Kiselev's Systematic Course of Arithmetic
by A. P. Kiselev
Translated by Valery Manokhin, PhD
Kiselev's definitive systematic arithmetic — the expanded companion to his classic arithmetic textbook. 207 pages, 264 numbered articles across seven divisions: whole numbers; concrete (denominate) numbers and the metric system; divisibility, primes, and factorisation; common fractions; decimal fractions with limits and repeating decimals; ratio and proportion; and a full course of word problems on proportional quantities. Includes elementary treatments most textbooks leave out — Euclid's proof of the infinitude of primes and the concept of a limit used to prove that 0.999… equals 1.
🇺🇸 Grades 3–7 (arithmetic with elementary proof)
🇬🇧 KS2–KS3 (Years 4–8)
🇨🇦 Grades 3–7
Adults and self-learners welcome — great mathematics has no age limit.
Table of contents
11 chapters, 37 sections — the full contents of the printed book.
Translator's Preface
Abstract Whole Numbers9 sections
- Numeration
- Addition
- Subtraction
- Slavic and Roman Numeration
- Change of sum and remainder
- Signs of the operations, parentheses, formulas
- Multiplication
- Division
- Change in the Product and the Quotient
Concrete Whole Numbers4 sections
- The Concept of Measuring Quantities
- Transformation of a concrete number
- Operations on concrete numbers
- Problems on the calculation of time
Divisibility of Numbers5 sections
- Tests of divisibility
- Prime and Composite Numbers
- On the divisors of a composite number
- Greatest common divisor
- Least Common Multiple
Common Fractions5 sections
- Reduction of Fractions
- Reduction of fractions to the least common denominator
- Finding a Fraction of a Given Number and the Reverse Problem
- Operations on Abstract Fractions
- Operations on concrete fractions
Decimal Fractions5 sections
- Principal properties of decimal
- Operations on Decimal Fractions
- Conversion of common fractions into decimals
- Conversion of repeating decimals into common fractions
- Metric System of Measures
Ratio and Proportion2 sections
- Ratio
- Proportion
Problems on Proportional Quantities7 sections
- The simple rule of three
- Compound rule of three
- Problems on Percentages
- Problems on the discounting of bills
- Chain Rule
- Problems on proportional division
- Problems on mixtures and alloys
Appendix: Approximate Calculations
Table of Prime Numbers Not Exceeding 6000
Appendix: Russian Units of Measure
Formats and editions
| Format | Price | ISBN-13 | Where | Buy |
|---|---|---|---|---|
| $49.95 | — | Gumroad · Instant download | Buy → | |
| Paperback | $54.95 | 978-1-919012-07-0 | Amazon | Buy → |
| Hardcover | $84.95 | 978-1-919012-08-7 | Amazon | Buy → |
Prices are the publisher list prices. Amazon sets the final price in each store.
Product details
- Publisher
- Northern Star Academic Press
- Language
- English
- Translator
- Valery Manokhin, PhD
- Print length
- 207 pages
- First published
- 2026-07-14
Published by Northern Star Academic Press · First faithful English translation from the original Russian edition
More in This Series
Kiselev's Arithmetic
by A. P. Kiselev
Ages 9–12 · Grades 3–6
The foundational arithmetic textbook used in Russian schools for over a century. 7 parts, 214 sections. Whole numbers through proportional quantities, with mathematical proofs for every operation.
Kiselev's Algebra I
by A. P. Kiselev
Ages 12–15 · Grades 6–8
6 chapters, 126 sections, 239 exercises. From relative numbers and polynomials through first-degree equations, powers, roots, and quadratics.
Kiselev's Algebra II
by A. P. Kiselev
Ages 14–17 · Grades 8–10
12 chapters plus Supplements, 187 sections. Functions, quadratic systems, inequalities, logarithms, progressions, complex numbers, the binomial theorem, and continued fractions.