Visual Group Theory, Lecture 1.1: What is a group?

Visual Group Theory, Lecture 1.1: What is a group?

In this lecture, we will introduce the concept of a group using the famous Rubik's cube. The formal definition will be given later, in Lecture 1.5. For now, we just want to provide the intuition.

[conradgarcia]

Thank you so much for this group theory lecture series. You provided a visual and intuitive explanation to one of the most profound and attractive subjects in mathematics. I'm looking forward to your next lectures.

[Pete-Prolly]

I thank you for this, and I REALLY thank you for using "Math vocabulary" instead of "cuber-vocabulary, " which has stipulative definitions for so many terms, like "parity, " (and a growing list of others.) I had a Rubik's as a kid but never solved one completely & unassisted until after I studied Group theory as an adult and changed the way I saw puzzles&problems.

[davidprice]

This lecture series is excellent. A very innovative approach to learning about group theory.

[robharwood]

I stumbled across Lecture 6.1, but before watching it, I immediately checked your channel for a playlist (you have some, yay!!) and started with this Lecture 1.1. After only a few minutes, I could tell your presentation and lecture style is excellent, and I've just subscribed to your whole channel! Thought I'd let you know how you gained an insta-subscribe. 😁 Really looking forward to this series, and probably your other ones as well!

P.S.: I'm a regular viewer of Prof. NJ Wildberger's channel, Insights Into Mathematics. He happens to have a 'controversial' position on the foundations of mathematics (which he explains in detail for those interested in such topics, in separate playlists), however my main point is that he also happens to be an excellent math lecturer as well. In other words, my interest in your channel/lectures is in some sense 'symmetrical' (to borrow an idea related to group theory 🤓😅) to my interest in Prof. Wildberger's channel/lectures. Just thought I'd let you know there's a similarity there. Cheers!

[aidanokeeffe]

I got so stuck on group theory, having had pandemic-aggravated senioritis when I was studying it for the first time. I'm hoping this will fill the gaps.

Thanks a lot for uploading the course, I will recommend it to some of my students. The idea of introducing the axioms by example in natural language first, then rephrasing them in a more formal statement is nice, but in this particular case I am not very convinced on how they match the usual group axioms -- e.g. associativity. I guess your reference to "sequences" of moves is an implicit statement of associativity that goes well with transformation groups, but does not fit well with more algebraic examples.

[puepx]

Best source about the subject. Greetings from Brazil.

[robharwood]

Here's an interesting question, sparked by your simple definition of a group: Is a Turing Machine (on, say, a k-symbol alphabet) a 'group'? Or rather, is the definition of the possible actions a Turing Machine can make (read a symbol on the (infinite) tape, write a symbol on the tape, move left on the tape, move right on the tape) a definition of a 'group'?

It seems to me from your definition that it would be a group. The actions are deterministic, reversible (assuming one of the 'symbols' is the 'blank' symbol), and any sequence of such actions can be considered an 'action' of its own (this is the basis of 'subroutines' in computer programming). Do you happen to know if this group has already been studied? Perhaps it already has an official name?

[cimtrae]

Prof. Macauley Thank you so much for this wonderful series. Any chance you could consider making a course on Geometric Algebra as well? It's becoming a very hot topic especially in Computer Graphics. But there are no courses that give intuitive understanding and also get someone proficient enough to start using it. Thank you.

[essadababneh]

please post MTHSC 851 and MTHSC 852 recordings. I saw the lecture notes and it is a shame that you have not posted your lectures. I will be very thankful if you do

[jy]

very clear and intuitive! Thank you, Professor Macauley!

[brendanchamberlain]

Thanks so much for making this lecture series open to the public!

[KulkarniSumant]

Infinitely many is a lose usage in maths unless it is really infinite!

[RARa]

First time I saw a youtube with zero dislikes..

[juanrandsonian]

only 12.5K subscribers??!! Come on! Dark times we live in...

[liviu]

Holy shit, this is 4th year content, no wonder I'm having a hard time.

[ycchen]

These lectures are great! Really appreciate it.
And also I would like to share a math study message here for anyone who might be interested: I would like to read <Presentations of Groups> by D. L. Johnson. And I would like to ask if anyone is interested to read together? Because having a reading partner will make study more fun, especially when go through detail proof together. You are also welcome to share this message to anyone who is interested. Thank you so much!

[bonbonpony]

10:00 Not all actions are generators. Generators are the subset of all possible actions in a group. You should read Nathan Carter's book more carefully :q

[jondollard]

Hi, on the very last comment in the summary is it correct to say 4.3x10^19 actions or rather should that read configurations? 6 actions (I.e. generators) make up the generating set for the rubiks cube.

[Darrida]

I wonder if Erno Rubik as an architect built any buildings?