102 Combinatorial Problems [Paperback]

Titu Andreescu (Author), Zuming Feng (Author)

Book Description

ISBN-10: 0817643176 | ISBN-13: 978-0817643171 | Publication Date: October 29, 2002 | Edition: 1

"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.

Editorial Reviews

Review

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)

Product Details

• Paperback: 128 pages
• Publisher: Birkhäuser Boston; 1 edition (October 29, 2002)
• Language: English
• ISBN-10: 0817643176
• ISBN-13: 978-0817643171
• Product Dimensions: 9.1 x 6 x 0.5 inches
• Shipping Weight: 8.5 ounces (View shipping rates and policies)
• Average Customer Review: 5.0 out of 5 stars  See all reviews (1 customer review)
• Amazon Best Sellers Rank: #389,556 in Books (See Top 100 in Books)

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Most Helpful Customer Reviews

27 of 29 people found the following review helpful:

5.0 out of 5 stars A well selected and organized problem set in combinatorics., January 13, 2003

By 

Sen Peng Eu "ESP=Math+Music+Literature" (Kaohsiung, Taiwan) - See all my reviews
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This review is from: 102 Combinatorial Problems (Paperback)

This is an excellent training source in combinatorics for mathematics olympiads and contests.

Problems in this book are divided into 2 sets, with each set containing 51 problems. Problems in the first set are introductory ones (hence, relatively easy), and that in the second set are advanced problems (And harder, much harder indeed in the last few problems). Problems are very well selected and carefully organized according to their difficulty and technic involved. They span from the very easy first some enumerative problems to the really hard IMO-level, even notorious National-MO problems. Moreover, problems are up-to-date hence it avoids well-known cliche problems. The book is published in the end of 2002, and in this book some of the 102 problems are selected from the IMO that year!

As a regular lecturer of Taiwan's IMO team, I highly recommend this problem book.