A Path to Combinatorics for Undergraduates

by Andreescu, Titu; Feng, Zuming

• ISBN13: 9780817642884
• ISBN10: 0817642889
• Format: Paperback
• Copyright: 2003-11-01
• Publisher: Birkhauser

Summary

A Path to Combinatorics for Undergraduates is a lively introduction not only to combinatorics, but also to mathematical ingenuity, rigor, and the joy of solving puzzles. This unique approach to combinatorics is centered around unconventional, essay-type combinatorial examples, followed by a number of carefully selected, challenging problems and extensive discussions of their solutions. Topics encompass permutations and combinations, binomial coefficients and their applications, bijections, inclusions and exclusions, and generating functions. Each chapter features fully-worked problems, including many from Olympiads and other competitions, as well as a number of problems original to the authors; at the end of each chapter are further exercises to reinforce understanding, encourage creativity, and build a repertory of problem-solving techniques. The authors' previous text, 102 Combinatorial Problems , makes a fine companion volume to the present work, which is ideal for Olympiad participants and coaches, advanced high school students, undergraduates, and college instructors. The book's unusual problems and examples will interest seasoned mathematicians as well.

Table of Contents

Preface

Introduction

Acknowledgments

Abbreviations and Notations

Addition on Multiplication?

Combinations

Properties of Binomial Coefficients

Bijections

Inclusions and Exclusions

Recursions

Calculating in Two Ways --- Fubini's Principle

Generating Functions

Review Exercises

Glossary

Further Reading

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