Visual Group Theory, Lecture 1.1: What is a group?
Why Mathematics Stack Exchange recommends it
Mathematics Stack Exchange answerers point people to it as an intuitive, diagram-driven way into group theory, especially when learners feel the abstract axioms lack meaning.
Recommended by 5 people across 5 different months, 2017 to 2020.
What it is
The first lecture in Matthew Macauley's Visual Group Theory series from Clemson University. It introduces the idea of a group informally through the Rubik's cube, building intuition before the formal definition arrives in Lecture 1.5.
What people said
Strong rec Miksu · 2017-10 · Mathematics Stack Exchange · on “How can I visualise groups in Group Theory?”
Here is a very good and informative video series about groups: Visual Group Theory [this video] . The series covers a lot of stuff. Everything from the axioms to Galois Theory. Everything is visualized by diagrams and intuitive observations. Then there is this [LINK] video. It's the best video I've ever found about applying group theory. P.s. I know the feeling you have. When I was learning group theory, I was also struggling with the lack of intuition behind the theory. But once you get over it, you'll find group theory super interesting topic.
Strong rec Frenzy Li · 2018-05 · Mathematics Stack Exchange · on “Book suggestion for a first course in abstract algebra”
Slightly off topic... if you allow online lectures, I'd nominate Visual Group Theory [this video] , a series that visually illustrates many concepts along the learning curve. Great to binge watch for starters.
Recommends mlainz · 2017-12 · Mathematics Stack Exchange · on “Why is the fact that a quotient group is a group relevant?”
In this videos, the concept of quotient group is explained graphically. You might also find it helpul for understanding normal groups [this video]
Recommends SARTHAK GUPTA · 2019-11 · Mathematics Stack Exchange · on “How to explain mathematics to lay audience”
You can start with the symmetries of a square and introduce them to the dihedral groups. It is found very frequently in our surroundings. The logo of Mercedes-Benz, starfish, snowflakes are a few of the examples. All this is given in the first chapter of the book Contemporary Abstract Algebra by Joseph A Gallian which can be found here [LINK] You can also refer the two books namely: An inquiry-based approach to abstract algebra by Dana Ernst Visual Group Theory by Nathan Carter The lecture videos available here ( [this video] ) might also be helpful.
Recommends user1618033988749895 · 2020-04 · Mathematics Stack Exchange · on “Finding / Proving the Order of Dihedral and Symmetric Subgroups”
Lately I've been trying to follow along with this YouTube lecture series called "Visual Group Theory" [this video] by Clemson's Mathew Macauley and have had some issues grasping the concept of a group's "order".. I (think I) understand how it works when referring to reflections, rotations, etc. in the sense that we are looking for the $"k"$ value that makes $x^k = e$ so examples when looking at $D_4$ where $R = 90^\circ rotation$ and $F = horizontal flip$ : $|R^2| = 2$ since two rotations bring you halfway and so doing this twice will preserve it's footprint $|RF| = 2$ since when performing this on a piece of paper with numbered corners i got back to my original starting point after performing RF