Initially I had sped through this section, not paid much attention to it and moved straight onto chapter 20. See, my assignment seems to give me a choice of whether to answer a question on fields and geometry from chapter 19, or to answer a question on cryptography from chapter 20. Cryptography sounded far more interesting (and something you could easily apply in code!), so I kind of skipped chapter 19 entirely.
I got half-way thought chapter 20 and found out online that nothing from chapter 20 will actually be in the exam. The exam contributes to 80% of my final grade for this module, so picking my battles, I dropped chapter 20 and returned to chapter 19.
In an apparent change of pace, chapter 19 was laid out into just two sections. The first was revisiting field extensions, introducing some more nuanced facts about them. The second was an introduction to ruler and compass constructions, providing proofs of why you can't trisect the angle and why you can't square the circle. It was interesting, but very involved. Especially when you're left to your own devices trying to prove why other geometric constructions might not be possible.
Now for a very quick write-up of chapter 20... :/