Which book, which year
Every title placed against the US, UK and Canadian curricula — set from each book’s own table of contents, not from its title. With what each one leaves out, and which of the overlapping volumes to buy.
The whole catalogue, by school year
Show
| Book | United States | United Kingdom | Canada | Not covered |
|---|---|---|---|---|
| Arithmetic and calculation | ||||
| Kiselev's Arithmetic | 4–7 Elementary math → Pre-Algebra | Years 5–8 KS2 into KS3 · pre-GCSE | Ontario 4–7 BC Math 4–7 · QC Elementary 4 – Secondary I | negative numbers · coordinate geometry · statistics and data handling · probability · percentages |
| Kiselev's Systematic Arithmetic | 5–8 Grade 6–7 math → Pre-Algebra | Years 6–9 KS2 into KS3 · interest work reaches GCSE Foundation | Ontario 5–8 BC Math 5–8 · QC Elementary 5 – Secondary II | negative numbers · coordinate geometry · statistics and data handling · probability |
| Malinin & Burenin | 5–8 Grade 6–7 math (the continued-fractions chapter is Precalculus) | Years 6–9 KS2 into KS3 | Ontario 5–8 QC Elementary 5 – Secondary II | negative numbers · coordinate geometry · statistics and data handling · probability · metric units — the problems use pre-revolutionary Russian measures, with a conversion table |
| Malinin & Burenin Problems | 5–8 Problem companion to Grade 6–7 math | Years 6–9 KS2–KS3 · GCSE Foundation | Ontario 5–8 QC Elementary 5 – Secondary II | statistics and data handling · probability · metric units — the problems use pre-revolutionary Russian measures, with a conversion table |
| Berezanskaya's Arithmetic Problems | 4–7 Elementary math → Grade 6 math | Years 5–8 KS2 into KS3 | Ontario 4–7 BC Math 4–7 | negative numbers · coordinate geometry · statistics and data handling · probability |
| Vereshchagin's Arithmetic Problems | 4–8 Elementary math → Pre-Algebra | Years 5–9 KS2 into KS3 | Ontario 4–8 QC Elementary 4 – Secondary II | percentages · negative numbers · statistics and data handling · probability · metric units — the problems use pre-revolutionary Russian measures, with a conversion table |
| Rachinsky's 1001 Problems | 4–8 Mental-arithmetic drill, not a course | Years 5–9 KS2–KS3 | Ontario 4–8 | statistics and data handling · probability · metric units — the problems use pre-revolutionary Russian measures, with a conversion table |
| Rachinsky Solutions | 4–8 Solutions companion | Years 5–9 KS2–KS3 | Ontario 4–8 | metric units — the problems use pre-revolutionary Russian measures, with a conversion table |
| Malinin's Mental Calculation | 2–7 Mental-arithmetic drill, graded by size of number | Years 3–8 KS2–KS3 | Ontario 2–7 | statistics and data handling · probability · metric units — the problems use pre-revolutionary Russian measures, with a conversion table |
| Berman's Calculation Techniques | 6–10 Grade 6–8 math → Algebra 1 → Algebra 2 (the error work is HS N-Q) | Years 7–11 KS3 → GCSE; significant figures and error bounds are Higher | Ontario 7–10 MTH1W · MPM2D · BC Math 7–10 | statistics and data handling · probability · coordinate geometry |
| Perelman's Entertaining Arithmetic | 4+ Enrichment | Year 5+ Enrichment · the non-decimal bases map to computing | Ontario 4+ binary work pairs with ICS3U · BC Computer Science 11 | statistics and data handling · probability |
| Algebra | ||||
| Barsukov's Algebra | 8–10 Algebra 1 in full, plus the quadratic-function half of Algebra 2 | Years 9–11 GCSE Foundation and Higher — covers the algebra strand almost completely | Ontario 9–11 MTH1W + MPM2D, quadratics reaching MCR3U · BC Math 9, FMP 10, Pre-Calc 11 | statistics and data handling · probability · graphs of the trigonometric functions and radian measure |
| Kiselev's Algebra I | 7–9 Pre-Algebra → Algebra 1 | Years 8–10 KS3 → GCSE Foundation and Higher | Ontario 8–10 MTH1W · MPM2D · BC Math 8–9, FMP 10 · QC Secondary II–IV | graphs and the function concept · coordinate geometry · statistics and data handling · probability |
| Kiselev's Algebra II | 9–12 Algebra 2, running into Precalculus | Years 10–13 GCSE Higher → A-level Pure → Further Maths (complex numbers) | Ontario 10–12 MPM2D → MCR3U → MHF4U · QC Secondary IV–V SN | graphs of the trigonometric functions and radian measure · statistics and data handling · probability |
| Elementary Algebra | 7–11 Algebra 1 and Algebra 2 as a skills spine — not a standalone course | Years 8–12 KS3 → GCSE Higher algebra strand → AS Pure | Ontario 8–11 supports MTH1W · MPM2D · the algebra of MCR3U | graphs and the function concept · coordinate geometry · exercises — this volume is exposition only · statistics and data handling · probability |
