Foundations of Combinatorics with Applications
by
Edward A. Bender & S. Gill Williamson

 

 

Intended audience: Upper division/beginning graduate.  Some ability to construct proofs is assumed.
Background: Some familiarity with calculus and proofs is assumed.

Comments and errata are appreciated.  ebender@ucsd.edu

This material is intended for double sided reproduction.  All files start on a right hand page.

ps pdf   Preface and Table of Contents

ps pdf   Part I: Counting and Listing -- Introduction  . . .  page 1
ps pdf   Chapter 1: Basic Counting  . . .  page 3
ps pdf   Chapter 2: Functions  . . .  page 37
ps pdf   Chapter 3: Decision Trees  . . .  page 61
ps pdf   Chapter 4: Sieving Methods [Symmetries and Inclusion-Exclusion]  . . .  page 89

ps pdf   Part II: Graph Theory -- Introduction  . . .  page 113
ps pdf   Chapter 5: Basic Concepts in Graph Theory  . . .  page 115
ps pdf   Chapter 6: A Sampler of Graph Topics  . . .  page 143

ps pdf   Part III: Recursion --Introduction  . . .  page 189
ps pdf   Chapter 7: Induction and Recursion  . . .  page 191
ps pdf   Chapter 8: Sorting Theory  . . .  page 219
ps pdf   Chapter 9: Rooted Plane Trees  . . .  page 239

ps pdf   Part IV: Generating Functions -- Introduction  . . .  page 259
ps pdf   Chapter 10: Ordinary Generating Functions  . . .  page 261
ps pdf   Chapter 11: Generating Function Topics  . . .  page 297

ps pdf   Appendices  . . .  page 351
              Appendix A:   Induction
              Appendix B:  Rates of Growth and Analysis of Algorithms
              Appendix C:  Basic Probability
              Appendix D:  Partial Fractions

ps pdf  Solutions to Odd Exercises  . . .  page 383

ps pdf   Index  . . .  page 449