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J Am Diet Assoc 3 We will also show the other side of the coin, that is, that sometimes totally elementary-looking problems turn out to be unexpectedly deep, or even unknown. This book is meant to be a textbook for an introductory combinatorics course that can take one or two semesters. In each section, we included exercises that contain material not explicitly discussed in the text before.
We chose to do this to provide instructors with some extra choices if they want to shift the emphasis of their course. It goes without saying that we covered the classics, that is, combinatorial choice problems, and graph theory. We included some more elaborate concepts, such as Ramsey theory, the Probabilistic Method, and Pattern Avoidance the latter is probably a first of its kind. While we realize that we can only skim the surface of these areas, we believe they are interesting enough to catch the attention of some students, even at first sight.
Most undergraduate students enroll in at most one Combinatorics course during their studies, therefore it is important that they see as many captivating examples as possible.
It is in this spirit that we included two new chapters in the second edition, on Algorithms, and on Computational Complexity.
We believe that the best undergraduate students, those who will get to the ix third February 10, x World Scientific Book - 9in x 6in A Walk Through Combinatorics end of the book, should be acquainted with the extremely intriguing questions that abound in these two areas. The third edition has two challenging new chapters, one on Block Designs and codes obtained from designs, and the other one on counting unlabeled structures.
We wrote this book as we believe that combinatorics, researching it, teaching it, learning it, is always fun. We hope that at the end of the walk, readers will agree. An exercise that is thought to be significantly easier than average is marked by a - sign. We provide Supplementary Exercises without solutions at the end of each chapter.
These typically include, but are not limited to, the easiest exercises in that chapter. A solution manual for the Supplementary Exercises is available for Instructors. I am certainly indebted to the books I used in my teaching during this time. Several exercises in the book come from my long history as a student mathematics competition participant. I am grateful to my students who never stopped asking questions and showed which part of the material needed further explanation.
Some of the presented material was part of my own research, sometimes in collaboration.
I am also indebted to my former advisor, Richard Stanley, who introduced me to the fascinating area of Pattern Avoidance, discussed in Chapter My gratitude is extended to Joseph Sciacca for the cover page.
After the publication of the first edition in , several mathematicians contributed lists of typographical errors to be corrected. I am thankful for their help in making the second edition better by communicating those lists to me, as well as for similar help from countless other contributors who will hopefully forgive that I do not list all of them here.
Most of the corrections for the second edition were provided by Margaret Bayer, and for the third edition by Glenn Tesler. Most of all, I must thank my wife Linda, my first reader, who made it possible for me to spend long hours writing this book while she also had her hands full.
See Exercise 3 of Chapter 15 for further explanation. Basic Methods 1. Seven Is More Than Six. Solutions Manuals are available for thousands of the most popular college and high school textbooks in subjects such as Math, Science Physics , Chemistry , Biology , Engineering Mechanical , Electrical , Civil , Business and more.
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