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The legendary Russian mathematics textbook, translated for the first time in its complete and unabridged form (preorder — early access)

The most successful algebra textbook in history — now in English for the first time.

In 1888, Russian schoolteacher A.P. Kiselev published Elementary Algebra. It became the standard in Russian schools — and stayed there for over 60 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 20th century — the same system 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

126 sections across 6 chapters:

Preliminary Concepts — Use of letters, algebraic expressions, operations, signs, order of operations, brackets. The properties of addition, subtraction, multiplication, and division — all stated as laws and proved from first principles.
Relative Numbers and Operations — Positive and negative numbers introduced through real-world problems (temperature, profit/loss, direction). Addition, subtraction, multiplication, and division of signed numbers — each operation derived from definitions with rigorous sign rules.
Monomials, Polynomials, and Algebraic Fractions — Addition, subtraction, multiplication, and division of algebraic expressions. Factorisation. The square and cube of a sum and difference. Algebraic fractions treated with the same rigour as arithmetic fractions.
First-Degree Equations — Properties of equalities. Equations with one, two, and three unknowns. Systems of equations solved by substitution and algebraic addition. Special cases and literal equations.
Extraction of Square Roots — Arithmetic and algebraic roots. Square roots of integers and fractions. Approximate roots to arbitrary precision.
Quadratic Equations — Normal form. Complete and incomplete quadratics. The quadratic formula derived, not memorised. Discriminant analysis and number of roots.

Plus a complete answer key to all exercises.

Who this is for

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 this edition

This is a faithful English translation of the definitive Kiselev Algebra Part I textbook.

Professional LaTeX typeset PDF. Print editions (paperback and hardcover) will follow on Amazon KDP.

This is an early-access preorder. You get the completed chapters now, and every subsequent chapter as it's completed. One purchase, full book included.

Translated by Valery Manokhin (PhD in Machine Learning, Royal Holloway, University of London; MBA, Warwick; MSc, UCL; CQF).

The numbers

Published: 1888
Sole official Soviet algebra textbook: 1938–1950s
Students educated: Tens of Millions
Properly translated into English: Never — until this edition
Sections: 126 across 6 chapters
Coverage: Preliminary concepts through quadratic equations

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