You may want to download the lecture slides that were used for these videos (PDF).
1. Inclusion/Exclusion – Prelude
This video reviews material you have probably been exposed to in previous courses, and asks some motivating questions. (4:01)
2. Inclusion/Exclusion
This video gives a more precise treatment of inclusion/exclusion, and finds a formula for the number of elements in a set X which satisfy none of the properties in a list of properties. (8:29)
3. Derangements
In this video we introduce the concept of a derangement and provide some examples. (4:10)
4. A Formula for Derangements
This video uses the inclusion/exclusion formula to derive a formula for the number of derangements of [n]. (9:42)
5. The Hatcheck Problem
This video introduces a historically famous problem: the hatcheck problem. We will use derangements to analyze this problem. (3:02)
6. The Hatcheck Problem (Solution)
The hatcheck problem is solved in this video. It is our first example of a calculation that can be done quickly with inclusion/exclusion. Surprisingly, the probability that a random permutation of length n is a derangement approaches 1/e as n goes to infinity. (3:43)
7. Counting Surjections
As a second example, we introduce and explore a problem: counting surjections. (7:56)
8. A Formula for Surjections
This video introduces and derives a formula for surjections by using inclusion/exclusion. (3:26)
9. Counting Surjections with Our Formula
We return to our problem, calculating S(5,3), using our newly-derived formula. (2:21)
10. The Euler ϕ-Function
As a final example, we introduce the Euler ϕ-function, and explore how it can be calculated using inclusion/exclusion. In order to compute the ϕ-function of a number n efficiently, we need to know the prime factorization of n. (11:29)