Kiselev’s Algebra, Part II — A Complete English Translation

In 1888, Russian schoolteacher A.P. Kiselev published Elementary Algebra. It became the standard in Russian schools — and stayed there for over sixty years. In 1938, after revision by the methodist A.N. Barsukov, it was officially approved as the sole algebra textbook for grades 6–10 across the entire Soviet Union.

Governments changed. The math didn't. It was too good to replace.

Millions of students learned algebra from this book. It trained generations of the strongest mathematical thinkers of the twentieth century — the same educational tradition that produced Kolmogorov, Gelfand, and Perelman. Yet it has never been properly translated into English — until now.

Why Kiselev, not another textbook?

Most modern algebra textbooks teach procedures. Kiselev teaches understanding. Every concept builds on the previous one with zero hand-waving. Every rule is derived, not dictated. Every definition is precise. Even in elementary algebra, Kiselev includes proofs and derivations — because understanding why something works is more powerful than memorising that it works.

The structure: define → derive → apply → practise.

Modern textbooks skip the "derive" step. That's where the understanding lives.

What's inside

187 sections across 12 chapters:

Identical Transformations with Powers and Roots — Raising to a power, squaring a polynomial, the concept of irrational numbers, transformation of irrational expressions, and irrational equations. Radicals handled with full rigour.

Functions and Their Graphs — Functional dependence, direct and inverse proportionality, and the linear function. The idea of a function introduced properly, then made visible on the coordinate plane.

The Quadratic Function — Supplementary facts about quadratic equations, the graph of the quadratic function, and systems of second-degree equations.

Inequalities — First-degree inequalities, their properties, and their solution.

Progressions — Arithmetic progression, geometric progression, and infinite progressions, including the sum of an infinite geometric series.

Generalization of the Concept of Exponents — Integer exponents, fractional exponents, the concept of the irrational exponent, and the exponential function. Exponents extended step by step from whole numbers to the reals.

Logarithms — General properties of logarithms, properties of decimal logarithms, construction and use of tables, and exponential and logarithmic equations.

Investigation of Equations — Investigation of first-degree equations with one unknown, of a system of two first-degree equations with two unknowns, and of the quadratic equation.

Imaginary and Complex Numbers — The number system extended beyond the reals, with operations on complex numbers derived from definitions.

Some Information on Algebraic Equations — Divisibility of polynomials, the remainder theorem, and the structure of higher-degree equations.

Indeterminate Equations — Equations solved in integers.

Combinations and Newton's Binomial — Combinations, permutations, and the binomial theorem.

Plus a complete answer key to all exercises.

Who Is This Book For? (Audience / Reader Description)

• Parents who want their children to actually understand algebra — not just pass tests
• Homeschooling families looking for a rigorous, structured curriculum
• Math teachers tired of textbooks that teach tricks instead of thinking
• Adults rebuilding their mathematical foundations properly
• Anyone who believes math education should be about understanding, not memorisation

About the Translator

The original textbook was written by A.P. Kiselev. This English edition was translated and typeset by Valery Manokhin, who holds a PhD in Machine Learning from Royal Holloway, University of London (supervised by Professor Vladimir Vovk), an MBA from Warwick Business School, an MSc in Computational Statistics and Machine Learning from UCL, and the Certificate in Quantitative Finance (CQF). He is the author of multiple bestselling technical books and the creator of the Awesome Conformal Prediction repository on GitHub. This translation of Kiselev's Algebra is a labour of care: the goal is to make the finest algebra textbook ever written accessible to English-speaking students, parents, and teachers for the first time.

About This Edition (additional notes for the listing page)

This is a faithful English translation of the definitive Kiselev Algebra Part II textbook, professionally typeset in LaTeX. The complete book is included — all 12 chapters and the full answer key.

Print editions (paperback and hardcover) are also available on Amazon KDP.