Counting The Art of Enumerative Combinatorics [Paperback]

This book provides an introduction to discrete mathematics. At the end of the book the reader should be able to answer counting questions such as: How many ways are there to stack n poker chips, each of which can be red, white, blue, or green, such that each red chip is adjacent to at least 1 green chip? The book can be used as a textbook for a semester course at the sophomore level. The first five chapters can also serve as a basis for a graduate course for in-service teachers.Counting: The Art of Enumerative Combinatorics provides an introduction to discrete mathematics that addresses questions that begin, How many ways are there to...For example, ?How many ways are there to order a collection of 12 ice cream cones if 8 flavors are available?? At the end of the book the reader should be able to answer such nontrivial counting questions as, ?How many ways are there to color the faces of a cube if ?k? colors are available with each face having exactly one color?? or ?How many ways are there to stack ?n? poker chips, each of which can be red, white, blue, or green, such that each red chip is adjacent to at least 1 green chip?? Since there are no prerequisites, this book can be used for college courses in combinatorics at the sophomore level for either computer science or mathematics students. The first five chapters have served as the basis for a graduate course for in-service teachers. Chapter 8 introduces graph theory.1. Elementary Enumeration.- 2. The Principle of Inclusion and Exclusion.- 3. Generating Functions.- 4. Groups.- 5. Actions.- 6. Recurrence Relations.- 7. Mathematical Induction.- 8. Graphs.- The Back of the Book.

From the reviews:

Much of Martins charming and accessible text could be used with bright school students. & The book is rounded off by a section called The back of the book which includes solutions and discussion of many exercises. George E. Martin is a remarkable writer who brings combinatorics alive. He has wriló>