You may want to download the lecture slides that were used for these videos (PDF).

## 1. Comparing Sequences & Hashes

In this video, we ask how we might determine whether two sequences are the same and introduce the idea of a hash. (6:50)

## 2. Fair Division

In this video we introduce the fair division problem. How might we solve such a problem, and determine whether a solution is in fact correct? (6:20)

## 3. Factoring

How can we factor very large numbers? In this video, we draw a connection between factoring and cryptography. (10:13)

## 4. Adding Fractions

Adding fractions requires finding a least common multiple – but how can we find one for very large integers? (2:33)