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Mathematics via problems. Part 1. Algebra. Translated from the Russian by Paul Zeitz and Sergei G. Shubinкнига
- Авторы: Skopenkov Arkadiy, Kanel-Belov A.Ya, Konyagin S.V., Shnurnikov I.N., Bershtein M.A., Vorontsov A.C., Sgibnev A.I., Senderov V.A.
- Год издания: 2021
- Место издания: MSRI Mathematical Circles Library 25. Providence, RI: American Mathematical Society (AMS) Berkeley, CA
- Объём: 196 страниц
- ISBN: 978-1-4704-4878-3
- Научно-популярное издание
- Аннотация: This is a translation (from the Russian) of the book “Elements of mathematics” published in 2018. It does not have one but two mighty translators, however the reviewer did not have the original to assess the quality of the translation.The listed author is joined by a number of contributing authors (who are former math Olympiad celebrities): A. Ya. Kanel-Belov, S. V. Konyagin, I. N. Shnurnikov, M. A. Bershtein, A. C. Vorontsov, A. I. Sgibnev, V. A. Senderov. This list is to be completed by numerous authors and creators of mathematical problems throughout generations, lumped together under an anonymous group labeled “folklore”.The chapter titles give us an idea of the subject content of the book: Divisibility. Multiplication modulo p. Polynomials and complex numbers. Permutations. Inequalities. Sequences and limits. Functions. Solving algebraic equations (the longest chapter). The book is intended for talented high school and undergraduate students who will learn these topics through non-routine problem solving. The harder problems are of the “Olympiad type” that are often used to prepare young students for competing in advanced school or undergraduate math Olympiads. Although the reviewer did not find types of problems that have not already appeared in print and used in competitions, the choice of problems is very good.The format is that the problems are given first (some with hints), with the hope that a reader will bite into them and attempt to solve them. Sections in every chapter increase in relative difficulty, sometimes culminating in the most difficult “asterisqued” sections. Then, at the end of every section, there are suggestions, answers or solutions to aforestated problems. The bibliography consists of 120 entries (permanent and online) that are not always directly related to the content.The book ends with a subject index. There are a few misprints, due to TeX formatting, or other. Some formulations may be imprecise, resulting in incorrect statements.Reviewer: Radoslav M. Dimitrić (New York)
- Добавил в систему: Белов Алексей Яковлевич