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Kiselev's Arithmetic
A Rigorous, Student-Friendly Approach to Arithmetic That Builds Real Mathematical Thinking
This book is 100% completeLast updated on 2026-03-05
Most people think they are bad at math. In reality, they were never taught arithmetic properly.
This book is a modern English edition of Arithmetic by Alexander P. Kiselev—the text that formed the backbone of mathematical education in Russia and USSR for over a century and helped produce generations of exceptionally strong mathematicians, scientists, and engineers.
Unlike modern textbooks that prioritise shortcuts, visuals, and lowered expectations, Kiselev builds arithmetic logically, systematically, and rigorously. Every method is explained. Every operation has meaning. Exercises are carefully sequenced to develop real understanding—not rote pattern-following.
This book does not promise “easy math”. It promises something better: clarity, confidence, and competence.
Whether you are a student, a parent, a tutor, or an adult rebuilding fundamentals, this book will change how you understand arithmetic—and why so much later mathematics suddenly becomes easier.
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About
About the Book
Kiselev’s Arithmetic trained generations of strong mathematicians by doing something modern textbooks increasingly avoid: it teaches you to think, not to memorize.
This edition is a carefully edited English translation and adaptation of Alexander P. Kiselev’s classic Arithmetic, written to be clear for today’s readers while preserving the book’s original strengths: logical structure, disciplined reasoning, and genuinely graduated practice.
Kiselev doesn’t rely on gimmicks, cartoons, or “feel-good” shortcuts. Instead, it builds mathematical understanding the way it should be built: step by step, with definitions, methods, and problems that reinforce real mastery.
What Makes This Edition Different- Student-friendly English, not diluted math
The language is modern and readable, but the reasoning remains precise. - Concepts first, procedures second
You learn what operations mean and why methods work—not just what buttons to press. - Built for real arithmetic competence
This is arithmetic as a foundation for algebra, problem solving, and later olympiad-style thinking—not arithmetic as rote computation.
This book is designed for:
- Students who want to become strong at math (not just “get by”)
- Parents and tutors who want a rigorous, coherent curriculum
- Adults rebuilding fundamentals properly (including engineers and data scientists)
- Anyone frustrated by modern materials that lower expectations and hide the logic
You will develop:
- numerical intuition and mental calculation ability
- correct written computation methods (that you can explain, not copy)
- fluency with fractions, ratios, and proportional reasoning
- disciplined reasoning through structured examples and exercises
- a foundation that makes algebra and later mathematics dramatically easier
Most math difficulties later in life come from weak arithmetic foundations: shaky fractions, unclear place value, and procedures learned without understanding.
Kiselev fixes this at the source.
It treats the reader as capable, and it rewards effort with genuine competence.
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Author
About the Author
Valery Manokhin
Valery Manokhin (PhD, MBA, CQF) is a data scienstist, machine learning researcher and book author. He earned his PhD in ML at Royal Holloway, University of London, under Prof. Vladimir Vovk, the creator of Conformal Prediction, and holds an MBA from Warwick and an MSc in Computational Statistics & Machine Learning from UCL.
His technical books — Mastering Modern Time Series Forecasting and Applied Conformal Prediction among them — are used by data scientists, ML engineers, and researchers in over 100+ countries.
In parallel, he produces English editions of classic Russian mathematics textbooks, beginning with Kiselev’s Arithmetic and now Algebra, Part I. The aim is straightforward: give English-speaking students access to the books that shaped generations of Russian mathematicians, in editions that match the originals’ rigour.
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