Mathematical Conversations

by E.B. Dynkin, Vladimir A. Uspensky, V.A. Uspenskii

Combining three books into a single volume, this text comprises Multicolor Problems, dealing with several of the classical map-coloring problems; Problems in the Theory of Numbers, an elementary... This description may be from another edition of this product.

• Format: Paperback
• Language: English
• ISBN: 0486453510
• ISBN13: 9780486453514
• Release Date: December 2006
• Publisher: Dover Publications
• Length: 290 Pages
• Weight: 0.65 lbs.
• Dimensions: 0.6" x 6.4" x 8.5"

Customer Reviews

It is less a conversation than it is a sequential series of problems

As the title implies, this book is about coloring maps (graphs), number theory and random walks. It is less a conversation than it is a sequential series of problems that move you step by step through increasingly complex mathematical thoughts. There are three distinct sections, presented in the following order: *) Multicolor problems *) Number theory *) Random walks The multicolor problems are about several different families of two-dimensional structures and how many colors are needed to mark each region with a color where no two contiguous regions have the same color. Some of the consequences of using coloration arguments are also given. For example the coloring of the squares in a chessboard and how that can be used to prove different facts about the movement of chess pieces around the board. The ultimate goal of stating and explaining the four color theorem is achieved, but since the book was originally published in 1963, that problem is stated as being currently unsolved. The number theory problems deal with modular arithmetic, divisibility and sequences. For the most part, the topics are typical of those in introductory number theory. The last section on random walks begins with a brief introduction to probability, in particular the algebra of Bernoulli trials. This is used as the foundation for describing random walks on an infinite line and the random movement between states where there are an infinite number. By far, the strongest feature of the book is the large number of problems used to demonstrate the topics. There are 55 problems in the multicolor section, 132 in the number theory section and 28 in the section on random walks. Detailed solutions to all of them are included, which makes the book an excellent learning tool as well as a reference.