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. "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.
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From 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." —MAA Online "...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." —Mathematics Bohemica "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)
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4 of 23 people found the following review helpful:
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Interesting and Clear,
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This review is from: A Path to Combinatorics for Undergraduates: Counting Strategies (Paperback)
The book is written very clearly and presents a lot of combinatorial subjects by very interesting examples.
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Inside This Book
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Key Phrases - Statistically Improbable Phrases (SIPs):
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incongruent triangles, winless team, neighboring knights, mathematical contests, considering rotations, mathematics competitions, third knight, coloring scheme, largest disk, undefeated team Key Phrases - Capitalized Phrases (CAPs): (learn more)
Counting Strategies, Inclusion Exclusion Principle, Math Materials New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
incongruent triangles, winless team, neighboring knights, mathematical contests, considering rotations, mathematics competitions, third knight, coloring scheme, largest disk, undefeated team Key Phrases - Capitalized Phrases (CAPs): (learn more)
Counting Strategies, Inclusion Exclusion Principle, Math Materials New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 27
books:
See all 27 books this book cites
- Enumerative Combinatorics, Volume 2 by Richard P. Stanley in Back Matter (1), and Back Matter (2)
- The Art and Craft of Problem Solving by Paul Zeitz in Back Matter
- Elementary Number Theory (AMS Chelsea Publishing) by Edmund Landau in Back Matter
- Elementary Number Theory by Charles Vanden Eynden in Back Matter
- Old and New Unsolved Problems in Plane Geometry and Number Theory (Dolciani Mathematical Expositions) by Victor Klee in Back Matter
See all 27 books this book cites
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