Kiselev's Elements of Algebra and Analysis, Part One
by A. P. Kiselev
Translated by Valery Manokhin, PhD
Part One builds a connected foundation: algebraic notation and operations, signed numbers, identities, equations and inequalities, polynomials, fractions, ratio and proportion, functions, coordinates and graphs, powers, roots and irrational numbers, progressions, logarithms with four-figure tables, compound interest and the binomial theorem. A distinct work from the 1888 Elementary Algebra.
· 313 pages
Where this fits in school — US, UK and Canada ↓ Adults and self-learners welcome — great mathematics has no age limit.
Where this fits in school
Full curriculum table — every book by school year →| United States | 8–11 | Algebra 1 and Algebra 2 in one volume |
|---|---|---|
| United Kingdom | Years 9–12 | GCSE Foundation and Higher → AS Pure |
| Canada | Ontario 9–11 | MTH1W → MPM2D → MCR3U |
Not covered in this book
graphs of the trigonometric functions and radian measure · statistics and data handling · probability
Source these strands elsewhere. They are missing from the book, not from this description.
How this book fits
See the whole sequence →Work through first
- Kiselev's Arithmetic$44.95
Covers much of the same ground
- Kiselev's Algebra I$44.95
These overlap heavily. Each note says what that book has which this one does not — the differences are what decide between them.
Problems to work alongside it
- Barsukov's Algebra$54.95
What comes next
Table of contents
55 section headings — the printed contents page in full.
Translator's Preface
Preliminary Concepts4 sections
- Algebraic Notation
- Properties of the First Four Arithmetic Operations
- Positive and Negative Numbers (Relative Numbers)
- The Concept of an Equation
Identical Transformations8 sections
- Polynomial and Monomial
- Algebraic Addition and Subtraction
- Algebraic Multiplication
- Algebraic Division
- Factorization
- Algebraic Fractions
- Ratio and Proportion
- Direct and Inverse Proportional Dependence
Graphical Representation of Functions3 sections
- The Concept of Function and Coordinates
- Graphs of Direct and Inverse Proportionality
- Graph of a First-Degree Binomial
Additional Information About Equations. Inequalities3 sections
- The Two Fundamental Properties of an Equation
- Positive, Negative, Zero, and Other Solutions
- First-Degree Inequalities
Systems of First-Degree Equations3 sections
- Two Equations with Two Unknowns
- Three Equations with Three Unknowns
- Special Cases of Systems of Equations
Powers and Roots6 sections
- Squaring Monomial Algebraic Expressions
- Squaring a Polynomial
- Graphs of y=x^2 and y=ax^2
- Raising Monomials to the Cube and Higher Powers
- Graphs of y=x^3 and y=ax^3
- Fundamental Properties of Extracting a Root
Extraction of the Square Root of Numbers3 sections
- Extraction of the Greatest Integer Square Root from a Given Integer
- Approximate Square Roots
- Graph of the Function y= x
Operations on Irrational Numbers and Expressions4 sections
- The Concept of an Irrational Number
- Irrational Values of Radicals
- Approximate Calculations
- Transformation of Irrational Expressions
Some Equations of Degree Higher Than the First5 sections
- Quadratic Equations
- The Quadratic Trinomial and Its Graph
- Biquadratic and Related Equations
- Irrational Equations
- Systems of Second-Degree Equations
Progressions3 sections
- Arithmetic Progression
- Geometric Progression
- Infinite Progressions
Generalization of the Concept of Exponents5 sections
- Integer Exponents
- Fractional Exponents
- Properties of Powers with Rational Exponents
- The Concept of an Irrational Exponent
- The Exponential Function
Logarithms5 sections
- General Properties of Logarithms
- Properties of Common Logarithms
- Construction and Use of Four-Digit Tables
- Exponential and Logarithmic Equations
- Compound Interest, Annuities, and Periodic Payments
Combinations and the Newton Binomial3 sections
- Combinations
- Newton's Binomial
- Applications of Newton's Binomial
Formats and editions
| Format | Price | ISBN-13 | Where | Buy |
|---|---|---|---|---|
| Kindle | $64.95 | — | Amazon | Buy → |
| Paperback | $59.95 | 978-1-919012-60-5 | Amazon | Buy → |
| Hardcover | $89.95 | 978-1-919012-61-2 | 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
- 313 pages
- First published
- 2026-08-29
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
US grades 4–7 · UK Years 5–8
The foundational arithmetic textbook used in Russian schools for over a century. 6 parts, 214 sections. Whole numbers through proportional quantities, with mathematical proofs for every operation.
Kiselev's Algebra I
by A. P. Kiselev
US grades 7–9 · UK Years 8–10
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
US grades 9–12 · UK Years 10–13
12 chapters plus Supplements, 187 sections. Functions, quadratic systems, inequalities, logarithms, progressions, complex numbers, the binomial theorem, and continued fractions.