**Topics from today's class**:

- Connected sum
- Composite knots
- Prime knots
- Analogies between multiplication of positive the positive integers and the connected sum of knots
- The unknot is not composite
- Prime decomposition theorem for knots
- Oriented knots
- Invertible knots
- The Reidemeister theorem

**Homework**:

- 1.8
- In class I mentioned that we do not actually need both type I Reidemeister moves. By giving a sequence of pictures, show that we can accomplish the Reidemeister move shown below using the other type I move, together with moves II and III.

**Presentations**:

- I'll take volunteers

**Read for next class**:

- Sections 1.4