math course selection

[preparephd]

Hi everyone,

 

I'm trying to choose between group theory and adv prob and stat (which will talk about Bayesian Stat). Which one is more useful?

I am planning to take real analysis and econometrics for sure and I want one more math class. Math department divides abstract algebra into 2 classes: group theory, ring and field.

Both group theory and adv prob and stat won't be offered again next year and ring and field will be offered next year.

My concern is if I should take ring and field, I might be better off to have some background in group theory as well.

FYI, I have taken both prob and stat. did very well in stat and did not so well as I expected in prob.

Please give me advice.

[bayesian]

Depends what you're taking the courses for. If it's math for math's sake, I think algebra is a much nicer subject than most stuff in analysis and probability (with the possible exception being some areas in functional analysis that are very elegant). If it's for econ-related stuff, the probability course is the way to go.

[preparephd]

^ bayesian, my goal is to attend econ phd program.

[Catrina]

What are your research interests, what range of programs are you targeting, and how confident are you about getting an A in each course? Edited April 16, 2014 by Catrina

[Food4Thought]

If I am just ignorant, someone correct me; however, I am not aware of a direct application of abstract algebra to economics. It seems like a neat class, and might be fun. If you want to take courses only because they are useful for the PhD in Econ, my gut instinct says to take the probability.

 

But to repeat Catrina's point, you must also be strategic about your choice. You must also account for the probability of getting A's in the respective courses.

[preparephd]

I have heard from many people that taking abstract algebra can be a strong signal. For grade,I get A on both proof class and stat class but I'm not sure how much harder adv stat and abstract algebra will be. I expect both classes to be small (about 10 people) and profs here curves the grade. So far I think I'm interested in macroecon, specifically international finance and public finance, but my interests might change as I still have two more years to explore.

[Catrina]

Both classes would be strong signals, so it would make sense to take the one that is more relevant for what you want to do. In this case, that is almost certainly the advanced probability and statistics course.

[rocketman87]

If I am just ignorant, someone correct me; however, I am not aware of a direct application of abstract algebra to economics. It seems like a neat class, and might be fun. If you want to take courses only because they are useful for the PhD in Econ, my gut instinct says to take the probability.

 

But to repeat Catrina's point, you must also be strategic about your choice. You must also account for the probability of getting A's in the respective courses.

 

 

When proving a Nash-Equilibrium in game theory, you need to know Brouwer's fixed point theorem, (or i guess you could prove using The Kakutani fixed point theorem), you must know some algebraic topology, which in order to do that you need some analysis and abstract algebra (modern algebra depending on what school). So yeah, abstract algebra helps.

[Noodles]

When proving a Nash-Equilibrium in game theory, you need to know Brouwer's fixed point theorem, (or i guess you could prove using The Kakutani fixed point theorem), you must know some algebraic topology, which in order to do that you need some analysis and abstract algebra (modern algebra depending on what school). So yeah, abstract algebra helps.

 

I was about to point this out. Abstract Algebra isn't necessary in special cases of Brouwer's fixed point, but in some more general treatments, Algebra is necessary and very useful. Also, abstract algebra can be useful to those interested in theoretical Econometrics, some of the more technical material in mathematical statistics and inference can be dealt with using some elementary abstract algebra.

[preparephd]

I was about to point this out. Abstract Algebra isn't necessary in special cases of Brouwer's fixed point, but in some more general treatments, Algebra is necessary and very useful. Also, abstract algebra can be useful to those interested in theoretical Econometrics, some of the more technical material in mathematical statistics and inference can be dealt with using some elementary abstract algebra.

 

If that's the case, between group theory and ring and field, which one is more important? At my college, group theory is not a prerequisite for ring and field. Do you recommend skipping group theory (and taking adv prob and stat next semester) and taking ring and field next year? Or should I do both group theory and ring and field in sequence. At least I have classical prob and stat in my hands but I do not have any algebra. For the sake of balancing workload, will that be ok to take both real analysis and abs algebra at the same time?

[Noodles]

If that's the case, between group theory and ring and field, which one is more important? At my college, group theory is not a prerequisite for ring and field. Do you recommend skipping group theory (and taking adv prob and stat next semester) and taking ring and field next year? Or should I do both group theory and ring and field in sequence. At least I have classical prob and stat in my hands but I do not have any algebra. For the sake of balancing workload, will that be ok to take both real analysis and abs algebra at the same time?

 

I have found group theory more useful, on the level of Artin or Dummit and Foote.

 

That being said, if your adv prob and stat class will cover Bayesian methods, I think that would be more applicable than Groups or Rings and Fields. I was just pointing out that abstract algebra can be used in economics, albeit scarce, subtle and sometimes indirect.

 

As for taking both RA and Abstract Algebra, I think it would depend on the level of the abstract algebra course. In my experience, courses dedicated to group theory and Rings and Fields separately are more manageable as they usually progress at a good pace.

[chateauheart]

Groups are used in algebraic topology more so than rings and fields, but there's not that much overlap in the topics covered. It's a stretch to say you need to take abstract algebra to understand fixed-point theorem proofs.

[to2012]

I think it's pretty unambiguous that a probability and statistics course is going to be more useful in economics than abstract algebra. I'm sure that people doing high-level theory use all kinds of mathematics, but only a very,very small portion of economics are doing those things. Really, I think that it is pretty clear that OP should take probability and stats. Probability appears everywhere in economics, even outside of econometrics. The more you've seen of it, the better.