A walk through combinatorics : an introduction to enumeration graph theory and selected other topics The first half of the book walks the reader through methods of counting both direct elementary methods and the more advanced method of generating functions. Then in the second half of the book the reader learns how to apply these methods to fascinating objects such as graphs designs random variables partially ordered sets and algorithms. In short the first half emphasizes depth by discussing counting methods at length; the second half aims for breadth by showing how numerous the applications of our methods are. New to this fifth edition of A Walk Through Combinatorics is the addition of Instant Check exercises more than a hundred in total which are located at the end of most subsections. As was the case for all previous editions the exercises sometimes contain new material that was not discussed in the text allowing instructors to spend more time on a given topic if they wish to do so. With a thorough introduction into enumeration and graph theory as well as a chapter on permutation patterns (not often covered in other textbooks) this book is well suited for any undergraduate introductory combinatorics class