Kiselev's Algebra, Part I — A Complete English Translation

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.

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.

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.

• 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

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).

• 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