Discover Algebraic Topology & Homology: A Beginner's Guide 📚

An introduction to homology, a key concept in algebraic topology. Take your personal data back with Incogni! Use code ALEPH at the link below and get 60% off an annual plan: http://incogni.com/aleph. Help fund future projects: https://www.patreon.com/c/aleph0 An equally valuable form of support is to simply share the videos. This video is a collaboration with Trevor from the channel Mathemaniac. Check out his video here: https://www.youtube.com/watch?v=H6YofGjvZIQ&ab_channel=Mathemaniac. A HUGE thank you to Brendan Shuttleworth for working with me to make the script and storyboard for this video. You rock Brendan! NEWSLETTER I have a weekly math newsletter where I collate resources to self-study a specific topic and deliver it to your inbox. if this is interesting to you, fill out the form below to signup: https://forms.gle/Rt1f5StAj3yZtakE6 SOURCES and REFERENCES for Further Reading: This video is a quick-and-dirty introduction to homology. But as with any quick introduction, there are details that I gloss over for the sake of brevity. To learn these details rigorously, I've listed a few resources down below. (a) Video Lectures by Pierre Albin: https://www.youtube.com/playlist?list=PLpRLWqLFLVTCL15U6N3o35g4uhMSBVA2b (b) “Algebraic Topology” by Allen Hatcher: https://pi.math.cornell.edu/~hatcher/AT/ATpage.html CORRECTIONS: 12:59 You take n-cycles/(n+1)-boundaries not n-chains. Follow me! Twitter: @00aleph00 ___ MUSIC CREDITS: The song is “Taking Flight”, by Vince Rubinetti. https://www.vincentrubinetti.com/ 00:00-1:11 Intro 1:11-2:15 The Overall Idea 2:25-4:25 Cells 4:25-6:15 The Circle 6:15-7:00 Sponsored Message 7:00-8:55 The Torus 8:55-11:10 Homology, in general 11:10-14:37 Singular Homology