| Kiselev's Algebra Problems | 7–11 Algebra 1 → Algebra 2 | Years 8–12 KS3 → GCSE Higher → AS Pure | Ontario 8–11 MTH1W → MPM2D → MCR3U | statistics and data handling · probability · graphs of the trigonometric functions and radian measure |
| Shaposhnikov & Valtsov, Part I | 7–10 Algebra 1, spilling into Algebra 2 | Years 8–11 KS3 → GCSE Foundation and Higher | Ontario 8–10 MTH1W · MPM2D | graphs and the function concept · coordinate geometry · statistics and data handling · probability |
| Shaposhnikov & Valtsov, Part II | 9–12 Algebra 2 → Precalculus | Years 10–13 GCSE Higher (surds are Higher-only) → A-level Pure → Further Maths | Ontario 10–12 MPM2D → MCR3U → MHF4U | graphs of the trigonometric functions and radian measure · statistics and data handling · probability |
| Elements of Algebra & Analysis I | 8–11 Algebra 1 and Algebra 2 in one volume | Years 9–12 GCSE Foundation and Higher → AS Pure | Ontario 9–11 MTH1W → MPM2D → MCR3U | graphs of the trigonometric functions and radian measure · statistics and data handling · probability |
| Elements of Algebra & Analysis II | 11–12 Precalculus → AP Calculus AB | Years 12–13 A-level Pure: differentiation, integration, coordinate geometry | Ontario 12 MHF4U · MCV4U (derivatives) · BC Pre-Calc 12 → Calculus 12 · QC CEGEP 201-NYA | vectors · statistics and data handling · probability |
| Geometry | ||||
| Kiselev's Planimetry | 8–10 Geometry — the whole course except coordinate geometry and transformations | Years 8–11 KS3 → GCSE Higher; circle theorems are Higher-only | Ontario 8–10 MPM2D (less its analytic unit) · BC Geometry 12 · QC Secondary II–IV | coordinate geometry · transformations on a grid · vectors · statistics and data handling · probability |
| Kiselev's Stereometry | 9–11 Geometry, solid strand (G-GMD) plus substantial enrichment | Years 10–13 GCSE Higher → A-level enrichment | Ontario 9–11 measurement strands · BC Geometry 12 · QC Secondary III–V | coordinate geometry · transformations on a grid · vectors · statistics and data handling · probability |
| Elementary Geometry | 8–11 Geometry, plane and solid, complete | Years 8–13 KS3 → GCSE Higher → A-level | Ontario 8–11 MPM2D · BC Geometry 12 | coordinate geometry · transformations on a grid · vectors · statistics and data handling · probability |
| Rybkin's Planimetry Problems | 8–11 Geometry problem companion, running into competition territory | Years 9–12 GCSE Foundation and Higher; cevians and power of a point are beyond A-level | Ontario 8–11 MPM2D and beyond | coordinate geometry · transformations on a grid · vectors · statistics and data handling · metric units — the problems use pre-revolutionary Russian measures, with a conversion table |
| Rybkin's Stereometry Problems | 10–12 Geometry (solid) and beyond | Years 11–13 GCSE Higher → A-level; prismatoids and inscribed spheres exceed both | Ontario 10–12 BC Geometry 12 | coordinate geometry · transformations on a grid · vectors · statistics and data handling |
| Delone: Geometry Problems | 10–12 + Enrichment and olympiad, not a course | Years 11–13 Further Maths enrichment · UKMT Senior Challenge and BMO | Ontario 11–12 CEMC contests — Euclid, Fermat | coordinate geometry · statistics and data handling · probability |
| Aleksandrov's Geometric Problems | 10–12 + Outside every US course — organised by method, not by topic | Years 11–13 Outside GCSE, A-level and Further Maths alike | Ontario 11–12 contest training only | coordinate geometry · statistics and data handling · probability |
| Raykovsky: Foundations of Geometry | 9–12 A primary source, not a course — see the note below | Years 10–13 No qualification maps to it cleanly | Ontario 9–12 historical reading | exercises — this volume is exposition only · coordinate geometry · transformations on a grid · statistics and data handling · probability |
| Trigonometry | ||||
| Rashevsky's Trigonometry | 10–12 Trigonometry / Precalculus — the triangle-solving half | Years 10–13 GCSE Higher (sine and cosine rules) → A-level Pure | Ontario 10–12 MPM2D → MCR3U · BC Pre-Calc 11–12 · QC Secondary IV–V SN | graphs of the trigonometric functions and radian measure · statistics and data handling · probability |
| Vereshchagin's Plane Trigonometry | 10–12 Trigonometry / Precalculus; the physics section reaches AP Physics 1 | Years 11–13 GCSE Higher → A-level Pure and Mechanics | Ontario 10–12 MPM2D → MCR3U → MHF4U; physics section pairs with SPH3U/SPH4U | graphs of the trigonometric functions and radian measure · statistics and data handling · probability |
| Analysis and university | ||||
