2nd Edition. — Alpine, USA: AoPS Incorporated, 2012. — 290 p. — ISBN 1934124060.AoPS 2-Book Set : Art of Problem Solving AoPS Intermediate Counting and Probability Textbook and Solutions Manual 2-Book Set : Continue your exploration of more advanced counting and probability topics from former USA Mathematical Olympiad winner David Patrick. This book is the follow-up to the acclaimed Introduction to Counting & Probability textbook. Topics covered in this book include inclusion-exclusion, 1-1 correspondences, the Pigeonhole Principle, constructive expectation, Fibonacci and Catalan numbers, recursion, conditional probability, generating functions, graph theory, and much more. As with all of the books in Art of Problem Solving's Introduction and Intermediate series, the text is structured to inspire the reader to explore and develop new ideas. Each section starts with problems, so the student has a chance to solve them without help before proceeding. The text then includes solutions to these problems, through which counting and probability techniques are taught. Important facts and powerful problem solving approaches are highlighted throughout the text. Contents Review of Counting & Probability Basics Sets and Logic A Piece of PIE Constructive Counting and 1-1 Correspondences The Pigeonhole Principle Constructive Expectation Distributions Mathimatical Induction Fibonacci Numbers Recursion Conditional Probability Combinatorial Identities Events With States Generating Functions Graph Theory Chaltenge problems
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