Olympiad Level Counting - How Many Subsets of {1,…,2000} Have a Sum Divisible by 5?

This course teaches students how to count the number of subsets of a given set with a specific property, focusing on subsets of {1,…,2000} with a sum divisible by 5. The learning outcomes include understanding generating functions, clever uses of complex numbers for counting, and evaluation tricks. The course uses a teaching method that includes puzzle statements, simpler examples, generating functions, roots of unity, and final tricks. The intended audience for this course is individuals interested in combinatorics, generating functions, and advanced counting techniques.