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?

SYLLABUS
18 weeks

### AoPS Holidays

There are no classes May 29–31, July 3–5, and September 4–6.

### 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!