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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.

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

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
FULL
Wednesday
Jun 7 - Oct 4
7:30 - 9:00
PM ET
Jun 7 - Oct 4
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
Friday
Jul 21 - Nov 17
7:30 - 9:00
PM ET
Jul 21 - 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
$410
$457 w/books
$410
With Books $457
ENROLL
Thursday
Oct 12 - Mar 1
7:30 - 9:00
PM ET
Oct 12 - 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
TBA $410
$457 w/books
$410
With Books $457
ENROLL

AoPS Holidays

There are no classes May 29, July 4, September 4, November 18 - 26, and December 21 - January 3.

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 think this course was really fun and challenging. I learned a lot, and really boosted my counting skills. I saw many cool topics, and loved it. Thanks AoPS!

ACS WASC
ACCREDITED
SCHOOL

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