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. This unique
approach to combinatorics is centered around unconventional,
essay-type combinatorial examples, followed by a number of
carefully selected, challenging problems and extensive discussions
of their solutions. Topics encompass permutations and combinations,
binomial coefficients and their applications, bijections,
inclusions and exclusions, and generating functions. Each chapter
features fully-worked problems, including many from Olympiads and
other competitions, as well as a number of problems original to the
authors; at the end of each chapter are further exercises to
reinforce understanding, encourage creativity, and build a
repertory of problem-solving techniques.
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 book's unusual
problems and examples will interest seasoned mathematicians as
well.
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