Kiselev's Elementary Algebra
by A. P. Kiselev
Translated by Valery Manokhin, PhD
The single-volume algebra course, covering in one book essentially what Algebra Part I and Part II cover between them. Concepts arrive in a deliberate order, rules are tied to the operations that justify them, and proof is treated as part of elementary education rather than an ornament. Keeps hand extraction of cube roots, indeterminate multipliers and compound interest; omits the functions-and-graphs material of the two-part course.
🇺🇸 Grades 6–10 (Pre-Algebra through Algebra II)
🇬🇧 Key Stage 3 through GCSE Higher
🇨🇦 Grades 6–10, Ontario
Adults and self-learners welcome — great mathematics has no age limit.
Table of contents
62 chapters, 17 sections — the full contents of the printed book.
Translator's Note
Section I. Preliminary Concepts
1. Algebraic Sign Notation
2. Principal Properties of the First Four Operations
3. Monomial and Polynomial
4. Reduction of Like Terms
Section II. The First Four Algebraic Operations
1. Algebraic Addition and Subtraction
2. Negative Number and Zero
3. Algebraic Multiplication
4. Multiplication of Negative Numbers
5. Multiplication of Arranged Polynomials
6. Special Cases of Multiplying Binomials
7. Algebraic Division
8. Some Cases of Division of Polynomials
9. Factoring Polynomials
10. Algebraic Fractions
11. Negative Exponents
12. Ratio and Proportion
Section III. First-degree Equations
1. General Principles for Solving Equations
2. Equations Containing Unknowns in Denominators
3. Equation with One Unknown
4. Two Equations with Two Unknowns
5. Three Equations with Three Unknowns
6. Equations with Many Unknowns
7. Special Cases of Systems of Equations
8. Method of Indeterminate Multipliers
9. Indeterminate, Inconsistent, and Conditional Equations
10. Investigation of First-degree Equations2 sections
- One Equation with One Unknown
- System of Two Equations with Two Unknowns
Section IV. Powers and Roots
1. Raising Monomials to a Power
2. Squaring Polynomials
3. Extracting a Root from a Monomial
4. Extracting the Square Root of the Greatest Whole Square Contained in a Given Number3 sections
- Extracting Approximate Square Roots
- Extracting Square Roots of Fractions
- Extracting the Square Root of a Polynomial
5. Extracting the Cube Root of the Greatest Whole Cube Contained in a Given Number2 sections
- Extracting Approximate Cube Roots
- Extracting Cube Roots of Fractions
6. The Notion of an Incommensurable Number
7. Operations with Radicals
Section V. Equations of Degree Higher than the First
1. Quadratic Equation
2. Some Special Cases of Quadratic Equations
3. Investigation of the Quadratic Equation
4. Complex Numbers
5. Freeing an Equation from Radicals
6. Higher-degree Equations Reducible to Quadratic Equations or to First-degree Equations
7. Some Remarks on Algebraic Equations
8. System of Second-degree Equations
Section VI. Inequalities and Indeterminate Equations
1. Inequalities
2. Indeterminate First-degree Equation with Two Unknowns
3. Two First-degree Equations with Three Unknowns
Section VII. Generalization of the Notion of Exponents1 section
- Fractional Exponents
Section VIII. Progressions and Logarithms
1. Progressions3 sections
- Arithmetic Progression
- Geometric Progression
- Infinite Geometric Progression
2. Logarithms6 sections
- Preliminary Concepts
- Logarithm of a Product, Quotient, Power, and Root
- Common Logarithms
- Construction and Use of Tables
- Exponential and Logarithmic Equations
- Compound Interest, Term Payments, and Periodic Instalments
Section IX. Additions
1. Combinations
2. Newton's Binomial
3. One Application of Newton's Binomial
4. Continued Fractions
5. Some Applications of Continued Fractions
6. Greatest and Least Value of a Quadratic Trinomial
How this book fits
See the whole sequence →Work through first
- Kiselev's Arithmetic$44.95
Covers the same ground
- Kiselev's Algebra II$54.95
- Kiselev's Algebra I$44.95
Pick one of these, not both.
Problems to work alongside it
What comes next
- Elementary Geometry$69.95
- Rashevsky's Trigonometry$39.95
Formats and editions
| Format | Price | ISBN-13 | Where | Buy |
|---|---|---|---|---|
| Paperback | $69.95 | 978-1-919012-68-1 | Amazon | Buy → |
| Hardcover | $109.95 | 978-1-919012-69-8 | 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
- 292 pages
- First published
- 2026-09-08
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.