# Foundation of Combinatorics with Applications

Written by: Edward A. Bender and S. Gill Williamson (both from the University of California San Diego)

I have been noticing a number of the higher math textbooks are not suggesting students take particular classes but, instead, have “a certain level of ability or ‘sophistication’ in dealing with mathematical concepts.” The authors of this free combinatorics textbook recommend students obtain that sophistication prior to attempting their discrete mathematics textbook Foundation of Combinatorics with Applications.

Edward A. Bender and S. Gill Williamson were members of the faculty at the University of California San Diego. They have included within each chapter some introductory material to aid students in developing “sone new thought patterns” required for success in the study of combinatorics. They consider their textbook suitable for an introductory course in combinatorics for math and mathematical computer science majors.

Each chapter is available in PDF form and a pre-printed version can be purchased. Self-study students should be glad to hear that the authors have provided a full solutions manual for the first 109 pages of the text and for the odd-numbered exercises on the remaining pages.

## Chapter Titles for the Foundation of Combinatorics with Applications

Part I: Counting and Listing
Chapter 1: Basic Counting
Chapter 2: Functions
Chapter 3: Decision Trees
Chapter 4: Sieving Methods
Part II: Graph Theory
Chapter 5: Basic Concepts in Graph Theory
Chapter 6: A Sampler of Graph Topics
Part III: Recursion
Chapter 7: Induction and Recursion
Chapter 8: Sorting Theory
Chapter 9: Rooted Plane Trees
Part IV: Generating Functions
Chapter 10: Ordinary Generating Functions
Chapter 11: Generating Function Topics
Appendices
Solutions to Odd Numbered Exercises
Index
Solutions Manual

View this Free Online Material at the source:

Foundation of Combinatorics with Applications