Combinatorial Reasoning: An Introduction to the Art of Counting

Combinatorial Reasoning: An Introduction to the Art of Counting Front Cover
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488 pages

Book Description

Written by well-known scholars in the field, this book introduces combinatorics alongside modern techniques, showcases the interdisciplinary aspects of the topic, and illustrates how to problem solve with a multitude of exercises throughout. The authors' approach is very reader-friendly and avoids the "scholarly tone" found in many books on this topic.

Combinatorial Reasoning: An Introduction to the Art of Counting:

  • Focuses on enumeration and combinatorial thinking as a way to develop a variety of effective approaches to solving counting problems
  • Includes brief summaries of basic concepts from probability, power series, and group to show how combinatorics interacts with other fields
  • Provides abstract ideas that are grounded in familiar concrete settings and features plentiful diagrams throughout to further add in reader understanding
  • Presents simple and helpful notations as needed, and simple cases are treated first before more general and/or advanced cases
  • Contains over 700 exercise sets, ranging from the routine to the advanced,¬†with either hints, short answers, or complete solutions for odd numbered problems.¬† An Instructor's Manual (available via request to the Publisher) provides complete solutions for all exercises

Table of Contents

Part I The Basics of Enumerative Combinatorics
Chapter 1 Initial Encounters with Combinatorial Reasoning
Chapter 2 Selections, Arrangements, and Distributions
Chapter 3 Binomial Series and Generating
Chapter 4 Alternating Sums, Inclusion-Exclusion Principle, Rook Polynomials, and Fibonacci Nim
Chapter 5 Recurrence Relations
Chapter 6 Special Numbers

Part II Two Additional Topics in Enumeration
Chapter 7 Linear Spaces and Recurrence Sequences
Chapter 8 Counting with Symmetries

Part III Notations Index, Appendices, and Solutions to Selected Odd Problems

Appendix A: Induction
Appendix B: Searching the Online Encyclopedia of Integer Sequences (OEIS)
Appendix C: Generalized Vandermonde Determinants

Book Details

  • Title: Combinatorial Reasoning: An Introduction to the Art of Counting
  • Author: ,
  • Length: 488 pages
  • Edition: 1
  • Language: English
  • Publisher:
  • Publication Date: 2014-05-05
  • ISBN-10: 1118652185
  • ISBN-13: 9781118652183
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