Kiselev's Algebra, Part I: The Classic Russian Mathematics Textbook — First Complete English Translation (Kiselev's Mathematics (English Editions) 2)

For nearly 90 years, A.P. Kiselev's Elementary Algebra was the standard secondary-school algebra textbook in Russian and Soviet schools. Tens of millions of children — by a demographic estimate, around eighty million — learned algebra from its pages. Now, for the first time, Part I is available as a complete English translation.Originally published in 1888 by Andrei Petrovich Kiselev, the book became the standard algebra text across the Russian Empire and, in A.N. Barsukov's 1938 reworking, the sole officially approved algebra textbook for grades 6–10 of Soviet schools. It remained the only algebra textbook of Soviet education until the mid-1950s — one of the longest runs of any algebra textbook in history. Kiselev's Elementary Algebra has been in continuous print for nearly 140 years.What makes Kiselev's Algebra different from every modern textbook:The rules of signed arithmetic — derived, not stated. Where modern textbooks say "minus times minus is plus, memorise the sign chart," Kiselev sets up a physical problem (a train passing through the station of Bologoye) and works through all four sign cases one by one before generalising. Students don't memorise that (−)×(−) = (+). They see why it has to be.The theory of first-degree equations, in full. Chapter 4 doesn't just teach the reader "how to solve for x." It treats equivalent equations and extraneous roots, then develops systems with one, two, and three unknowns — including the methods of substitution and algebraic addition, with attention to indeterminacy. This is the kind of rigour modern algebra courses defer to college.Square roots, extracted by hand, to any accuracy. Chapter 5 doesn't just define the square root. It teaches the student to extract a root from any whole number, and then to any decimal accuracy required. This is craft mathematics — the kind that disappeared from Western textbooks when calculators arrived.The quadratic equation, treated whole. Chapter 6 derives the formula for the roots of ax² + bx + c, simplifies it for the case of even b, and treats the question of how many roots a quadratic equation has. The student leaves with the formula, the proof, and the theory of root count — not a memorised expression.Concepts are built from the ground up. Relative numbers are introduced through a careful treatment of quantities that can be understood in two opposite senses — debt and credit, distance to the right and left, time before and after a fixed instant. Algebraic fractions are then developed in parallel with polynomials, in their own right rather than as letter-substituted arithmetic.144 pages. Six chapters: preliminary concepts; relative numbers and operations on them; monomials, polynomials, and algebraic fractions; equations of the first degree; extraction of square roots; and quadratic equations. The complete first half of Kiselev's Elementary Algebra, in its first English edition.This translation preserves Kiselev's original section numbering, the structure of his exposition, and the precision of his prose. The typography is modern; the mathematics is Kiselev's.Ideal for: homeschool families using a classical or rigorous mathematics curriculum, parents supplementing their children's algebra education, teachers seeking a proof-based approach, advanced students preparing for higher mathematics, adults rebuilding their mathematical foundations, and anyone interested in the textbook tradition of the Russian school of mathematics.Translated by Valery Manokhin, PhD (Royal Holloway, University of London) — independent machine learning researcher and publisher of English editions of classic Russian mathematics textbooks.The companion volume — Kiselev's Arithmetic — is available separately on Amazon. Read more