Is this really totally useless for economists?
Am I am a dumbass to actually take abstract algebra before?
Fields and algebras seem to be used in econometrics 1 (taking it this semester, didn't take abstract).You seriously don't have the slightest clue WTF you're talking about.
Sigma fields and borel sets aren't abstract algebra? I wouldn't know I didn't take it.
A sigma algebra is not what is mean by "algebras" in abstract algebra, even though it ends with the word "algebra".
https://en.wikipedia.org/wiki/Algebra_over_a_field
The only "field" you will ever work with is the field of real numbers and sometimes complex numbers.
"Field" theory also means something you will never ever see as an economist. I
http://www-iri.upc.es/people/thomas/Collection/details/57204.html
Fields and algebras seem to be used in econometrics 1 (taking it this semester, didn't take abstract).
You seriously don't have the slightest clue WTF you're talking about.
Sigma fields and borel sets aren't abstract algebra? I wouldn't know I didn't take it.
A sigma algebra is not what is mean by "algebras" in abstract algebra, even though it ends with the word "algebra".
https://en.wikipedia.org/wiki/Algebra_over_a_field
The only "field" you will ever work with is the field of real numbers and sometimes complex numbers.
"Field" theory also means something you will never ever see as an economist. I
http://www-iri.upc.es/people/thomas/Collection/details/57204.html
In fact, one would never even discuss sigma algebras in abstract algebra, since it is a structure that only comes up in measure theory, which is a different subject.
some guy was talking about algebraic geometry applications in economics: https://www.research-collection.ethz.ch/bitstream/handle/20.500.11850/72441/eth-7391-02.pdf
Probably has applicability in game theory from a google search but I really have no idea.
I'm sure one can find an example of one person somewhere using some type of obscure mathematical tool from some area of abstract algebra or orthomodular lattice theory once.
However, that does not mean that someone who is unsophisticated in math in the first place should take an elementary abstract algebra course.
Fields and algebras seem to be used in econometrics 1 (taking it this semester, didn't take abstract).You seriously don't have the slightest clue WTF you're talking about.
Sigma fields and borel sets aren't abstract algebra? I wouldn't know I didn't take it.
Econometrics I at 90% of schools is either course on mathematical statistics which is simply your probability course w/calclus on steroids. You may have *gasp* theorems and proofs. It is just a stats course.
Or it is a course on classical linear regression and different solutions when assumptions of OLS are. 95% of math whether your at Harvard or U Kansas will be linear algebra, math stats/probability and calculus. If your at a top department that aims to train econometric theory you might get to use *gasp* measure theory *gasp*. That only because measure theory can be used in probability.
Really when you see these math obsessed threads you can smell the undergrad. Majority of articles in top journals do not use that much math. They require you to understand what a regression is or a solution to an optimization problem is. Unless you plan on being a micro theorist a.ka. unemployed or HRM star : the only math you will ever need to read majority of papers is knowing how to basic matrix algebra, how to take a partial derivative and understanding how to read/write a proof/theorem.
The main reason you will ever use advanced mathematics or see it is for generalization. Optimization problems described in terms of compact sets, fixed points are far more general than assuming functional forms like CRRA utility or cobb douglass production. However, it is far more common to see the latter than the former.
To be fair, lattices are usually thought of by mathematicians as abstract algebraic objects, and these have found some use in economics.
That said, you're probably better off just learning directly the 1-2% that is applicable, than trying to sift through the 98% that smarter people have thought about and decided isn't worth the bother trying to use.
There's been some recent developments by Drinfeld-Kontsevich-Lurie wherein one uses etale cohomology to develop a model where a group of people can use to jointly choose a collective good for themselves. Each person can buy votes for or against a proposal by paying into a fund the square of the number of votes that he or she buys. The money is then returned to voters on a per capita basis.
https://link.springer.com/article/10.1007/s00182-017-0577-7
So can anyone tell me wtf this is?
It's combinatorial game theory but instead of being on some sort of discrete stucture (network , grid, board, etc.) it is played on an Abelian group. It has some superficial similarities to the Banach-tarski game by the look of it but is otherwise unrelated.