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 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.