Introduction to Group Theory

A more high brow video. An introduction to group theory - the mathematics of symmetry. This is what I really study.

[luisfmh]

I'm a first year math student and I like to look up my professor's field of study, but most of the time it's hard to understand what it is that they're studying. Like I hear algebra or topology and I think I understand what it means but when I look it up I end up more confused. I think it would be awesome if professors (at least the ones teaching first and maybe second year courses) would do a video or presentation in layman's terms about what it is that their specialization is in. Sort of like this video!

[bobbobson]

2:13 I never knew James was such a small man.

[NoriMori]

"Group theory is the study of symmetry."

I certainly wasn't expecting _that_. 12 seconds in and my mind is already blown.

[bboyHarrypotter]

Can you do an entire series on this? I would watch it and give you my first child.

[LiiMuRi]

As a solid state chemist I come across symmetry and space groups all the time. It's a very important part of developing new materials. Thanks for all the mathematicians who have worked on the subject and thus made my work a it easier. :)

[ARVash]

Very interesting, I had heard of group theory before but never knew what it was about. thanks for taking time to give a bird's eye view about the subject. I'd love to see ones on other types of math like this.

[LydellAaron]

Thank you for sharing your interest. Your explanation was very helpful. I liked your insight into shuffling and the potential applications therein.

[KaelynWillingham]

Oh my god, group theory sounds SO interesting. Abstract algebra seems really cool, from my brief research.

[singingbanana]

@dylanparker72 Groups act by permuting elements of a set, or by being written as a matrix and acting on a vector space. Symmetric groups permute the numbers 1 to n - like the cards in the video. Dihedral groups permute the corners of polygons - like the square in the video. The General Linear Group is the group of matrices and acts on vectors. So does the Special Linear Group, preserving volume, and the Orthogonal Groups, preserving length and angle.

[MusIsWorld]

I've been looking for this kind od video for a long time. Simple and clear Introduction to these higher mathematics. Just so I can have a basic idea about this kind of math. Thank you very much sir. I'm reaLly hoping you would do this more often.

[gerat]

not only that, but as you get to groups with more structure on them and when viewed homologically, there are entire classes of groups that are homomorphic, or even different entirely with the same homological properties (preserving 'exactness', preserving certain properties like 'solvability') not only on these classes of groups, but on describing all the possible maps between such groups (which is often another group, or a ring).

[kanga]

these are pretty advanced inorganic chemistry theorys, but if you're interested, here's a few:
we use symmetry to simplify Schrodinger equations, so we don't have to do calculations for the whole molecule. other examples include
-ligand to metal charge transfer theory,
-spectroscopic theories
-coordination chemistry
-nomenclature of molecules
and many others

[singingbanana]

Exactly, like my examples you want to rotate the pieces until you get back to where you started - the solved position. The maths for the Rubik groups is quite advance and might not be accessible in a short video, but I might try in the future.

[erthx]

Very clear introductory instruction. For a mathematician your quite good at turning formalism into common sense.

[joshuawassef]

I always thought what I learned in abstract algebra was totally useless. You explained it better in a couple of minutes. Thanks, dude.

[MichyQuint]

Keep sharing your knowledge and enthusiasm for math. You've inspired me to continue my studies.

[juanjoseguva]

You are everything that's right with this world, it inspires faith in humanity. I love knowing that there actally are people out there that find maths and such to be true beauty, and not the jersey shore.

[WorldOfDeepThought]

Very interesting topic. Any video recommendations to learn about this?

[theboombody]

I'm glad I found this channel. I stopped my mathematical study at the undergraduate level, when I took real analysis and found out how calculus worked. For some reason I avoided the group theory classes.

I do have some interest in cardinality though, and its paradoxical implications. I've argued with VeritySeeker before, and he's a good mathematical youtube source as you mention in another comment. You're a bit more user friendly though.

[ssankoo]

Nice video, I really like that you tell us what you do in an understandable way. Thanks!