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Intermediate Counting & ProbabilityTopics in discrete mathematics, including clever onetoone correspondences, principle of inclusionexclusion, generating functions, distributions, the pigeonhole principle, induction, constructive counting and expectation, combinatorics, systems with states, recursion, conditional probability, and introductory graph theory. 
18 weeks 
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 
Luis Ares 
$450
$501 w/books

$450
ENROLL
With Books $501

Spring 2020  This course will be offered in Spring 2020. Click here to join our mailing list to be notified when the course schedule is available. 
AoPS Holidays
There are no classes November 25–December 1, or 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  Onetoone Correspondences 
Lesson 6  Onetoone 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
An intermediate textbook in counting and probability for students in grades 912, containing topics such as inclusionexclusion, recursion, conditional probability, generating functions, graph theory, and more.
