A Path to Combinatorics for Undergraduates: Counting Strategies
by Titu Andreescu, Zuming Feng
English | 2003 | ISBN: 0817642889 | 249 pages | PDF | 3.96 MB

&8220;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 reader&x27;s 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 Sperner&x27;s Theorem, Catalan paths, integer partitions and Young&x27;s diagrams, and Lucas&x27; and Kummer&x27;s Theorems on divisibility. Strong emphasis is placed on connections between combinatorial and graph-theoretic reasoning and on links between algebra and geometry.
The authors&x27; 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 book&x27;s 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 to mathematical ingenuity, rigor, and the joy of solving puzzles.&8221;

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