A peek into the world of Riemann surfaces, and how complex analysis is algebra in disguise. Secure your privacy with Surfshark! Enter coupon code ALEPH for an extra 3 months free at https://surfshark.deals/ALEPH. Help fund future projects: https://www.patreon.com/aleph0 An equally valuable form of support is to simply share the videos. SOURCES and REFERENCES for Further Reading: This video is a quick-and-dirty introduction to Riemann Surfaces. But as with any quick introduction, there are many details that I gloss over. To learn these details rigorously, I've listed a few resources down below. (a) Complex Analysis To learn complex analysis, I really like the book "Visual Complex Functions: An Introduction with Phase Portraits" by Elias Wegert. It explains the whole subject using domain coloring front and center. Another one of my favorite books is "A Friendly Approach To Complex Analysis" by Amol Sasane and Sara Maad Sasane. I think it motivates all the concepts really well and is very thoroughly explained. (b) Riemann Surfaces and Algebraic Curves A beginner-friendly resource to learn this is "A Guide to Plane Algebraic Curves" by Keith Kendig. It starts off elementary with lots of pictures and visual intuition. Later on in the book, it talks about Riemann surfaces. A more advanced graduate book is "Algebraic Curves and Riemann Surfaces" by Rick Miranda. SOCIALS Follow me! Twitter: @00aleph00 ___ MUSIC CREDITS: The song is “Taking Flight”, by Vince Rubinetti. https://www.vincentrubinetti.com/ 00:00-00:54 Intro 00:55-04:30 Complex Functions 4:31-5:53 Riemann Sphere 5:54-6:50 Sponsored Message 6:51-11:06 Complex Torus 11:07-11:50 Riemann Surfaces 12:11-13:53 Riemann's Existence Theorem