Kiselev's Problems and Exercises in Elementary Algebra : Companion to Elements of Algebra - First Complete English Translation

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, the companion problem book is available as a complete English translation.

Originally published by Andrei Petrovich Kiselev in the late 1880s alongside his two-volume Elementary Algebra, the problem book served as the third stage of his pedagogy: concept, worked example, independent practice. Kiselev's textbooks became the standard algebra texts across the Russian Empire and, in A.N. Barsukov's 1938 reworking, the sole officially approved algebra textbooks for grades 6–10 of Soviet schools. They remained in continuous classroom use until the mid-1950s and have been in continuous print for nearly 140 years.

1273 problems, matched section by section to Kiselev's Elements of Algebra, covering the full sweep of secondary algebra from signed arithmetic to mathematical induction.

What makes this volume different from every modern problem book:

The eight parts mirror Kiselev's pedagogy exactly. Part I — relative numbers and signed arithmetic. Part II — monomials, polynomials, and algebraic fractions. Part III — equations of the first degree, single-variable and systems. Part IV — square and higher roots. Part V — quadratic equations, the discriminant, biquadratics. Part VI — arithmetic and geometric progressions, logarithms, compound interest. Part VII — permutations, combinations, and the binomial theorem. Part VIII — mathematical induction.

Faithful to the original. Problem wording, order, units, and numerical data are preserved exactly. No problem has been added, omitted, or rearranged. The 1–1273 numbering, essential to Kiselev's system of internal cross-references, is reproduced unchanged so this volume sits side by side with the textbook as Kiselev intended.

A graded problem set, not a drill book. Kiselev's problems progress from direct application of a concept, through systems and substitutions, to multi-step problems where the algebra is in service of a worded scenario. Part VIII closes the volume with mathematical induction — the bridge to higher mathematics.

Sixteen chapters, 1273 numbered problems. The complete companion problem book to Kiselev's Elementary Algebra, in its first English edition.

Ideal for: homeschool families using a classical mathematics curriculum, parents supplementing their children's algebra education, teachers seeking a proof-based problem source, advanced students preparing for higher mathematics or olympiads, and undergraduates rebuilding their secondary algebra before tackling analysis.

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.

The companion volumes — Kiselev's Arithmetic, Kiselev's Elementary Algebra Part I, and Kiselev's Elementary Algebra Part II — are available separately on Amazon.