How to Count: An Introduction to Combinatorics (Discrete Mathematics and its Applications v. 60 2nd Revised edition)

How to Count: An Introduction to Combinatorics (Discrete Mathematics and its Applications v. 60 2nd Revised edition)

By: R. B. J. T. Allenby (author), Alan Slomson (author)Hardback

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Description

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 Polya's counting theorem.

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About Author

Alan Slomson taught mathematics at the University of Leeds from 1967 to 2008. He is currently the secretary of the United Kingdom Mathematics Trust. R.B.J.T. Allenby taught mathematics at the University of Leeds from 1965 to 2007.

Contents

What's It All About? What Is Combinatorics? Classic Problems What You Need to Know Are You Sitting Comfortably? Permutations and Combinations The Combinatorial Approach Permutations Combinations Applications to Probability Problems The Multinomial Theorem Permutations and Cycles Occupancy Problems Counting the Solutions of Equations New Problems from Old A "Reduction" Theorem for the Stirling Numbers The Inclusion-Exclusion Principle Double Counting Derangements A Formula for the Stirling Numbers Stirling and Catalan Numbers Stirling Numbers Permutations and Stirling Numbers Catalan Numbers Partitions and Dot Diagrams Partitions Dot Diagrams A Bit of Speculation More Proofs Using Dot Diagrams Generating Functions and Recurrence Relations Functions and Power Series Generating Functions What Is a Recurrence Relation? Fibonacci Numbers Solving Homogeneous Linear Recurrence Relations Nonhomogeneous Linear Recurrence Relations The Theory of Linear Recurrence Relations Some Nonlinear Recurrence Relations Partitions and Generating Functions The Generating Function for the Partition Numbers A Quick(ish) Way of Finding p(n) An Upper Bound for the Partition Numbers The Hardy-Ramanujan Formula The Story of Hardy and Ramanujan Introduction to Graphs Graphs and Pictures Graphs: A Picture-Free Definition Isomorphism of Graphs Paths and Connected Graphs Planar Graphs Eulerian Graphs Hamiltonian Graphs The Four-Color Theorem Trees What Is a Tree? Labeled Trees Spanning Trees and Minimal Connectors The Shortest-Path Problem Groups of Permutations Permutations as Groups Symmetry Groups Subgroups and Lagrange's Theorem Orders of Group Elements The Orders of Permutations Group Actions Colorings The Axioms for Group Actions Orbits Stabilizers Counting Patterns Frobenius's Counting Theorem Applications of Frobenius's Counting Theorem Polya Counting Colorings and Group Actions Pattern Inventories The Cycle Index of a Group Polya's Counting Theorem: Statement and Examples Polya's Counting Theorem: The Proof Counting Simple Graphs Dirichlet's Pigeonhole Principle The Origin of the Principle The Pigeonhole Principle More Applications of the Pigeonhole Principle Ramsey Theory What Is Ramsey's Theorem? Three Lovely Theorems Graphs of Many Colors Euclidean Ramsey Theory Rook Polynomials and Matchings How Rook Polynomials Are Defined Matchings and Marriages Solutions to the A Exercises Books for Further Reading Index

Product Details

  • publication date: 13/08/2010
  • ISBN13: 9781420082609
  • Format: Hardback
  • Number Of Pages: 444
  • ID: 9781420082609
  • weight: 975
  • ISBN10: 1420082604
  • edition: 2nd Revised edition

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  • 1st Class Delivery: Yes
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