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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. 
18 weeks 
18 weeks ARE YOU READY? DO YOU NEED THIS? SYLLABUS 
Schedule
Sunday
Jun 30  Nov 3 
7:30  9:00 PM ET
Jun 30  Nov 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 
Jacob GuoXue 
$560
(~$32/lesson)
$616 w/books

$560
(~$32/lesson)
CLOSED
With Books $616

Tuesday
Sep 17  Feb 4 
7:30  9:00 PM ET
Sep 17  Feb 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 
Jeffrey Hankins 
$560
(~$32/lesson)
$616 w/books

$560
(~$32/lesson)
ENROLL
With Books $616

Thursday
Nov 7  Mar 27 
7:30  9:00 PM ET
Nov 7  Mar 27
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 
Kathryn Lesh 
$560
(~$32/lesson)
$616 w/books

$560
(~$32/lesson)
ENROLL
With Books $616

Monday
Feb 10  Jun 16 
7:30  9:00 PM ET
Feb 10  Jun 16
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 
Ashley Ahlin 
$560
(~$32/lesson)
$616 w/books

$560
(~$32/lesson)
ENROLL
With Books $616

Sunday
Mar 23  Aug 3 
7:30  9:00 PM ET
Mar 23  Aug 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 
Aaron Doman 
$560
(~$32/lesson)
$616 w/books

$560
(~$32/lesson)
ENROLL
With Books $616

AoPS Holidays
There are no classes October 31, November 25 ‐ December 1, December 21 ‐ January 3, May 24 ‐ 26, July 4 ‐ 6, and August 29 ‐ September 1, 2025.
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
1  Review of Counting and Probability Basics 
2  Principle of Inclusion & Exclusion 
3  Advanced Inclusion & Exclusion 
4  Constructive Counting 
5  Onetoone Correspondences 
6  The Pigeonhole Principle 
7  Constructive Expectation 
8  Distributions 
9  Mathematical Induction and Fibonacci Numbers 
10  Recursion and Catalan Numbers 
11  Conditional Probability 
12  Combinatorial Identities 
13  Events with States 
14  Generating Functions (Part 1) 
15  Generating Functions (Part 2) 
16  Graph Theory (Part 1) 
17  Graph Theory (Part 2) 
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.
Related course: Intermediate Counting and Probability 