Why is group theory the single greatest subject on God's green Earth?

Why is group theory the single greatest subject on God's green Earth?

what's an example of its use in engineering, CS, or social sciences

list one thing group theory is useful for
hard mode: no physics or chemistry or math

describes the symmetries of different minerals in geology.

prove it

I can't tell if I actually like group theory or if I'm just fond of it because it was the first time I was introduced to the novelties of abstract algebra

Everything after it (rings, fields, modules) was pretty uninspiring by comparison

You did groups before rings and fields? Interesting, I learned them before groups. I have to say that I find groups far more fascinating.

That is because you just heard about it.

true
im interested in algebraic algebra now

bump

Describes transformations in geometry and optics in a natural way.

Trivial example of crystal structure: All crystals which are on a regular cartesian grid. But well, one could probably argue that it is a flavour of chemistry as it's the organization of atoms in matter.

>Everything after it (rings, fields, modules) was pretty uninspiring by comparison


Did you just do the ring and field units in a typical intro algebra course? Or did you take full courses in commutative algebra and galois theory?

That is weird. Usually you do groups first and progressively add more structure, getting rings and fields.

In mathematics and abstract algebra, group theory studies the algebraic structures known as groups. The concept of a group is central to abstract algebra: other well-known algebraic structures, such as rings, fields, and vector spaces, can all be seen as groups endowed with additional operations and axioms.

Yes this is correct. Group is a more basic building block than rings and fields.

So that's it?
It's just a description? No special theorems that are useful in geometry of crystals or optics?

You have all the theorems about groups and subgroups of course. What they are useful for depends on which group you pick.

groups are nice but groupoids and monads are where the real math is

Astronomy seems the most god like to me.

You probably meant philosophy
It's alright user, I got your back

Semigroups find applications in CS, within automata theory especially.

This is what Evariste Galois invented overnight before he died right?

because you are an undergrad fag
with an iq of 110 with edgy beliefs.

>implying

group theory attracts people from all walks of education, even PhDs

>list one thing group theory is useful for
>except for each and every field it's used
wew lad

Haskell uses a lot of algebraic ideas.

Group theory is pretty essential in cryptography.

Social sciences analyze social networks and algebraic graph theory is a thing.

You'll find that it's mostly blue