Introduction to Combinatorics

In Introduction to Combinatorics, Wallis (emer., Southern Illinois Univ.) and George (Gordon State College) present a well-thought-out compilation of topics covering elementary combinatorics. At the beginning, the authors present a thorough background on the fundamentals of combinatorics with topics such as permutations and combinations, the pigeonhole principle, and the principle of inclusion and exclusion. Later chapters are independent of one another and can be selected based on student and instructor interests. These topics include graph theory, coding theory, and balanced incomplete block designs. At the end of each chapter, there are exercises and problems. These vary in difficulty from straightforward practice to more involved proof problems. Solutions and/or hints are provided in the back of the book. In addition, three appendixes discuss proof techniques, matrices and vectors, and historical figures; these allow flexibility in covering the material in various ways that can be based on students’ backgrounds. Overall, this textbook is a highly readable work that will benefit and enlighten all those interested in learning about combinatorics. It will work in a traditional classroom setting and for independent study. Given the level of material, it is geared toward junior or senior level undergraduate students. --S. L. Sullivan, Catawba College