Introduction to Counting & Probability
by David Patrick
Learn the basics of counting and probability from former USA Mathematical Olympiad winner David Patrick. 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.
As you'll see in the excerpts below, 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. In addition to the instructional material, the book contains over 400 problems. The solutions manual contains full solutions to all of the problems, not just answers.
This book is ideal for students who have mastered basic algebra, such as solving linear equations. Middle school students preparing for MATHCOUNTS, high school students preparing for the AMC, and other students seeking to master the fundamentals of counting and probability will find this book an instrumental part of their mathematics libraries.
Our free innovative online learning system, Alcumus, is designed to support users of this textbook.
About the author: Dr. David Patrick earned his Ph. D. in mathematics from MIT. 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. He is currently an instructor and textbook developer at Art of Problem Solving.
ISBN: 978-1-934124-10-9
Text: 256 pages. Solutions: 120 pages.
Paperback. 10 7/8 x 8 3/8 x 1/2 inches.
Pricing Information
Discount Information: Additional 10% discount for orders of 5-9 copies of the same text; 20% discount for 10+ copies.
Excerpts
Table of Contents -
Excerpt 1 -
Excerpt 2 -
Index
Diagnostic Tests
- Pre-test: Students should be able to complete most or all of the pre-test before beginning this book.
- Post-test: Students who can comfortably solve most or all of the problems on the post-test will likely find this book to be mostly review.
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 couldn't be more impressed. It's well written, easy to understand, with good problems and lots of interesting tidbits and asides. I'm really very enthusiastic about this approach...I can't wait to see the others in the series."
- Steve Olson, author of "Count Down"
"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."
- Amazon customer review
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