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A path to combinatorics for undergraduates
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A path to combinatorics for undergraduates

A path to combinatorics for undergraduates

Titu Andreescu, Zuming Feng

228 pages, parution le 28/12/2003

Résumé

This unique apprach to combinatorics is centered around challenging examples, fully-worked solutions, and hundreds of problems-many from Olympiads and other competitions, and many original to the authors. Each chapter highlights a particular aspect of the subject and casts combinatorial concepts in the guise of questions, illustrations, and exercises that are designed to encourage creativity, improve problem-solving techniques, and widen the reader's mathematical horizons.

Topics encompass permutations and combinations, binomial coefficients and their applications, recursion, bijections, inclusions and exclusions, and generating functions. The work is replete with a broad range of useful methods and results, such as Sperner's Theorem, Catalan paths, integer partitions and Young's diagrams, and Lucas' and Kummer's Theorems on divisibility. Strong emphasis is placed on connections between combinatorial and graph-theoretic reasoning and on links between algebra and geometry.

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 stimulate seasoned mathematicians as well. 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.

Contents

  • Preface
  • Introduction
  • Acknowledgements
  • Abbreviations and notation
  • Addition or multiplication
  • Combinations
  • Properties of binomial coefficients
  • Bijections
  • Recursions
  • Inclusion and exclusion
  • Calculating in to ways : Fubini's principle
  • Generating Functions
  • Review exercices
  • Glossary
  • Index
  • Further reading
  • Afterword

Caractéristiques techniques

  PAPIER
Éditeur(s) Birkhäuser
Auteur(s) Titu Andreescu, Zuming Feng
Parution 28/12/2003
Nb. de pages 228
Format 15 x 23
Couverture Broché
Poids 340g
Intérieur Noir et Blanc
EAN13 9780817642884
ISBN13 978-0-8176-4288-4

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