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 weeks

Diagnostics

ARE YOU READY? DO YOU NEED THIS?

Documents

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

Schedule

Tuesday
Jun 22 - Sep 7
7:30 - 9:00
PM ET
Jun 22 - Sep 7
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
$355
$400 w/books
$355
With Books $400
CLOSED
Tuesday
Jun 22 - Sep 7
7:30 - 9:00
PM ET
Jun 22 - Sep 7
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
$355
$400 w/books
$355
With Books $400
FULL
Thursday
Jul 22 - Oct 7
7:30 - 9:00
PM ET
Jul 22 - Oct 7
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
$355
$400 w/books
$355
With Books $400
ENROLL
Monday
Aug 16 - Nov 8
7:30 - 9:00
PM ET
Aug 16 - Nov 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
$355
$400 w/books
$355
With Books $400
ENROLL
Wednesday
Sep 1 - Nov 17
7:30 - 9:00
PM ET
Sep 1 - Nov 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
$355
$400 w/books
$355
With Books $400
ENROLL
Friday
Sep 17 - Dec 10
7:30 - 9:00
PM ET
Sep 17 - Dec 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
$355
$400 w/books
$355
With Books $400
ENROLL
Tuesday
Sep 21 - Dec 14
4:00 - 5:30
PM ET 
Sep 21 - Dec 14
4:00 - 5:30 PM Eastern
3:00 - 4:30 PM Central
2:00 - 3:30 PM Mountain
1:00 - 2:30 PM Pacific
Click here to see more time zones
$355
$400 w/books
$355
With Books $400
ENROLL
Sunday
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
$355
$400 w/books
$355
With Books $400
ENROLL
Thursday
Oct 21 - Jan 27
7:30 - 9:00
PM ET
Oct 21 - Jan 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
$355
$400 w/books
$355
With Books $400
ENROLL
Monday
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
$355
$400 w/books
$355
With Books $400
ENROLL
Wednesday
Dec 1 - Mar 2
7:30 - 9:00
PM ET
Dec 1 - Mar 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
$355
$400 w/books
$355
With Books $400
ENROLL
Sunday
Dec 12 - Mar 13
7:30 - 9:00
PM ET
Dec 12 - Mar 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
$355
$400 w/books
$355
With Books $400
ENROLL

AoPS Holidays

There are no classes September 4–6, October 31, November 22–28, and December 20–January 2.

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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