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

Wednesday
Jul 13 - Sep 28
7:30 - 9:00
PM ET
Jul 13 - Sep 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
$370 (~$31/week)
$419 w/books
$370 (~$31/week)
With Books $419
CLOSED
Friday
Jul 29 - Oct 14
7:30 - 9:00
PM ET
Jul 29 - Oct 14
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
$370 (~$31/week)
$419 w/books
$370 (~$31/week)
With Books $419
CLOSED
Sunday
Aug 21 - Nov 13
7:30 - 9:00
PM ET
Aug 21 - Nov 13
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
$370 (~$31/week)
$419 w/books
$370 (~$31/week)
With Books $419
ENROLL
Tuesday
Aug 30 - Nov 15
7:30 - 9:00
PM ET
Aug 30 - Nov 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
$370 (~$31/week)
$419 w/books
$370 (~$31/week)
With Books $419
ENROLL
Friday
Sep 16 - Dec 9
7:30 - 9:00
PM ET
Sep 16 - Dec 9
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
$370 (~$31/week)
$419 w/books
$370 (~$31/week)
With Books $419
ENROLL
Sunday
Sep 25 - Dec 18
7:30 - 9:00
PM ET
Sep 25 - Dec 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
$370 (~$31/week)
$419 w/books
$370 (~$31/week)
With Books $419
ENROLL
Friday
Oct 7 - Jan 13
4:30 - 6:00
PM ET  
Oct 7 - Jan 13
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
$370 (~$31/week)
$419 w/books
$370 (~$31/week)
With Books $419
ENROLL
Monday
Oct 17 - Jan 30
7:30 - 9:00
PM ET
Oct 17 - Jan 30
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
$370 (~$31/week)
$419 w/books
$370 (~$31/week)
With Books $419
ENROLL
Tuesday
Nov 8 - Feb 14
7:30 - 9:00
PM ET
Nov 8 - Feb 14
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
$370 (~$31/week)
$419 w/books
$370 (~$31/week)
With Books $419
ENROLL
Wednesday
Nov 30 - Mar 1
7:30 - 9:00
PM ET
Nov 30 - 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
$370 (~$31/week)
$419 w/books
$370 (~$31/week)
With Books $419
ENROLL
Friday
Dec 9 - Mar 10
7:30 - 9:00
PM ET
Dec 9 - Mar 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
$370 (~$31/week)
$419 w/books
$370 (~$31/week)
With Books $419
ENROLL

AoPS Holidays

There are no classes September 3‐5, October 31, November 21‐27, December 21‐January 3, and May 27‐29.

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 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.

The course really taught me how to think in a problem-solving fashion, and applying previous knowledge to new concepts and proofs. I learned a lot about how to prove things and how to explain them in a logical manner. I think it was a great course to begin studies in discrete mathematics.

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