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Intermediate Counting & ProbabilityTopics in discrete mathematics, including clever one-to-one correspondences, principle of inclusion-exclusion, 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
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Wednesday
May 21 - Sep 17 |
7:30 - 9:00 PM ET
May 21 - Sep 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 |
Sindi Sabourin |
$585
(~$33/lesson)
$641 w/books
|
$585
(~$33/lesson)
CLOSED
With Books $641
|
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STARTING SOON |
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Sunday
Jun 22 - Nov 2 |
7:30 - 9:00 PM ET
Jun 22 - Nov 2
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 |
Homero Gallegos |
$585
(~$33/lesson)
$641 w/books
|
$585
(~$33/lesson)
ENROLL
With Books $641
|
|
Sunday
Sep 28 - Feb 15 |
7:30 - 9:00 PM ET
Sep 28 - Feb 15
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 |
Christopher Luke Uchizono |
$585
(~$33/lesson)
$641 w/books
|
$585
(~$33/lesson)
ENROLL
With Books $641
|
|
Tuesday
Nov 4 - Mar 24 |
7:30 - 9:00 PM ET
Nov 4 - Mar 24
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 |
sarah-marie belcastro |
$585
(~$33/lesson)
$641 w/books
|
$585
(~$33/lesson)
ENROLL
With Books $641
|
AoPS Holidays
There are no classes July 4 ‐ 6, August 29 ‐ September 1, October 31, November 24 ‐ November 30, December 20 ‐ January 2, and May 23 ‐ 25, 2026.
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 | One-to-one 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
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Intermediate Counting & Probability
An intermediate textbook in counting and probability for students in grades 9-12, containing topics such as inclusion-exclusion, recursion, conditional probability, generating functions, graph theory, and more.
Related course: Intermediate Counting and Probability |
