Entertaining Arithmetic

by Ya. I. Perelman

Recreational arithmetic · All levels

The classic of Russian popular mathematics. Puzzles, riddles, and curiosities that make arithmetic genuinely entertaining.

Markov: Probabilities

by Andrei A. Markov

University level

The foundational 1900 work on probability theory by the mathematician who gave us Markov chains. A modern annotated English translation.

Rybkin's Planimetry Problems

by N. A. Rybkin

Ages 12–16 · Grades 6–9

The companion problem collection to Kiselev's classical Russian geometry — now in English for the first time. Rybkin's Planimetry Problems is the set Russian students worked through alongside Kiselev's geometry textbook for over a century. Kiselev gives the definitions, theorems, and proofs; Rybkin gives the problems that turn those proofs into geometric intuition. 970 problems across 16 sections, organised chapter-by-chapter to mirror Kiselev's Planimetry — from preliminary concepts and lines through triangles, quadrilaterals, similar figures, the circle, regular polygons, and the measurement of areas. Worked solutions for the harder problems, hints for the rest.

Malinin & Burenin

by A. Malinin & K. Burenin

Applied arithmetic · Flexible level

A complete English translation of Malinin and Burenin's Imperial Russian arithmetic textbook. 11 chapters, 301 sections. Covers numeration, operations on whole numbers, divisibility, fractions, ratios, proportions, percentage, interest, and Diophantine problems.

Kiselev's Systematic Arithmetic

by A. P. Kiselev

Ages 9–13 · Grades 3–7

Kiselev's definitive systematic arithmetic — the expanded companion to his classic arithmetic textbook. 207 pages, 264 numbered articles across seven divisions: whole numbers; concrete (denominate) numbers and the metric system; divisibility, primes, and factorisation; common fractions; decimal fractions with limits and repeating decimals; ratio and proportion; and a full course of word problems on proportional quantities. Includes elementary treatments most textbooks leave out — Euclid's proof of the infinitude of primes and the concept of a limit used to prove that 0.999… equals 1.

Barsukov's Algebra

by A. N. Barsukov

Ages 12–15 · Grades 6–8

The Soviet school's standard algebra textbook — ten editions, roughly ten million copies. The first complete, faithful English translation of Barsukov's course, prepared from the original Russian and typeset to modern standards with source-exact section numbering. Twelve chapters, 130 numbered sections: from algebraic expressions and rational numbers through factoring, algebraic fractions, coordinates and graphs, systems of equations, the square root worked digit-by-digit, quadratic equations, and functions and graphs. Includes a full chapter on the slide rule — a subject once central to technical education, almost never found in a modern Western algebra text.

Berezanskaya's Arithmetic Problems

by E. S. Berezanskaya

Ages 9–13 · Grades 3–7

The iconic companion to Kiselev's Arithmetic — the problem collection Russian classrooms used side-by-side with Kiselev for over 70 years. 2,354 problems across eight chapters in the canonical order: numeration; the four operations on whole numbers; divisibility; common fractions; decimal fractions; ratio and proportion; percentages; and a concluding chapter of mixed problems drawing on everything before. Oral drills, written exercises, and word problems of real substance, sequenced from easy to demanding. The first complete, faithful English translation, with source-exact problem numbering.

Vereshchagin's Arithmetic Problems

by I. P. Vereshchagin

Ages 10–16 · Grades 4–10

The largest arithmetic problem collection of imperial Russia — 3,238 problems with the complete answer key, in English for the first time. Approved by the Ministry of Public Education for the Empire's secondary schools and teachers' seminaries, and separately for the girls' gymnasia of the Empress Maria department, it ran to eighteen editions. Three Parts and fifty-seven sections cover whole numbers and compound named numbers; divisibility; common and decimal fractions; the metric system; ratio and proportion; and the commercial rules — the rule of three, percentage, interest, discount, partnership and alligation. Vereshchagin insisted his data be real, so the problems run on railway timetables, the heights of Elbrus and Everest, the assay of the new silver ruble, and Eratosthenes measuring the earth between Syene and Alexandria. Translated from the seventh edition of 1891, with source-exact problem numbering.

Rachinsky Solutions

by Valery Manokhin

Mental arithmetic solutions · Flexible level

The essential companion to Rachinsky's 1001 Problems — every problem solved, every error corrected. Step-by-step arithmetic reasoning for all 1,001 problems in the 1899 collection, with 12 errata corrections to misprints in the original answer key (problems #188, #410, #454, #468, #519, #563, #705, #779, #796, #836, #889, #892 — independently verified). Includes a complete conversion table for pre-revolutionary Russian units (puds, funts, zolotniks, sazhens, arshins, vershoks, desyatinas, chetveriks). 257 pages, professionally typeset. Solutions organised by problem number to match the companion problem book exactly.

Aritmética (Español)

by A. P. Kiselev

The first faithful and complete Spanish translation of the classic Russian arithmetic textbook.