Edición de la obra Experimental mathematics
| Autor | Arnolʹd, V. I. |
|---|---|
| Editorial | MSRI Mathematical Sciences Research Institute, American Mathematical Society |
| Fecha de publicación | 2015 |
| Lugar | Berkeley, California, Providence. Rhode Island |
| Idioma | inglés |
| Páginas | 158 |
| ISBN-13 | 9780821894163 |
| OCLC | 904801193 |
| LCCN | 2015009318 |
| Serie | MSRI mathematical circles library -- 16 |
| Número de Cutter | A762e |
One of the traditional ways mathematical ideas and even new areas of mathematics are created is from experiments. One of the best-known examples is that of the Fermat hypothesis, which was conjectured by Fermat in his attempts to find integer solutions for the famous Fermat equation. This hypothesis led to the creation of a whole field of knowledge, but it was proved only after several hundred yeras. This book, based on the author's lectures, presents several new directions of mathematical research. All of these directions are based on numerical experiments conducted by the author, which led to new hypotheses that currently remain open, i.e., are neither proved nor disproved. The hypotheses range from geometry and topology (statistics of plane curves and smooth functions) to combinatorics (combinatorial complexity and random permutations) to algebra and number theory (continuous fractions and Galois groups). For each subject, the author describes the problem and presents numerical results that led him to a particular conjecture. In the majority of cases there is an indication of how the readers can approach the formulated conjectures (at least by conduting more numerical experiments). Written in Arnold's unique style, the book is intended for a wide range of mathematicians, from high school students interested in exploring unusual areas of mathematics on their own, to college and graduate students, to researchers interested in gaining a new, somewhat nontraditional perspective on doing mathematics. -- from back cover.