The polynomials studied in this book take their origin in number theory. The authors show how, by drawing simple pictures, one can prove some long-standing conjectures and formulate new ones. The theory presented in this book touches upon many different fields of mathematics. The major part of this book is quite elementary and is easily accessible to an undergraduate student. The less elementary parts, such as Galois theory or group representations and their characters, would need a more profound knowledge of mathematics.
This book is an introduction to certain new directions in the (very classical) theory of combinatorial maps, otherwise called embedded graphs. Namely, we consider the theory of "dessins d'enfants", matrix integrals in map enumeration and in quantum gravity, moduli spaces of algebraic curves, Hurwitz spaces, and Vassiliev knot invariants. The Appendix written by Don Zagier presents a concise introduction to finite group representation theory and to its applications to enumeration problems.
Second printing: 2013.
A Russian translation is published by the Moscow Center of Continuous Mathematical Education, 2010, 480 pages.
A certain number of misprints and errors found up to now, as well as some clarifying remarks, are given here: ERRATA and COMMENTS
A course of algorithmic thinking for the 12-15 year olds. Was reprinted in 1997 and 1998.
A fourth edition: A. K. Zvonkin, S. K. Lando, and A. L. Semenov, Informatica. Algorithmica, Moscow, Prosveshchenie, 2006, 240 pages.
This book is an account of the author's experience in math activities with very young children (4 to 7 years). A journal, a collection of exercises, and author's reflexions.
Nine editions: 2006, 2007, 2010, 2012, 2014, 2015, 2017, 2019, 2020.
In 2008, the book was nominanted to a short list of a newly established prize PROSVETITEL' ("Enlightener") for the best scientific-popular book.
American translation:Math from Three to Seven: The Story of a Mathematical Circle for Preschoolers, AMS and MSRI publishers, 2011, XIV+301 pages.
Korean translation:Mathematical Diary: How We Played Math with Kids, Tin Drum Publishing Co., 2012, 640 pages.
Spanish translation:Matemáticas de 3 a 7 años: La historia de un Círculo Matemático para niños, EDICIONES SM, 2016, 352 pages.
Hebrew translation:The text is not (yet?) published as a book but the file is available here: Zvonkin-Hebrew (translation by Rachel Faran, 2022), 203 pages.
Go to the site of LaBRI