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View Full Version : Course Selection Advice needed Again



JQX
10-29-2014, 04:34 AM
My last term of undergrad but I can only choose one from the following 3 math courses:

1.Elementary Numerical Analysis
2.Complex Analysis
3.Abstract Algebra



What are your suggestions? Thanks in advance!

Econhead
10-29-2014, 04:54 AM
I am not familiar with complex analysis, but I advise strongly against abstract algebra. I have not witnessed any applicability (personally), unless you consider mental summersaults applicable. Further, I have only seen one user indicate that they thought that it was adaptable.

JQX
10-29-2014, 04:56 AM
I am not familiar with complex analysis, but I advise strongly against abstract algebra. I have not witnessed any applicability (personally), unless you consider mental summersaults applicable. Further, I have only seen one user indicate that they thought that it was adaptable.

thanks for your input, econhead.

Ok, then I get to choose between Numerical Analysis or Complex Analysis

Insti
10-29-2014, 05:41 AM
I would say numerical analysis is slightly more useful than complex analysis. It will teach you a bit about programing matlab to solve stuff for you which is useful for some types of macro and finance.

fantinity
10-29-2014, 10:08 AM
I think, complex analysis and abstract algebra are both completely useless. It's that part of math they don't use in econ.

Numerical analysis is ok, matlab can really help in graduate studies.

econphd14
10-29-2014, 04:16 PM
Numerical analysis is the most useful, while complex analysis will be the best preparation, as it tends to be the most rigorous.

Python7768
10-29-2014, 05:27 PM
I think, complex analysis and abstract algebra are both completely useless. It's that part of math they don't use in econ.

Numerical analysis is ok, matlab can really help in graduate studies.

I agree that numerical analysis is a good one, and maybe even the best of these choices (although I'm biased because I think computational work is fun).

IMHO, people can go a little too far overboard on complex analysis and abstract algebra being completely useless... It may not be particularly useful if you are doing mostly applied work, but many of the breakthroughs in economic theory come because there is a problem that no one can solve until someone finds the right tool (often that tool is found within mathematics). Abstract Algebra may not be terribly useful in first year courses, but it may become useful if someone finds the right problem to solve with it. One example where it was used is proving Brouwer's Fixed Point theorem which is used to show existence of NE. Also, Complex Analysis is useful in econometrics.

chateauheart
10-29-2014, 05:49 PM
^I don't think first courses in abstract algebra generally cover any algebraic topology. Unless someone is absolutely interested in being not just a theorist but a 'foundational' game theorist (assuming you will be coming from a top program as well - because the market will be atrocious), investing in a sequence of courses in algebra and then algebraic topology is a purely recreational pursuit.

fantinity
10-29-2014, 07:14 PM
Well, I fail to see how complex analysis can be used anywhere in economics (that may be short-sided, however). I studied the advanced one three years ago in undergrad, and since then I've done a good deal of grad courses and read a lot of papers. Complex numbers never came up once, while matlab was very useful. Then again, I never specialized in econometrics -- how would you use it there?

JQX
10-30-2014, 05:00 AM
I agree that numerical analysis is a good one, and maybe even the best of these choices (although I'm biased because I think computational work is fun).

IMHO, people can go a little too far overboard on complex analysis and abstract algebra being completely useless... It may not be particularly useful if you are doing mostly applied work, but many of the breakthroughs in economic theory come because there is a problem that no one can solve until someone finds the right tool (often that tool is found within mathematics). Abstract Algebra may not be terribly useful in first year courses, but it may become useful if someone finds the right problem to solve with it. One example where it was used is proving Brouwer's Fixed Point theorem which is used to show existence of NE. Also, Complex Analysis is useful in econometrics.


Thanks for you advice. Yes, that's what I am considering about. Numerical Analysis may be very useful in some applied work(Using Matlab). But Complex Analysis is more theretical and more proof-intensive. Some fancy theory in economics may utilize stuff from complex analysis (I just guess)

Will taking complex Analysis and getting a good grade in this course give the adcom a better signal than taking numerical analysis ?

Insti
10-31-2014, 03:34 PM
Thanks for you advice. Yes, that's what I am considering about. Numerical Analysis may be very useful in some applied work(Using Matlab). But Complex Analysis is more theretical and more proof-intensive. Some fancy theory in economics may utilize stuff from complex analysis (I just guess)

Will taking complex Analysis and getting a good grade in this course give the adcom a better signal than taking numerical analysis ?


No area of econ utilizes complex analysis. Have you ever heard of a conpanys profits being 10+5i? There are no complex numbers in econ and this makes complex analysis next to useless. Sure it will teach you how to be rigorous but you will not he able to apply any of the techniques learnt there ever. Most of them are specific to complex numbers. Also no math taken in undergrad can be considered "fancy". There are so many people are with such better math skills, noone would be impressed by having more math in your research articles.

Python7768
11-03-2014, 04:12 PM
No area of econ utilizes complex analysis. Have you ever heard of a conpanys profits being 10+5i? There are no complex numbers in econ and this makes complex analysis next to useless. Sure it will teach you how to be rigorous but you will not he able to apply any of the techniques learnt there ever. Most of them are specific to complex numbers. Also no math taken in undergrad can be considered "fancy". There are so many people are with such better math skills, noone would be impressed by having more math in your research articles.

A company's profits don't have to be complex to make it useful within economics. I didn't claim that it was used everywhere, I claimed that it was useful in some circumstances particularly within econometrics (more specifically time series econometrics). Here is a very widely cited paper within economics that uses complex numbers (I would claim the majority, if not all, macroeconomists are familiar with this paper): "Measuring Business Cycles: Approximate Band-Pass Filters for Economic Time Series" by Marianne Baxter and Robert King (link http://sws.bu.edu/mbaxter/papers/mbc.pdf). There are others that use very similar math. Complex Analysis is used very often within filtering frameworks.


^I don't think first courses in abstract algebra generally cover any algebraic topology. Unless someone is absolutely interested in being not just a theorist but a 'foundational' game theorist (assuming you will be coming from a top program as well - because the market will be atrocious), investing in a sequence of courses in algebra and then algebraic topology is a purely recreational pursuit.

This is a good case against Abstract Algebra. Unless you enjoy it from a recreational standpoint (or are the next John Nash) it will only provide very marginal benefits.

Overall, if you have very little programming experience then I think numerical analysis will still be the best course, but if you are lacking in formal math on your profile then complex analysis might be nice to have mostly for signal purposes. Numerical analysis would probably be more useful for passing first year courses.

Econhead
11-03-2014, 04:16 PM
... "Measuring Business Cycles: Approximate Band-Pass Filters for Economic Time Series" by Marianne Baxter and Robert King (link http://sws.bu.edu/mbaxter/papers/mbc.pdf)...

Link fixed.

Food4Thought
11-03-2014, 05:22 PM
Thanks for you advice. Yes, that's what I am considering about. Numerical Analysis may be very useful in some applied work(Using Matlab). But Complex Analysis is more theretical and more proof-intensive. Some fancy theory in economics may utilize stuff from complex analysis (I just guess)

Will taking complex Analysis and getting a good grade in this course give the adcom a better signal than taking numerical analysis ?

Results from complex analysis will not be useful in economics. In economics, we deal only with real quantities. That being said, the results in complex analysis are absolutely magical, and one may want to take the class to practice theoretical math.