A Path to Combinatorics for Undergraduates
BeschreibungThis 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. "A Path to Combinatorics for Undergraduates" is a lively introduction not only to combinatorics, but to mathematical ingenuity, rigor, and the joy of solving puzzles.
InhaltsverzeichnisPreface * 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
PressestimmenFrom the reviews:
"A good foundation in combinatorics is provided in the early chapters that cover ideas in combinatorial geometry.... This book serves as a solid stepping stone for more advanced combinatorics studies in related mathematical science fields or in computer science."
- L'Enseignement Mathématique
"This book is an introduction to counting strategies in combinatorial theory. The main mathematical ideas are carefully worked into organized, challenging, and instructive examples given in the nine chapters of this book. In the last chapter we find 111 problems (without solutions). The greater part of them are from various mathematical contests. The...experience of the authors in preparing students for various mathematical competitions allowed them to present a big collection of beautiful problems. By studying this book, undergraduates will be well-equipped to further their knowledge in more abstract combinatorics and its related fields."
"...the book provides quite an amazing collection of combinatorial problems, many of them original, and many of them from a hard to find sources like Russian olympiads. (...) The presentation of the solutions is very clear and instructive, with emphasis on common mistakes."
"The goal of the book is to explain the main concepts and ideas of combinatorics to undergraduate students. Extremely helpful is the extensive use of examples for explanation purposes, which makes this book so pleasant to read. All the ideas and problems are addressed by giving rich examples, and what is even more, each example is solved in high detail immediately after it is posed. ... So it is highly recommended to read everything in the book." (Simon Seichter, Simulation News Europe, Vol. 16 (1), 2006)
Untertitel: Counting Strategies. 2004. Auflage. Book. Sprache: Englisch.
Erscheinungsdatum: November 2003
Seitenanzahl: 252 Seiten