/sci/ - Science & Math

>>10523891
somebody butthurt?

>>10523911
Give me 1 (one) applied use of upper level abstract algebra.

Don't give me easy group/ring theory shit as that's obvious and can be learned in like 2 weeks

>>10523916
i'm going to take that as a yes

>>10523891
Where did she touch your prime ideal domain?

>>10523916
Squaring the circle
Solving the quintic

>>10523891
Why does the cover look so bad?

>>10523891

>>10524572
It's abstract

>>10523919

Usefulness is in the eye of the beholder.
>>10523916
Public and private key cryptography (often involves finite fields and their rings of matrices and polynomials) and more generally, algebraic coding theory.
It's also a prereq to study tons of other mathematical subjects (e.g. algebraic geometry, algebraic topology) which are behind other non-trivial industry applications: https://www.quora.com/What-are-some-real-life-applications-of-abstract-algebra

>>10523916
Quantum field theory

>>10523916
practical uses
>error correcting codes that make disk storage secure and resistant to small failures
>compiler construction and comprehension
>All of modern cryptography
>justification/derivation of efficient algorithms in computers/electronic devices
>symbolic debugging

theoretical uses
>powerful results in TCS such as integer partitioning (which has direct relationships to phase transitions in statistical physics)
>generating functions
>Graph isomorphism
>coding theory
>Algebraic geometry and computational geometry
>all flavors of topology
>quantum field theory
>general relativity
>symmetry groups in physics
>quantum information
>particle physics (boson interactions)

These are only the results off the top off my head. Tell me if you want more. Algebra has been useful for a very, very long time. Don't mistake purity with lack of usability.

>>10525609
That kid who knows his shit but goes too fast to read the instructions
>>10525529
The kid who does both

>>10525690
intentional overkill

>>10523916
galois theory has applications in topology

>>10523916
Abstract Algebraic Neural Networks

>>10527001
>theoretical mathematics has applications to theoretical mathematics

>>10527568
>which has applications in applied mathematics which has applications all over STEM

>>10523916
NO BODY CARES ABOUT APPLICATIONS YOU SEETHING BRAINLET. GO BACK TO WHATEVER EE FORUM YOU CAME FROM YOU PISSANT!

>>10525609
dont humor the brainlet. let him wallow in his ignorance

>>10525609
>compiler construction and comprehension
>justification/derivation of efficient algorithms in computers/electronic devices
wtf I'm interested now?

>>10523956

you dont actually need a proof to know that these are impossible

literature

>>10525609
I know: Group theory gets used in quantum mechanics and elsewhere in physics, but the group theory used is trivial. E.g., never hear of Sylow's theorem, the Jordan-Holder theorem, the Feit and Thompson work on simple groups, etc. For group representations,you need to know very little about group theory to do group representations (I wrote my undergrad honors paper in it). Heck, I wrote a paper on multidimensional, distribution-free hypothesis tests based on groups of measure-preserving transformations, and the group theory needed was trivial. Similarly for the use of group theory in ergodic theory, ODE, and integer linear programming. Groups are nice, but really need to know only about 10 pages of the basics and can pick it up in an hour whenever need it. Or, you want group theory to attack Rubik's cube?

Yes, Hamming used some finite field theory in error correcting codes: Now that work and a dime won't cover a 10 cent cup of coffee. Instead, coding theory has moved on. Yes, yes, I know, from A. Wiles we finally have a proof of Fermat's last theorem; other than Wiles, who made any money with that?

Algebraic geometry is building expensive houses on-spec that stand empty too long. There's just no significant promise of return on investment there, or elsewhere in abstract algebra. E.g., the US NSA pushed hard on finite field theory for years before RSA showed that they had been wasting their time.

US mathematics' long, disastrous, self-destructive love affair with algebra, algebraic geometry, algebraic topology, algebraic number theory has been a major contributor to shrinking Federal research grants to mathematics, shrinking departments, mathematicians who'd swap their Ph.D. for an electrician's license, and the technology world putting mathematics on the back burner if not in the trash. Can cover nearly all abstract algebra in 1 word: Useless.

>>10529093
stale pasta

>>10529187
If I have a choice between taking Abstract Algebra 2 and categorical data analysis, what do?

If I have a choice between taking Abstract Algebra 2 and categorical data analysis, what do?

>>10529187
The pasta was from literally a month ago
Anyway I never understood this, since I took way more analysis than algebra (3 semester undergrad courses, 1 grad vs. 2 semester undergrad courses), albeit taking classes in other topics featuring algebra.

>>10524829
Wait... Is the title a reference to Crime and Punishment?

>>10529804
>The pasta was from literally a month ago

>>10529694
>If I have a choice between taking Abstract Algebra 2 and categorical data analysis, what do?
>>>/adv/

Ecology. It's just watered down chem/physics/clacl1/basic bio.

>>10529804
>moshi moshi? newfren desu

>>10523916
You can solve some Quantum Mechanic properties of molecules using some skills learned from abstract algebra