Combinatorial Reasoning: An Introduction to the Art of Counting,

by Duane DeTemple, William Webb.


# ISBN-13: 9781118652183 
# Publisher: Wiley
# Publication date: 5/5/2014
# Edition number: 1
# Pages: 488

Overview:
========

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.


* 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 theory 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


Contents
========

  PART I THE BASICS OF ENUMERATIVE COMBINATORICS

    1 Initial Encounters with Combinatorial Reasoning
    2 Selections, Arrangements, and Distributions
    3 Binomial Series and Generating Functions
    4 Alternating Sums, Inclusion-Exclusion Principle, Rook Polynomials,
      and Fibonacci Nim
    5 Recurrence Relations
    6 Special Numbers


  PART II TWO ADDITIONAL TOPICS IN ENUMERATION

    7 Linear Spaces and Recurrence Sequences
    8 Counting with Symmetries


  PART III NOTATIONS INDEX, APPENDICES, AND SOLUTIONS TO SELECTED ODD PROBLEMS

    Index of Notations

    Appendix A Mathematical Induction

      A.1 Principle of Mathematical Induction
      A.2 Principle of Strong Induction
      A.3 Well Ordering Principle

    Appendix B Searching the Online Encyclopedia of Integer Sequences (OEIS)

      B.1 Searching a Sequence
      B.2 Searching an Array
      B.3 Other Searches
      B.4 Beginnings of OEIS

    Appendix C Generalized Vandermonde Determinants

    Hints, Short Answers, and Complete Solutions to Selected Odd Problems


Authors
=======

Duane DeTemple, PHD, is Professor Emeritus in the Department of Mathematics at
Washington State University (WSU).

He  is the  recipient of  the  2007 WSU  Sahlin Faculty  Excellence Award  for
Instruction  as well  as the  Distinguished  Teaching Award  from the  Pacific
Northwest Section of the Mathematical Association of America.

...

William  Webb,  PHD,  is  Professor   in  the  Department  of  Mathematics  at
Washington  State  University  and  President of  the  Fibonacci  Association.

His  research interests  include the  properties of  recurrence sequences  and
binomial coefficients. He  is the author of numerous  research publications on
combinatorics, number theory, fair division, and cryptography.

 
http://books.google.com/books?isbn=1118833708

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