Bugaev's Elementary Algebra
by N. V. Bugaev
Translated by Valery Manokhin, PhD
The algebra course by N. V. Bugaev, later president of the Moscow Mathematical Society, in first faithful English translation from the original Russian edition. Fifteen chapters and 160 numbered sections lead from worked examples to general rules: fundamental concepts and operations, the greatest common divisor and least common multiple, algebraic fractions, equations of the first degree, powers and roots with imaginary quantities, quadratic equations, inequalities, indeterminate equations, continued fractions, ratio and proportion, progressions, logarithms with compound interest, and ordered selections with Newton's binomial. Supplements add a short history of algebra, irrational equations and simultaneous equations of the second degree. More than 400 numbered review questions close the book.
15 chapters· 160 numbered articles· 287 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 | 8–12 | Algebra 1 through Algebra 2, running into Precalculus |
|---|---|---|
| England | Years 9–13 | KS3 → GCSE Higher → A-level Pure |
| Canada (Ontario) | Ontario 8–12 | MTH1W → MPM2D → MCR3U · QC Secondary III–V SN |
Not covered in this book
graphs and the function concept · coordinate geometry · 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 1908 volume covers the same course in 292 pages and 326 numbered articles, with no exercises or review questions. This one is 287 pages, 160 sections, and closes with more than 400 numbered review questions. Neither carries functions or graphs.
- Davidov's Algebra$59.95
Davidov's is longer — 509 pages, 478 numbered articles — and prints full solutions to its problems, where this volume has review questions only. Neither carries functions or graphs.
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
- Kiselev's Calculus$54.95
- Rashevsky's Trigonometry$39.95
Further reading
- Fuss's Algebra$54.95
A historical text to read beside the course, not a substitute for it.
Table of contents
11 section headings — the printed contents page in full.
Translator's Preface
I. Fundamental Algebraic Concepts
II. Operations with Algebraic Quantities
III. The Greatest Common Divisor and Least Common Multiple of Algebraic Expressions
IV. Algebraic Fractions
V. Equations of the First Degree
VI. Powers and Roots5 sections
- Roots
- Operations with irrational quantities
- Extraction of the square root of numbers and polynomials
- Extraction of the cube root
- Preliminary notions of imaginary quantities
VII. Equations of the Second Degree with One Unknown
VIII. Inequalities
IX. Indeterminate Equations
X. Continued Fractions
XI. Ratios and Proportions
XII. Progressions
XIII. Logarithms
XIV. Ordered Selections and Newton's Binomial Theorem
XV. Supplements6 sections
- Brief remarks on the history of algebra
- Conditions for the divisibility of a polynomial by the difference x − a
- Property of the trinomial of the second degree
- Solution of irrational equations. Freeing equations from roots
- Simultaneous equations of the second degree with two unknowns
- The sum of the squares and cubes of natural numbers
Questions on Algebra
Section Guide
Formats and editions
| Format | Price | ISBN-13 | Where | Buy |
|---|---|---|---|---|
| Paperback | $64.95 | 978-1-80910-070-2 | Amazon | Buy → |
| Hardcover | $99.95 | 978-1-80910-071-9 | 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
- 287 pages
- First published
- 2026-11-03
Published by Northern Star Academic Press · First faithful English translation from the original Russian edition
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