Which Russian arithmetic course? Kiselev, Kiselev's Systematic Course, Malinin & Burenin, Rashevsky
Four complete arithmetic courses are in the catalogue. They cover the same subject in different depths and for different readers. Pick one; then add a problem book.
The books compared
| Book | Size | Written for | US placement | Goes further on | Not in the book |
|---|---|---|---|---|---|
| Kiselev's Arithmetic$44.95 | 6 parts, 214 sections, 192 pages | a child meeting arithmetic for the first time | grades 4–7 | a proof for every operation | negative numbers, coordinates, statistics, probability, percentages |
| Kiselev's Systematic Arithmetic$49.95 | 264 numbered articles, 207 pages | the student going deeper | grades 5–8 | divisibility and primes, ratio and proportion, limits (0.999… = 1) | negative numbers, coordinates, statistics, probability |
| Malinin & Burenin$44.95 | 11 chapters, 301 sections | a full school course, through percentage and interest | grades 5–8 | percentage, interest, Diophantine problems, continued fractions | negative numbers, coordinates, statistics, probability |
| Rashevsky's Arithmetic$39.95 | 9 sections, 95 pages | a reader who wants the whole subject back in order | grades 5–8; also an adult refresher | plans, diagrams and graphs | negative numbers, statistics, probability |
How to choose
- A child starting arithmetic, grades 4–7
- Kiselev's Arithmetic. It is the school course, written for a first reading, with a proof for every operation.
- A strong student, or a second pass
- Kiselev's Systematic Arithmetic. It covers the same ground at greater length and treats divisibility, ratio and proportion far more fully. It also includes elementary results most textbooks leave out, such as Euclid's proof that the primes never end.
- One book that runs on to percentage and interest
- Malinin & Burenin. Its eleven chapters add percentage, interest and Diophantine problems; its own problem collection is a separate volume, Malinin & Burenin Problems.
- An adult, or a quick complete review
- Rashevsky's Arithmetic. It is the whole subject in 95 pages, and the only one of the four that ends with plans, diagrams and graphs.
Add a problem book
Each course is exposition first. Work it alongside one of the problem collections.
- Berezanskaya's Arithmetic Problems — graded problems that follow the course; 2,354 exercises · $39.95
- Vereshchagin's Arithmetic Problems — graded problems that follow the course; 3,238 exercises · $44.95
- Malinin & Burenin Problems — the companion to the Malinin & Burenin course · $44.95
- Rachinsky's 1001 Problems — mental arithmetic, with a separate volume of worked solutions (Rachinsky Solutions) · $39.95
- Egorov's Arithmetic Problems — 1,600 problems on whole numbers only, grades 3–5 · $39.95
- Perelman's Entertaining Arithmetic — for enrichment, with Amenitsky's Arithmetic Games · $34.95
What comes next
Each leads into the first course in algebra: Kiselev's Algebra I or his single-volume Kiselev's Elementary Algebra; Rashevsky's Elementary Algebra or Davidov's Algebra in one volume; and Malinin and Burenin's Algebra, which continues their arithmetic. See Which algebra book, with exercises and answers?.