How to Count: An Introduction to Combinatorics, Second Edition

R.B.J.T. Allenby, Alan Slomson

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August 12, 2010 by Chapman and Hall/CRC
Textbook - 444 Pages - 164 B/W Illustrations
ISBN 9781420082609 - CAT# C8260
Series: Discrete Mathematics and Its Applications

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Features

  • Explains how to solve various combinatorial problems, from Euler’s problem of polygon division, Fibonacci numbers, and the Königsberg bridges problem to the four-color problem, labeled trees, and card shuffling
  • Uses problems to introduce the theory
  • Contains enough material for a short course on graph theory
  • Presents proofs of key results as well as numerous worked examples
  • Includes paired exercises, along with a full solution to one of the exercises in each pair
  • Lists suggestions for further reading

Solutions manual available for qualifying instructors

Summary

Emphasizes a Problem Solving Approach
A first course in combinatorics

Completely revised, How to Count: An Introduction to Combinatorics, Second Edition shows how to solve numerous classic and other interesting combinatorial problems. The authors take an easily accessible approach that introduces problems before leading into the theory involved. Although the authors present most of the topics through concrete problems, they also emphasize the importance of proofs in mathematics.

New to the Second Edition
This second edition incorporates 50 percent more material. It includes seven new chapters that cover occupancy problems, Stirling and Catalan numbers, graph theory, trees, Dirichlet’s pigeonhole principle, Ramsey theory, and rook polynomials. This edition also contains more than 450 exercises.

Ideal for both classroom teaching and self-study, this text requires only a modest amount of mathematical background. In an engaging way, it covers many combinatorial tools, such as the inclusion-exclusion principle, generating functions, recurrence relations, and Pólya’s counting theorem.