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Introduction to Counting & Probability

Fundamentals of counting and probability, including casework, multiplication, permutations, combinations, Pascal's triangle, probability, combinatorial identities, and the Binomial Theorem.

12 lessons

Diagnostics

ARE YOU READY? DO YOU NEED THIS?

Documents

SYLLABUS
12 lessons ARE YOU READY? DO YOU NEED THIS? SYLLABUS  

Schedule

Thursday
Mar 2 - May 18
7:30 - 9:00
PM ET
Mar 2 - May 18
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
$380 (~$32/week)
$429 w/books
$380 (~$32/week)
With Books $429
CLOSED
Sunday
Mar 19 - Jun 11
7:30 - 9:00
PM ET
Mar 19 - Jun 11
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
$380 (~$32/week)
$429 w/books
$380 (~$32/week)
With Books $429
ENROLL
Monday
Mar 20 - Jun 12
7:30 - 9:00
PM ET
Mar 20 - Jun 12
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
$380 (~$32/week)
$429 w/books
$380 (~$32/week)
With Books $429
ENROLL
Friday
Apr 7 - Jun 23
7:30 - 9:00
PM ET
Apr 7 - Jun 23
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
$380 (~$32/week)
$429 w/books
$380 (~$32/week)
With Books $429
ENROLL
Tuesday
Apr 25 - Jul 18
7:30 - 9:00
PM ET
Apr 25 - Jul 18
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
$380 (~$32/week)
$429 w/books
$380 (~$32/week)
With Books $429
ENROLL
Sunday
May 14 - Aug 6
7:30 - 9:00
PM ET
May 14 - Aug 6
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
$380 (~$32/week)
$429 w/books
$380 (~$32/week)
With Books $429
ENROLL
Thursday
May 25 - Aug 10
7:30 - 9:00
PM ET
May 25 - Aug 10
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
$380 (~$32/week)
$429 w/books
$380 (~$32/week)
With Books $429
ENROLL
Tuesday
May 30 - Aug 22
4:30 - 6:00
PM ET  
May 30 - Aug 22
4:30 - 6:00 PM Eastern
3:30 - 5:00 PM Central
2:30 - 4:00 PM Mountain
1:30 - 3:00 PM Pacific
Click here to see more time zones
$380 (~$32/week)
$429 w/books
$380 (~$32/week)
With Books $429
ENROLL
Friday
Jun 16 - Sep 1
7:30 - 9:00
PM ET
Jun 16 - Sep 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
$380 (~$32/week)
$429 w/books
$380 (~$32/week)
With Books $429
ENROLL
Tue & Thurs
Jul 11 - Aug 17
1:00 - 2:30
PM ET  
Jul 11 - Aug 17
1:00 - 2:30 PM Eastern
12:00 - 1:30 PM Central
11:00 - 12:30 PM Mountain
10:00 - 11:30 AM Pacific
Click here to see more time zones
$380
$429 w/books
$380
With Books $429
ENROLL
Sunday
Jul 30 - Oct 22
7:30 - 9:00
PM ET
Jul 30 - Oct 22
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
$380 (~$32/week)
$429 w/books
$380 (~$32/week)
With Books $429
ENROLL
Wednesday
Aug 9 - Oct 25
7:30 - 9:00
PM ET
Aug 9 - Oct 25
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
$380 (~$32/week)
$429 w/books
$380 (~$32/week)
With Books $429
ENROLL
Fall 2023This course will be offered in Fall 2023. Click here to join our mailing list to be notified when the course schedule is available.

AoPS Holidays

There are no classes May 27‐29, July 4, September 2‐4, October 31, November 20‐27, and December 21‐January 3, 2024.

Who Should Take?

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. 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.

Lessons

Lesson 1 Lists, Venn Diagrams, Addition, Multiplication
Lesson 2 Casework, Constructions, and Restriction
Lesson 3 Overcounting and Combinations
Lesson 4 Combinations and Distinguishability
Lesson 5 Challenging Problems Day
Lesson 6 Introduction to Probability
Lesson 7 Probability and Arithmetic
Lesson 8 Geometric Probability, Think About It!, and Expected Value
Lesson 9 Pascal's Triangle and Identities
Lesson 10 Distributions and The Hockey Stick Identity
Lesson 11 The Binomial Theorem
Lesson 12 Challenging Problems Day 2

Required Textbook

Introduction to Counting & Probability
By David Patrick
A thorough introduction for students in grades 7-10 to counting and probability topics such as permutations, combinations, Pascal's triangle, geometric probability, basic combinatorial identities, the Binomial Theorem, and more.

I liked this class. The concepts seemed interesting and new and much better than what I would learn in school. I learned a lot about combinations and how they work. I really enjoyed this class.

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