The Dorofeev Solutions
Worked solutions to Dorofeev, Potapov and Rozov, reasoned in full
2026 · 543 pp
Full worked solutions to every problem in Dorofeev, Potapov and Rozov's *Elementary Mathematics*, across algebra and analysis, trigonometry, geometry, and the non-standard problems. Each solution uses only school mathematics, is argued step by step, and is checked against the authors' own answer key. Where a problem rewards a second approach, both are shown.
Dorofeev, Potapov and Rozov is the problem book that taught a generation to look for reasons rather than tricks, not least the students who grew up on it preparing for the IITs. Its problems do not yield to a remembered method. Each one asks for an idea, and the idea then has to be argued all the way down.
This volume works every one of them. The solutions run across algebra and analysis, trigonometry, geometry and the non-standard problems, each reached with nothing beyond school mathematics, justified step by step, and checked against the authors’ own answer. Where a problem rewards a second approach, both are shown.
What the problems teach, and what these solutions try to keep, is that rigour and imagination belong together. The careful proof and the inventive leap turn out to be one move.
A note on the solutions. These solutions are my own. They are not the work of Dorofeev, Potapov and Rozov, nor are they endorsed by them. Each problem has been worked from scratch and checked against the authors’ answer key, yet a book of this size will still hold mistakes of its own, and if you find one I would be glad to hear of it. In the few places where the printed key is itself wrong or incomplete, the solution follows the corrected mathematics rather than the key.
Found an error? Let me know and I will correct it.