| Kiselev's Calculus | 11–12 AP Calculus AB foundation — not AB-complete, and not BC | Years 12–13 A-level Pure: differentiation and integration | Ontario 12 MCV4U derivatives; the integral half is beyond Ontario secondary · BC Calculus 12 | series, parametric and polar calculus, and differential equations · vectors · statistics and data handling · probability |
| Markov: Probabilities | 12 and university University probability — the binomial law and the law of large numbers | Year 13 and university A-level Statistics reaches the results; the proofs are undergraduate | Beyond MDM4U first-year university · QC CEGEP | statistics and data handling |
| Gunter & Kuzmin, Part I | University 1–2 Calculus I–III and Linear Algebra | Undergraduate first year; conics, matrices and complex numbers overlap Further Maths | University 1–2 QC CEGEP 201-NYA / NYB / NYC | |
| Gunter & Kuzmin, Part II | University 2–4 ODEs, PDEs, Complex Analysis, Numerical Analysis, Probability | Undergraduate 2–3 undergraduate | University 2–4 | |
| Gunter & Kuzmin | University 1–4 Parts I and II in one volume | Undergraduate undergraduate | University 1–4 | |
Ranges, not rules. A student coming from a conventional school usually sits a year lower than their school year suggests, because the proof load is higher. The translated editions of Kiselev’s Arithmetic sit exactly where the English one does.
Three pairs cover the same ground. Which do you buy?
Two of these pairs are translations of different Russian originals — Kiselev’s own pre-revolutionary text on one side, the later Soviet revision on the other. They are not two printings of one book, and the differences decide the purchase. Every number below was counted from the books.
Elementary Geometry, or Planimetry and Stereometry?
| Elementary Geometry Translates: Kiselev’s own single volume, 23rd edition, 1914 $69.95 | Kiselev's Planimetry Translates: The later Soviet edition, revised by N. A. Glagolev $59.95 | Kiselev's Stereometry Translates: The later Soviet edition, revised by N. A. Glagolev $49.95 | |
|---|---|---|---|
| Pages | 380 | 242 | 138 |
| Figures | 450 | 262 | 158 |
| Exercises | 370 | 248 | 61 |
| Kiselev’s article numbers printed | §1–§502 | — | — |
| Trigonometric functions of an acute angle | — | ✓ | — |
| Orthogonal projection | — | — | ✓ |
| Appendix on construction methods | ✓ | — | — |
Which to buy
One volume, or two. The pair is not the fuller treatment: side by side the single volume matches it on pages, and carries more figures, more exercises and about a fifth more prose.
Choose the single volume unless you specifically want the trigonometry chapter or the chapter on orthogonal projection, which only the pair has.
Elementary Algebra, or Algebra Part I and Part II?
| Elementary Algebra Translates: Kiselev’s own single volume, 1908 $69.95 | Kiselev's Algebra I Translates: The later Soviet edition, revised by A. N. Barsukov $44.95 | Kiselev's Algebra II Translates: The later Soviet edition, revised by A. N. Barsukov $54.95 | |
|---|---|---|---|
| Pages | 292 | 144 | 259 |
| Numbered articles | 326 | 126 | 187 |
| Exercises | 0 | 268 | 321 |
| Answers supplied | — | 241 | 55 |
| Coordinates, functions and graphs | — | — | ✓ |
| Ratio and proportion | ✓ | — | — |
| Compound interest and annuities | ✓ | — | partly |
Which to buy
This is the pair where "buy one" is the wrong advice. The 1908 single volume covers the syllabus of both, several topics more deeply, and adds ratio and proportion, undetermined multipliers, hand cube roots and annuities — but it contains no exercises at all, and not one coordinate, function or graph in 292 pages.
As a course: Elementary Algebra to read, Part II for the functions and graphs, and Part I or Shaposhnikov & Valtsov for the practice. On its own, Elementary Algebra is a reading course, not a working one.
Higher Mathematics, or Parts I and II separately?
| Gunter & Kuzmin Translates: Parts I and II bound together $99.95 | Gunter & Kuzmin, Part I Translates: The first half, sold separately $64.95 | Gunter & Kuzmin, Part II Translates: The second half, sold separately $54.95 | |
|---|---|---|---|
| Pages | 814 | 448 | 379 |
Which to buy
The same text, bound one way or two. Buy the combined volume for the whole sequence, or a single part if you only need that half.
What these books do not teach
Worth knowing before you buy, not after. These are 19th- and early-20th-century texts, and six strands that modern exams require are absent from the catalogue at school level.
- statistics and data handling
- probability at school level — the only probability book here is Markov’s, and it is undergraduate
- coordinate geometry
- transformations on a grid
- vectors
- graphs of the trigonometric functions and radian measure