A Path to Combinatorics for Undergraduates : Counting Strategies This unique approach to combinatorics is centered around challenging examples fully worked solutions and hundreds of problems many from Olympiads and other competitions and many original to the authors. Each chapter highlights a particular aspect of the subject and casts combinatorial concepts in the guise of questions illustrations and exercises that are designed to encourage creativity improve problem solving techniques and widen the readers mathematical horizons. Topics encompass permutations and combinations binomial coefficients and their applications recursion bijections inclusions and exclusions and generating functions. The work is replete with a broad range of useful methods and results such as Sperners Theorem Catalan paths integer partitions and Youngs diagrams and Lucas and Kummers Theorems on divisibility. Strong emphasis is placed on connections between combinatorial and graph theoretic reasoning and on links between algebra and geometry. The authors previous text 102 Combinatorial Problems makes a fine companion volume to the present work which is ideal for Olympiad participants and coaches advanced high school students undergraduates and college instructors. The books unusual problems and examples will stimulate seasoned mathematicians as well. A Path to Combinatorics for Undergraduates is a lively introduction not only to combinatorics but also to mathematical ingenuity rigor and the joy of solving puzzles