Shafarevich, I. R. Selected chapters from algebra. (Translated from the Russian). (English) Zbl 0998.00001 Teach. Math. 1, 1-22 (1998). Summary: The aim of this publication (this paper together with its several continuations) is to present algebra as a branch of mathematics by treating the contents close to the usual teaching matter. The whole exposition presupposes a not large frame of knowledge: operations with integers and fractions, square roots, removing of parentheses and other transformations of literal terms, properties of inequalities. The exposition clusters around a number of main themes: ‘number’, ‘polynomial’, ‘set’, each of which is treated in a series of chapters listed in detail in the preface.As indicated in the preface, the following chapters are planned: 1. Numbers, 2. Polynomials, 3. Sets, 4. Numbers (continued), 5. Polynomials (continued), 6. Sets (continued), 7. Numbers (continued), Appendix I (Chebyshev’s estimates of the number of primes, less than a given bound), 8. Numbers (continued), 9. Polynomials (continued), 10. Numbers (continued), 11. Polynomials (continued), 12. Polynomials (continued), 13. Polynomials (continued), Appendix II (equations of degree 5, icosahedron, the problem of resolvents), 14. Numbers (conclusion), Appendix III (construction of the regular 17-gon), 15. Polynomials (conclusion). This article contains the first chapter, for chapter 2 see the following article [ibid. 2, No. 1, 1-30 (1999)]. Cited in 1 Review MSC: 00A05 Mathematics in general 00A35 Methodology of mathematics Keywords:numbers; polynomials; sets Citations:Zbl 0998.00002 PDFBibTeX XML