Need Help?
Need help finding the right class? Have a question about how classes work?
Click here to Ask AoPS!
Intermediate Counting & ProbabilityTopics in discrete mathematics, including clever onetoone correspondences, principle of inclusionexclusion, generating functions, distributions, the pigeonhole principle, induction, constructive counting and expectation, combinatorics, systems with states, recursion, conditional probability, and introductory graph theory.This course is University of California ag approved. Click here for more details. 
18 weeks 
18 weeks ARE YOU READY? DO YOU NEED THIS? 
Schedule
Monday
Feb 27  Jul 3 
7:30  9:00
PM ET
Feb 27  Jul 3
7:30  9:00 PM Eastern 6:30  8:00 PM Central 5:30  7:00 PM Mountain 4:30  6:00 PM Pacific Click here to see more time zones 
Joy Jiao 
$410
$457 w/books

$410
FULL
With Books $457

Wednesday
Jun 7  Oct 4 
7:30  9:00
PM ET
Jun 7  Oct 4
7:30  9:00 PM Eastern 6:30  8:00 PM Central 5:30  7:00 PM Mountain 4:30  6:00 PM Pacific Click here to see more time zones 
Dylan Yott 
$410
$457 w/books

$410
ENROLL
With Books $457

Friday
Jul 21  Nov 17 
7:30  9:00
PM ET
Jul 21  Nov 17
7:30  9:00 PM Eastern 6:30  8:00 PM Central 5:30  7:00 PM Mountain 4:30  6:00 PM Pacific Click here to see more time zones 
Eric Wofsey 
$410
$457 w/books

$410
ENROLL
With Books $457

Thursday
Oct 12  Mar 1 
7:30  9:00
PM ET
Oct 12  Mar 1
7:30  9:00 PM Eastern 6:30  8:00 PM Central 5:30  7:00 PM Mountain 4:30  6:00 PM Pacific Click here to see more time zones 
TBA 
$410
$457 w/books

$410
ENROLL
With Books $457

AoPS Holidays
There are no classes May 29, July 4, September 4, November 18  26, and December 21  January 3.
Who Should Take?
Students should have a complete mastery of basic counting as described in the diagnostic test above before taking this course. Students should also have a solid algebra background through our Intermediate Algebra class (or a typical honors Algebra 2 class and some Precalculus). Students who have completed the Art of Problem Solving Intermediate Algebra and Introduction to Counting & Probability classes should feel comfortable taking this class. (However, students are not required to take these classes before taking Intermediate Counting & Probability  use the diagnostic test above to determine if this class is right for you.)Lessons
Lesson 1  Review of Counting and Probability Basics 
Lesson 2  Principle of Inclusion & Exclusion 
Lesson 3  Advanced Inclusion & Exclusion 
Lesson 4  Constructive Counting 
Lesson 5  Onetoone Correspondences 
Lesson 6  Onetoone Correspondences Continued and Pigeonhole 
Lesson 7  Constructive Expectation 
Lesson 8  Distributions 
Lesson 9  Mathematical Induction and Fibonacci Numbers 
Lesson 10  Recursion and Catalan Numbers 
Lesson 11  Conditional Probability 
Lesson 12  Combinatorial Identities 
Lesson 13  Events with States 
Lesson 14  Generating Functions, Week 1 
Lesson 15  Generating Functions, Week 2 
Lesson 16  Graph Theory, Week 1 
Lesson 17  Graph Theory, Week 2 
Lesson 18  Bonus Topics and Challenging Problems 
Required Textbook
Intermediate Counting & Probability
An intermediate textbook in counting and probability for students in grades 912, containing topics such as inclusionexclusion, recursion, conditional probability, generating functions, graph theory, and more.
