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Patrick D. Intermediate Counting and Probability

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Patrick D. Intermediate Counting and Probability
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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