This book continues the exploration of counting and probability topics, initiated by its predecessor – Introduction to Counting and Probability. 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.

The instructional material is designed to:

• Encourage student enquiry and exploration through problems
• Efficiently use theoretical narrative to reinforce concepts
• Emphasize powerful problem solving techniques and pattern recognition
• Provide a large repository of problems arranged by complexity

The solutions manual, sold separately, contains complete solutions to all the problems.

Sample Excerpts: Table of Contents - Excerpt - Index

Recommended Age and Grade

This is suited for use by advanced and grade level high school students. Students are assumed to have a thorough understanding of the basics of Counting and Probability.

Using the Book

This book may be used as:

• A self-study course in advanced Counting and Probability topics for motivated students
• A teaching aid for classroom instruction as well as tutoring
• Comprehensive home-schooling instructional material
• Preparatory material for various Math competitive events and assessment tests
• Reference material as a rich source of well categorized exercises and challenge problems
• Reference material for the AOPS online course titled "Intermediate Counting and Probability”

Testimonials

"Thank you so much for writing this book! I received it yesterday and it's fantastic. I just want to thank you for releasing another amazing book." - AoPS student

"Every time one of your books arrives on my doorstep I couldn't be more impressed with what you're doing out there...For the right kind of student -- and I was one myself, I just wish these books had been around when I was a kid -- your books must be like a prayer answered. And as I've always said to every math teacher I meet, this is the way to teach mathematics to everyone." - Steve Olson, author of "Count Down"

About the Author

Dr. David Patrick earned his Ph. D. in mathematics from MIT, and is currently an instructor and textbook developer at Art of Problem Solving. He is the author of Introduction to Counting and Probability, and Intermediate Counting and Probability. He is a past USA Mathematical Olympiad winner, a two time Math Olympiad Program invitee, a perfect scorer on the AHSME (predecessor of the AMC 12), and top 10 scorer on the Putnam Exam. Dr. Patrick has taught undergraduate math courses at the University of Washington, and coached aspiring mathematicians over the years for various competitive events. The solutions are co-authored by Naoki Sato, a curriculum developer and the director of WOOT at Art of Problem Solving. He won first place in the 1993 Canadian Mathematical Olympiad and is a 2-time medalist at the International Mathematical Olympiad.