Short description:

 This book presents methods of solving problems in three areas of elementary combinatorial mathematics: classical combinatorics, combinatorial arithmetic, and combinatorial geometry. In each topic, brief theoretical discussions are immediately followed by carefully worked-out examples of increasing degrees of difficulty, and by exercises that range from routine to rather challenging. While this book emphasizes some methods that are not usually covered in beginning university courses, it nevertheless teaches techniques and skills that are useful not only in the specific topics covered here. There are approximately 310 examples and 650 exercises.

Jirí Herman is the headmaster of a prestigious secondary school (Gymnazium) in Brno, Radan Kucera is Associate Professor of Mathematics at Masaryk University in Brno, and Jaromír Simsa is a researcher at the Mathematical Institute of the Academy of Sciences of the Czech Republic. The translator, Karl Dilcher, is Professor of Mathematics at Dalhousie University in Canada. This book can be seen as a continuation of the previous book by the same authors and also translated by Karl Dilcher, Equations and Inequalities: Elementary Problems and Theorems in Algebra and Number Theory (Springer-Verlag 2000).

Long description:

This book can be seen as a continuation of Equations and Inequalities: El­ ementary Problems and Theorems in Algebra and Number Theory by the same authors, and published as the first volume in this book series. How­ ever, it can be independently read or used as a textbook in its own right. This book is intended as a text for a problem-solving course at the first­ or second-year university level, as a text for enrichment classes for talented high-school students, or for mathematics competition training. It can also be used as a source of supplementary material for any course dealing with combinatorics, graph theory, number theory, or geometry, or for any of the discrete mathematics courses that are offered at most American and Canadian universities. The underlying "philosophy" of this book is the same as that of Equations and Inequalities. The following paragraphs are therefore taken from the preface of that book.

From the reviews:

THE BULLETIN OF MATHEMATICS BOOKS

"In each topic, brief theoretical discussions are immediately followed by carefully worked-out examples of increasing degrees of difficulty, and by exercises that range form routine to rather challenging. While this book emphasizes some methods that are not usually covered in beginning university courses, it nevertheless teaches techniques and skills that are useful not only in the specific topics covered here."

"This excellent book presents a wide range of combinatorial problems of all degrees of difficulties. The authors show how to approach the solution of such problems ? . A large number of (solved) exercises give the reader the opportunity to check his advances." (Hansueli Hösli, Zentralblatt MATH, Vol. 1055, 2005)

"This is a book about solving problems in combinatorics ? . It covers a wide range of enumeration results ? . All concepts and methods are introduced in problems followed by detailed solutions. ? Besides the problems in the main text, there are hundreds of nice exercises each of which comes with either a hint or an answer. The index makes it possible to select exercises either according to the objects in the problem statement or the method used in the solution." (T. Eisenkölbl, Monatshefte für Mathematik, Vol. 144 (2), 2005)

"This book is written along the lines of the author?s previous volume ? . In each topic there is a brief description of the theory, then carefully chosen worked examples in increasing order of difficulty, and then exercises ? . With the outline solutions providing hints if necessary, the reader is thus lead along carefully chosen paths ? . All the more welcome, then, is a book like this which attempts to get the reader to think about mathematics ? ." (Ian Anderson, The Mathematical Gazette, Vol. 88 (512), 2004)

"This is a translation of the second Czech edition of a book whose title translates as Methods forSolving Mathematical Problems, vol. II. It is a rich compendium of problems (310 worked examples, plus 650 exercises having hints or solutions ? . The translation is generally excellent ? . This book would be ideal for preparing high school students for competitions ? and is an outstanding source of classroom and homework problems for college students taking a course in combinatorics." (S.W. Golomb, Mathematical Reviews, 2003j)

"Most problem books have a limited number of rather challenging problems. While these problems tend to be quite beautiful, they can appear forbidding and discouraging to a beginning student ? . After going through the chapters the reader will be convinced that the authors are not making these errors. The chapter headings describe the covered material quite well ? . This book is intended as a text for a problem-solving course at the first-or second-year university level ? ." (Péter Hajnal, Acta Scientiarum Mathematicarum, Vol. 69, 2003)

Table of Contents:

1 Combinatorics.- 2 Combinatorial Arithmetic.- 3 Combinatorial Geometry.- 4 Hints and Answers.