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Introduction to Counting & Probability
Summary
In this online class, students dive into the fundamentals of counting and probability, including casework, multiplication, permutations, combinations, Pascal's triangle, probability, combinatorial identities, and the Binomial Theorem.
This advanced math course is offered in two formats: a live online course or a self-paced course. Both formats include instructor feedback, office hours, and a class message board for student support.
Introduction to Counting & Probability: Weekly Live
Length: 12 Weeks
Our live Introduction to Counting & Probability course brings together advanced problem solvers from around the world for 90-minute classes. Experienced instructors lead students to creatively problem-solve with casework, permutations, combinations, Pascal's triangle, combinatorial identities, and the Binomial Theorem.
Students refer to our Introduction to Counting & Probability textbook and videos, while honing their skills on various types of engaging homework problems. They can also use the class message board to collaborate with their peers and reach out to instructors outside of class.
Live Online Course Features
Why AoPS?
Extraordinary Live Instruction from Accomplished Faculty
Dana Paquin
Brian Edwards
Josh Zucker
Ashley Ahlin
Miles Dillon Edwards
Our teachers were outstanding math students themselves, and many were winners of major math awards as well as recipients of degrees from schools like MIT, Harvard, Stanford, and Princeton. Our instructors understand from their personal experiences how to inspire and challenge eager learners, and they serve as role models for our students who aspire to similar success.
Active Learning
Students learn best by actively engaging with challenging problems. Our lessons start with thought-provoking questions, encouraging independent insights and problem-solving strategies. Instructors offer hints and guidance as needed and reinforce key concepts after problems are solved. To support diverse learning styles, we provide live classes, textbooks, videos, homework problems, and opportunities for discussion with instructors and peers.
Focus on Non-Routine, Challenging Problems
In today's world, many jobs previously requiring routine problem-solving are now handled by computers. To prepare students for the future, we focus on teaching them how to apply core principles to new, non-routine problems. This approach ensures that students develop essential skills for top-tier colleges and competitive careers, preparing them for lifelong learning rather than rote memorization.
Schedule: Introduction to Counting & Probability
The current and upcoming sections of this course are listed below. All sections cover the same course material.
|
Sunday
Feb 9 - Apr 27 |
3:30 - 5:00 PM ET –
Feb 9 - Apr 27
3:30 - 5:00 PM Eastern 2:30 - 4:00 PM Central 1:30 - 3:00 PM Mountain 12:30 - 2:00 PM Pacific Click here to see more time zones |
Luís Finotti |
$400
(~$34/lesson)
$449 w/books
|
$400
(~$34/lesson)
CLOSED
$449 w/books
|
|
Sunday
Mar 16 - Jun 8 |
7:30 - 9:00 PM ET
Mar 16 - Jun 8
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 |
Angel Bell |
$400
(~$34/lesson)
$449 w/books
|
$400
(~$34/lesson)
ENROLL
$449 w/books
|
|
Wednesday
Apr 16 - Jul 2 |
7:30 - 9:00 PM ET
Apr 16 - Jul 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 |
Dana Paquin |
$400
(~$34/lesson)
$449 w/books
|
$400
(~$34/lesson)
ENROLL
$449 w/books
|
|
Thursday
May 15 - Jul 31 |
7:30 - 9:00 PM ET
May 15 - Jul 31
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 |
Asa Frank |
$400
(~$34/lesson)
$449 w/books
|
$400
(~$34/lesson)
ENROLL
$449 w/books
|
|
Sunday
Jun 1 - Aug 24 |
7:30 - 9:00 PM ET
Jun 1 - Aug 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 |
Charles Buehrle |
$400
(~$34/lesson)
$449 w/books
|
$400
(~$34/lesson)
ENROLL
$449 w/books
|
|
Thursday
Jun 12 - Aug 28 |
7:30 - 9:00 PM ET
Jun 12 - Aug 28
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 Seales |
$400
(~$34/lesson)
$449 w/books
|
$400
(~$34/lesson)
ENROLL
$449 w/books
|
|
Wednesday
Jul 2 - Sep 17 |
7:30 - 9:00 PM ET
Jul 2 - 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 |
Heather Finotti |
$400
(~$34/lesson)
$449 w/books
|
$400
(~$34/lesson)
ENROLL
$449 w/books
|
|
Sunday
Jul 27 - Oct 19 |
7:30 - 9:00 PM ET
Jul 27 - Oct 19
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 |
Johann Edir Hernandez Ybarra |
$400
(~$34/lesson)
$449 w/books
|
$400
(~$34/lesson)
ENROLL
$449 w/books
|
| Fall 2025 | This course will be offered in Fall 2025. Click here to join our mailing list to be notified when the course schedule is available. | |||
AoPS Holidays
Who Should Take This Class?
This course is appropriate for students in grades 6-9 who have mastered basic algebra up through solving linear equations and manipulating multi-variable expressions. Students who have completed our Introduction to Algebra A course should have sufficient background.
- To determine if you’re ready for the course, students can take the diagnostic pretest.
- To determine if you need this course, students can take the diagnostic post-test.
This course is roughly the same difficulty as our Introduction to Number Theory class. For those preparing for contests, this course should help with MATHCOUNTS and the AMC 8/10/12 tests.
Weekly Live vs. Self-Paced
Our weekly live class is designed for students who prefer a live group experience. In this format, students learn in an online classroom, engaging in real-time with their instructor and peers. For students interested in setting their own study schedule, we recommend considering the self-paced version of this course.
- Counting Lists of Numbers
- Counting with Addition and Subtraction
- Permutations
- Casework
- Complementary Counting
- Constructive Counting
- Counting with Restrictions
- Permutations with Repeated Elements
- Counting Pairs of Items
- Counting with Symmetries
- Combinations
- Combinatorial Identities
- Paths on a Grid
- Distinguishability
- Applications of Lessons 1-4
- Definition of Probability
- Counting Techniques in Probability
- Probability and Addition
- Complementary Probability
- Probability and Multiplication
- Probability and Dependent Events
- Using Symmetry in Problem-Solving
- Probability Using Lengths
- Probability Using Areas
- Definition of Expected Value
- Problem-Solving with Expected Value
- Constructing Pascal's Triangle
- Pascal's Triangle as Combinations
- More Combinatorial Identities
- Distributions
- Sticks and Stones
- The Hockey Stick Identity
- Proving the Binomial Theorem
- Applying the Binomial Theorem to Problems
- The Binomial Theorem in Identities
- Applications of Lessons 6-11
Required Textbook
Related course: Introduction to Counting and Probability
