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.

This course is University of California a-g approved. Click here for more details.

18 weeks

Diagnostics

ARE YOU READY? DO YOU NEED THIS?

Documents

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

Schedule

Thursday
Oct 13 - Mar 2
7:30 - 9:00
PM ET
Oct 13 - 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
$390
$437 w/books
$390
With Books $437
Monday
Feb 27 - Jul 3
7:30 - 9:00
PM ET
Feb 27 - Jul 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
$410
$457 w/books
$410
With Books $457
ENROLL
Summer 2017This course will be offered in Summer 2017. Click here to join our mailing list to be notified when the course schedule is available.

AoPS Holidays

There are no classes May 29 or July 4.

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 have loved every Art of Problem Solving course I have ever taken, but this one may have been my favorite of all. Every week, I learned many new concepts, and Counting & Probability turned from my least favorite area of math to one of my favorites. The instructor was very knowledgeable and helpful. I look forward to taking more Art of Problem Solving classes in the future!

ACS WASC
ACCREDITED
SCHOOL

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