Introduction to Counting & Probability

Testimonials

"My son, a 6th grader, was introduced to MathCounts this year. He made it to state; but was in over his head in terms of what he had not yet learned. We ordered The Art of Problem Solving, Volumes I and II with solutions. He has been studying and learning ever since, growing by leaps and bounds. He is now so far ahead of the Middle School curriculum in math, that we aren't sure what to do with him." - Sharon Dominguez, parent

"I've never seen math books as good as the ones from Art of Problem Solving- really, this is the way all kids should learn math." - customer review

"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"

"I have been coaching MATHCOUNTS since its inception...and have been the coach of the Indiana team at the National competition for eleven years...During this time I have purchased many useful materials, but I feel your materials are the best I have used with my students..." - Robert J. Fischer, Indiana MATHCOUNTS coach

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by David Patrick

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Single Text Book

Product Description

This is a unique book that provides school level instructional material in the specifics of counting and probability. Topics covered in the book include permutations, combinations, Pascal's Triangle, basic combinatorial identities, expected value, fundamentals of probability, geometric probability, the Binomial Theorem, and much more. Counting and Probability is a recurring theme in all math competitive events and standardized assessment tests, and middle/high school students preparing for various competitive exams will derive great value from this book.

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 1 - Excerpt 2 - Index

Recommended Age and Grade

This book is suited for use by highly advanced elementary school students, advanced and grade level middle school students, and grade level high school students. Students are assumed to have a thorough understanding of the basics of Algebra such as linear equations.

Using the Book

This book may be used as:

A self-study course in the basics of Counting and Probability
A teaching aid for classroom instruction as well as tutoring
Comprehensive home-schooling instructional material
Preparatory material for Math competitive events and assessment tests
Reference material as a rich source of categorized exercises and challenge problems
Reference material for the AOPS online course titled "Introduction to Counting and Probability"

Testimonials

"The new book is great. I have started to use it in my classes on a regular basis. I can see the improvement in my kids over just a short period. I think that probability is one of the hardest topics for students and teachers. This book helps both. A great job!!!" - Jeff Boyd, coach of the 2005 and 2007 MATHCOUNTS National Championship teams from Texas
"I just received the counting book (by the way, absolutely AWESOME book!!!! Blew my expectations away!!) and I will buy the other books as they come out." - AoPS Community member IntrepidMath
"I've never seen math book as good as the ones from Art of Problem Solving- really, this is the way all kids should learn math." - Customer review

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 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.