This volume and ""Kvant Selecta: Algebra and Analysis, I"" (""MAWRLD/14"") are the first volumes of articles published from 1970 to 1990 in the Russian journal, ""Kvant"". The influence of this magazine on mathematics and physics education in Russia is unmatched. This collection represents the Russian tradition of expository mathematical writing at its best. Articles selected for these two volumes are written by leading Russian mathematicians and expositors. Some articles contain classical mathematical gems still used in university curricula today. Others feature cutting-edge research from the twentieth century.The articles in these books are written so as to present genuine mathematics in a conceptual, entertaining, and accessible way. The volumes are designed to be used by students and teachers who love mathematics and want to study its various aspects, thus deepening and expanding the school curriculum. The first volume is mainly devoted to various topics in number theory, whereas the second volume treats diverse aspects of analysis and algebra.
Binomial coefficients, polynomials, and sequences (Several approaches to a certain problem) by V. N. Vaguten Formulas for prime numbers by Yu. V. Matiyasevich Fermat's theorem for polynomials by B. Martynov Commuting polynomials by I. Yantarov On the removal of parentheses, on Euler, Gauss, and Macdonald, and on missed opportunities by D. B. Fuchs Chebyshev polynomials and recurrence relations by N. Vasil'ev and A. Zelevinskii Why resistance does not decrease by O. V. Lyashko Evolution processes and ordinary differential equations by V. I. Arnol'd Irrationality and irreducibility by V. A. Oleinikov Irreducibility and irrationality by V. A. Oleinikov The arithmetic of elliptic curves by Yu. P. Solov'ev Pascal's hexagrams and cubic curves by N. B. Vasil'ev Kepler's second law and the topology of abelian integrals (According to Newton) by V. I. Arnol'd Partitions of integers by F. V. Vainstein On the Denogardus great number and Hooke's law by V. Yu. Ovsienko Polynomials having least deviation from zero by S. Tabachnikov.