Intermediate Counting & Probability Online Math Course
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Intermediate Counting & Probability

Topics 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

Diagnostics

ARE YOU READY? DO YOU NEED THIS?

Documents

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

Schedule

Tuesday
Oct 15 - Mar 3
7:30 - 9:00
PM ET
Oct 15 - Mar 3
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
$450
$501 w/books
$450
With Books $501
CLOSED
Wednesday
Mar 25 - Jul 22
7:30 - 9:00
PM ET
Mar 25 - Jul 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
$470
$521 w/books
$470
With Books $521
ENROLL
Summer 2020This course will be offered in Summer 2020. Click here to join our mailing list to be notified when the course schedule is available.

AoPS Holidays

There are no classes December 21–January 3, May 23–25, July 3–5, and September 5–7.

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

Lesson 1 Review of Counting and Probability Basics
Lesson 2 Principle of Inclusion & Exclusion
Lesson 3 Advanced Inclusion & Exclusion
Lesson 4 Constructive Counting
Lesson 5 One-to-one Correspondences
Lesson 6 One-to-one Correspondences Continued and Pigeonhole
Lesson 7 Constructive Expectation
Lesson 8 Distributions
Lesson 9 Mathematical Induction and Fibonacci Numbers
Lesson 10 Recursion and Catalan Numbers
Lesson 11 Conditional Probability
Lesson 12 Combinatorial Identities
Lesson 13 Events with States
Lesson 14 Generating Functions, Week 1
Lesson 15 Generating Functions, Week 2
Lesson 16 Graph Theory, Week 1
Lesson 17 Graph Theory, Week 2
Lesson 18 Bonus Topics and Challenging Problems

Required Textbook

Intermediate Counting & Probability
By David Patrick
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.

I enjoyed this class very much and learned quite a lot. Before I took the course, I was having a lot of difficulty with counting and probability, especially with distributions and expected value. Even the basic concepts were confusing to me at times, but over and over again throughout the course, the instructor's explanations and the homework assignments would bring the material into focus for me. I'm extremely glad I took the course, because the textbook alone wasn't enough.

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