What's the motivation for learning abstract algebra?

>math is useful for X
>except it's not really useful for X, it just provides a way to formally describe the way X works
>X would work fine without math
>but because we know how X works, we were able to generalize it and make a more useful X

Abstract algebra is when you take some object you know and love, like the integers, and you write down only the properties you care about, and then consider all possible objects satisfying those properties.

By proving things about this collection of objects you gain insight into the integers (not to mention all these other objects you looked at) and not only that, but the truths you derive are true of the integers precisely because the integers have membership in this class of objects.

A lot can be said about how groups and group actions are objects abstracting symmetry, or rings generalize arithmetic, but regardless of whether these objects have other uses, hiding some of the irrelevant facts about a specific object can be helpful in learning about that object.

Symmetry makes things easier. Physicists have been using this observation for a very long time.

Why do people who know nothing about a topic make up facts to support their views on said topic?

>Cryptography
>CS monkeys don't go near this.
wot?

Math is for beta cucks too afraid to do Physics.

>says the animeposter pedo beta cuck

so what if I like qt girls? enjoy that granny whos been fucked by several Jamals

/thread
this covers pretty much all basic motivations

>Thinks learning RSA is learning crypto

Physics is shit tier because it is related to the real world, and the world itself is so full of niggers that being interested in it makes you so bad an omegacuck you become a megacuck

Programming itself (Software Engineering) does not but programming language theory (CS) does.

At my university crypto is all done between the pure math and comp sci departments. Courses are listed under both math and comp sci and students take both.

That said my university used to be really big into crypto and the crypto emphasis in both computer science and math has lost a lot of popularity over time. I have no idea if other universities mainly handle crypto in engineering but this is the first I've heard of it.

you start from set theory, take a nonempty set S and give it an operation on its elements, then give some basic rules for this operation (closure, associativity, commutativity, etc.) Each time you add a rule you get a new object.

You can go further by adding more operations and also giving S special elements like 0 or 1 which are neutral for those operations.

By changing what S is and also the rules of the operation ( + = max(a,b) , etc..). You get a bunch of different algebraic systems.

Mathematicians look at all these things and ask questions like: what's the difference between these different "algebras"? Do they behave like the integers, like the real numbers, like ...?

This allows you do find crazy systems where you're doing addition of sets of functions , or finding the "greatest common divisor" of a set of polynomials, etc.. It opens a door for a lot of weird shit and mathematicians like that. And of course I ahven't even mentioned about the links to other areas of math like geometry and topology.

...