Combinatorial Reasoning - Duane DeTemple, William Webb (2014) torrent

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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