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From students
"I tremendously learned a lot from this course. I am glad that I learned some powerful techniques. . . Thank you for the great teaching and thank you for offering this course."
"This was a great course and you can't find a better instructor than Mr. Patrick. I learned a lot about Counting and Probability from this course."
"I thoroughly enjoyed this course. Everything was explained clearly enough for me to understand, and I learned more than I ever expected. The problems posted both on the forum and on the midterm and final were challenging and fun."
"I loved the class and would like to thank you for offering such a wonderful opportunity. I learned a lot of useful stuff which I didn't know before and I am even more inspired to do math."
This course covers a variety of powerful tools in discrete mathematics, including clever one-to-one correspondences, principle of inclusion-exclusion, generating functions, distributions, pigeonhole principle, induction, constructive counting and expectation, combinatorics, recursion, and conditional probability. Discrete mathematics is an important area for computer science; students who complete this course will have a huge advantage when they encounter discrete mathematics in college.
Week 1: Review of Counting & Probability Basics
Week 2: Principle of Inclusion & Exclusion I
Week 3: Principle of Inclusion & Exclusion II
Week 4: Constructive Counting
Week 5: One-to-one Correspondences and Counting
Week 6: The Pigeonhole Principle
Week 7: Constructive Expectation
Week 8: Distributions
Week 9: Mathematical Induction and Fibonacci Numbers
Week 10: Recursion and Catalan Numbers
Week 11: Conditional Probability
Week 12: Combinatorial Identities
Week 13: Events with States
Week 14: Generating Functions I
Week 15: Generating Functions II
Week 16: Graph Theory I
Week 17: Graph Theory II
Week 18: Challenging Problems
Students should have a complete mastery of basic counting as described in the diagnostic test below before taking this course. Students should also have a solid algebra background through at least algebra II. Students who have completed the Art of Problem Solving Algebra 3 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 below to determine if this class is right for you.)
We recommend trying the following tests to determine whether the class is appropriate for you:
Are You Ready?
Do You Need This?
This course requires the textbook Intermediate Counting & Probability. There is a discount if you buy the text when registering for the course.
Future dates for this course have not been scheduled yet.
