102 Combinatorial Problems: From the Training of the USA Imo Team

ISBN-13: 9780817643171 / Angielski / Miękka / 2002 / 115 str.

Zuming Feng

Opis

"102 Combinatorial Problems" consists of carefully selected problems that have been used in the training and testing of the USA International Mathematical Olympiad (IMO) team. Key features: * Provides in-depth enrichment in the important areas of combinatorics by reorganizing and enhancing problem-solving tactics and strategies * Topics include: combinatorial arguments and identities, generating functions, graph theory, recursive relations, sums and products, probability, number theory, polynomials, theory of equations, complex numbers in geometry, algorithmic proofs, combinatorial and advanced geometry, functional equations and classical inequalities The book is systematically organized, gradually building combinatorial skills and techniques and broadening the student's view of mathematics. Aside from its practical use in training teachers and students engaged in mathematical competitions, it is a source of enrichment that is bound to stimulate interest in a variety of mathematical areas that are tangential to combinatorics.

Recenzje

From the reviews:

"Andreescu's 51 'introductory problems' and 51 'advanced problems,' all novel, would nicely supplement any university course in combinatorics or discrete mathematics. This volume contains detailed solutions, sometimes multiple solutions, for all the problems, and some solutions offer additional twists for further thought . . . "

-CHOICE

"Another excellent effort towards building combinatorial skills especially for students engaged in mathematical competitions is presented in this book through 102 selected Combinatorial problems."

-ZENTRALBLATT MATH

"Each solution is given in full, and often with alternative versions as well. Some solutions introduce standard combinatorial tools like inclusion-exclusion, generating functions, and graphs. Others stray into probability, number theory, complex numbers, inequalities and functional equations. The book will be useful for teachers looking for challenging problems for able students and for those preparing for Olympiads."

-The MATHEMATICAL GAZETTE

"This book contains 102 highly selected combinatorial problems used in the training and testing of the USA International Mathematical Olympiad team. Half of the problems are introductory, while the rest are more difficult. All problems have complete solutions. . . It is not a collection of very difficult, impenetrable questions. Instead, the book gradually builds students' combinatorial skills and techniques. It aims to broaden a student's view of mathematics in perparation for possible participation in mathematical competitions."

-IASI POLYTECHNIC MAGAZINE

"Both of the two authors serves as a coach of the USA International Mathematical Olympiad (IMO) Team for several years. ... the book gradually builds students' combinatorial skills and techniques. It aims to broaden a student's view of mathematics in preparation for possible participation in mathematical competitions. ... this is a book for problem-solvers. ... The present collection of problems and the presented solutions are carefully designed to develop the readers' problem-solving abilities. ... Have fun working on them!" (Péter Hajnal, Acta Scientiarum Mathematicarum, Vol. 69, 2003)

Spis treści

Preface and Introduction * Acknowledgments * Abbreviations and Notations * Introductory Problems * Advanced Problems * Solutions to Introductory Problems * Solutions to Advanced Problems * Glossary * Further Reading