To solve the vortex velocity equations under certain conditions, I need to know some algebraic geometry in projective space. To that end, I'm outlining Ideals, Varieties, and Algorithms by Cox, Little, and O'Shea. Here, I'll share my notes and videos for selected sections from chapters 1-4 and 8. Learn with me!
In this playlist, I work through the major results and some examples
from the Cox, Little, and O'Shea text. To see links to all videos on the playlist,
hover over the three stacked lines in the top right corner of the video window.
The playlist is a work-in-progress. I plan to cover selected sections from chapters
1-4 and 8. I hope to finish the playlist by the end of the Spring 2021 semester.
I occasionally make errors - that's part of doing math!
If you see something, say something. ;)
Chapter 1 introduces foundational notation and terminology, including a discussion of polynomials, polynomial rings, affine varieties, ideals, and some techniques and results in k[x] that suggest techniques and results that will be used in k[x1,...,xn]. The study guide includes interesting questions, learning outcomes, and problem sets for the chapter.
Most of the notes below are accessible pdfs created in MS Word, but I've recently had requests for pdfs of the notes I create in my videos. I plan to scan and post those here when available as well. Some of the notes for the earliest videos have already been recycled, so they will not be made available.