Kvant Selecta: Algebra and Analysis, II
About this Title
Serge Tabachnikov, University of Arkansas at Fayetteville, Fayetteville, AR, Editor
This volume is not part of this online collection, but can be purchased through our online bookstore.
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.
Advanced high school and undergraduate students interested in mathematics; mathematics teachers in high schools and colleges.
Table of Contents
- 1. Binomial coefficients, polynomials, and sequences (Several approaches to a certain problem)
- 2. Formulas for prime numbers
- 3. Fermat’s theorem for polynomials
- 4. Commuting polynomials
- 5. On the removal of parentheses, on Euler, Gauss, and Macdonald, and on missed opportunities
- 6. Chebyshev polynomials and recurrence relations
- 7. Why resistance does not decrease
- 8. Evolution processes and ordinary differential equations
- 9. Irrationality and irreducibility
- 10. Irreducibility and irrationality
- 11. The arithmetic of elliptic curves
- 12. Pascal’s hexagrams and cubic curves
- 13. Kepler’s second law and the topology of Abelian integrals (According to Newton)
- 14. Partitions of integers
- 15. On the Denogardus great number and Hooke’s law
- 16. Polynomials having least deviation from zero