Chapter 6: Homomorphism and the First Isomorphism Theorem in Group Theory

The isomorphism theorem is a very useful theorem when it comes to proving novel relationships in group theory, as well as proving something is a normal subgroup. But not many people can understand it intuitively and remember it just as a kind of algebraic coincidence. This video is about the intuition behind the idea of homomorphism - functions preserving group structures, and the closely related isomorphism theorem. This channel is meant to showcase interesting but underrated maths (and physics) topics and approaches, either with completely novel topics, or a well-known topic with a novel approach. If the novel approach resonates better with you, great! But the videos have never meant to be pedagogical - in fact, please please PLEASE do NOT use YouTube videos to learn a subject. There are second, third and even fourth isomorphism theorem (the fourth one is usually disputed), but all can be derived from the first one, using clever constructions of homomorphisms. Apparently, when I was typing the description (after the video is edited), I knew that the name "homomorphism" is probably mistranslated from German. Originally, it was supposed to mean "similar", not "same". This video series is about understanding the group theory intuitively, complementing how most people learn about it, because it is usually introduced as part of abstract algebra. Other than commenting on the video, you are very welcome to fill in a Google form linked below, which helps me make better videos by catering for your math levels: https://forms.gle/QJ29hocF9uQAyZyH6 If you want to know more interesting Mathematics, stay tuned for the next video! SUBSCRIBE and see you in the next video! If you are wondering how I made all these videos, even though it is stylistically similar to 3Blue1Brown, I don't use his animation engine Manim, but I will probably reveal how I did it in a potential subscriber milestone, so do subscribe! #mathemaniac #grouptheory #isomorphism #homomorphism Social media: Facebook: https://www.facebook.com/mathemaniacyt Instagram: https://www.instagram.com/_mathemaniac_/ Twitter: https://twitter.com/mathemaniacyt For my contact email, check my About page on a PC. See you next time!