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A Path to Combinatorics for Undergraduates is a lively introduction not only to combinatorics, but also to mathematical ingenuity, rigour and the joy of solving puzzles. The 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’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’s Theorem, Catalan Paths, integer partitions and Young’s diagrams and Lucas’ and Kummer’s Theorems on divisibility. Strong emphasis is placed on connections between combinatorial and graph-theoretic reasoning and on links between algebra and geometry.
ISBN-9788181283368
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Pages : 248
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