Kiselev Algebra - Part II: The Classic Russian Mathematics Textbook - First Complete English Translation (Russian Math Classics — English Editions)

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 II 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.

Part II is the advanced volume. Where Part I covers the foundations, Part II develops the topics the rest of secondary algebra rests on: functions, the quadratic function, inequalities, powers with arbitrary real exponents, logarithms, progressions, complex numbers, the general theory of algebraic equations, the binomial theorem, and continued fractions.

What makes Part II different from every modern textbook:

Functions, built from the dependence of quantities — not from set theory. Chapter 2 introduces the function concept the way it actually arose in mathematics: as a way of describing how one quantity varies with another. The intuition comes first; the formal definition is added later when it has something to attach to.

The quadratic function, treated as a whole subject. Chapter 3 develops the parabola geometrically, completes the square, derives Vieta's formulae, and closes with a unified treatment of quadratic inequalities. The student leaves with the curve, the algebra, and the theory — not just a formula.

Powers and logarithms, derived in order. Kiselev does not present logarithms as inverse exponentials and stop there. He builds the power function for rational exponents, extends it to irrational exponents by a careful limit argument, and only then defines the logarithm as the exponent of a power.

Complex numbers, built geometrically. Chapter 9 introduces the imaginary unit through the geometry of the complex plane, not as a formal symbol. Operations — including extraction of roots via de Moivre's formula — are derived from the geometric representation. The cleanest path from real to complex that secondary algebra offers.

The Supplements — material no other school text covers. Beyond the twelve numbered chapters, Part II treats the equivalence of equations, the general theory of algebraic equations of higher degree, the resolvent of the cubic, and continued fractions. This is the bridge to university mathematics — material that disappeared from Western secondary curricula a century ago.

Twelve chapters plus Supplements and Answers, 187 sections, 43 figures. The complete second half of Kiselev's Elementary Algebra, in its first English edition. The translation preserves Kiselev's original section numbering, the structure of his exposition, and the precision of his prose.

Ideal for: homeschool families using a classical mathematics curriculum, teachers seeking a proof-based approach, advanced students preparing for higher mathematics or olympiads, undergraduates rebuilding their secondary algebra before tackling analysis, and anyone interested in the textbook tradition of the Russian school of mathematics.

Translated by Valery Manokhin, PhD (Royal Holloway, University of London), as part of russianmathbooks.com — a project producing English editions of classic Russian mathematics textbooks.

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.