Malinin and Burenin's Guide to Algebra and Collection of Algebraic Problems
by A. F. Malinin & K. P. Burenin
Translated by Valery Manokhin, PhD
The algebra course and its problem collection in one volume, in first faithful English translation from the original Russian edition. An Introduction and sixteen chapters, 429 numbered articles, run from positive and negative numbers and the operations on algebraic expressions through equations of the first degree in one and several unknowns; powers and roots, with the square and cube roots of numbers and the square root of polynomials; quadratic equations, imaginary expressions and the trinomial of the second degree; inequalities; indeterminate equations; proportions; arithmetic and geometric progressions; logarithms; combinations and Newton’s binomial; continued fractions; the method of limits; and series. Problem sets follow the articles throughout — more than 3,300 numbered problems, 620 of them in a closing chapter of miscellaneous problems — and 2,698 answers are printed at the back.
16 chapters · 429 numbered articles · 3338 exercises · 458 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 (limits and series) |
|---|---|---|
| United Kingdom | Years 9–13 | KS3 → GCSE Higher → A-level Pure |
| Canada | Ontario 8–12 | MTH1W → MPM2D → MCR3U → MHF4U · QC Secondary III–V SN |
Not covered in this book
graphs and the function concept · coordinate geometry · statistics and data handling · probability · metric units — some problems use old Russian measures (versts, sazhens, arshins, poods)
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
- Malinin & Burenin$44.95
Covers much of the same ground
- Elementary Algebra$69.95
Kiselev's single volume is 292 pages of exposition with no exercises at all. This book is 458 pages, 429 numbered articles and more than 3,300 problems with 2,698 answers, and adds chapters on limits and series. Neither carries functions or graphs.
Rashevsky's is 272 pages with 49 figures and teaches first- and second-degree functions through their graphs, which this book does not. Its six exercise sets are short and unanswered, and it has no continued fractions, no indeterminate equations and no chapter on series.
- Davidov's Algebra$59.95
Davidov's is 509 pages and 478 numbered articles with full worked solutions rather than answers, and adds equations of the third and fourth degree. This book has more than 3,300 numbered problems, 620 of them in a closing miscellaneous chapter, with 2,698 answers. 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.
What comes next
- Kiselev's Calculus$54.95
- Rashevsky's Trigonometry$39.95
Further reading
A historical text to read beside the course, not a substitute for it.
Table of contents
18 section headings — the printed contents page in full.
A note on the authors and this translation
Introduction
Chapter I. Positive and negative numbers
Chapter II. Operations on algebraic expressions5 sections
- Reduction
- Addition
- Subtraction
- Multiplication
- Division
Chapter III. Equations2 sections
- Solution of equations of the first degree with several unknowns
- Various values that the unknown can take in solving equations
Chapter IV. Powers and roots5 sections
- Raising to a power
- Extraction of roots
- Extraction of the square root of numbers
- Extraction of the cube root of numbers
- Extraction of the square root of polynomials
Chapter V. Quadratic equations4 sections
- Equations reducible to quadratic equations
- Quadratic equations with several unknowns
- Imaginary expressions
- On the trinomial of the second degree
Chapter VI. Inequalities
Chapter VII. Indeterminate equations
Chapter VIII. Proportions
Chapter IX. Progressions2 sections
- Arithmetic progression
- Geometric progression
Chapter X. Logarithms
Chapter XI. Theory of combinations
Chapter XII. Newton's binomial
Chapter XIII. Continued fractions
Chapter XIV. The method of limits
Chapter XV. Series
Chapter XVI. Miscellaneous problems
Solutions to the problems
Formats and editions
| Format | Price | ISBN-13 | Where | Buy |
|---|---|---|---|---|
| Kindle | $74.95 | — | Amazon | Buy → |
| Paperback | $69.95 | 978-1-80910-044-3 | Amazon | Buy → |
| Hardcover | $99.95 | 978-1-80910-045-0 | 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
- 458 pages
- First published
- 2026-10-01
Published by Northern Star Academic Press · First faithful English translation from the original Russian edition
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