NOTES

# Algebraic Topology

My good friend Chuck assuaged my fears about studying under NJ Wildberger (“will my brain explode if I give up Real numbers?“), so I am returning to his videos, which I find super helpful for a junior mathematician gathering the tools they need for the epic climbs they are planning (at least that’s the prevailing metaphor I’ve been feeling in my studies). I had started the differential geometry series, but am backing that off even further to the Algebraic Topology series, and will use this article to keep track of key terms from the course.

## Lecture 1

**Homeomorphism** maps the topological similarity of two shapes, with the classic example
being the doughnut and the coffee cup.

**Algebraic Varieties** are sets of solutions of a system of polynomial equations
over the “Real” numbers.