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NB888 · 2009 July 5th, 04:18 AM

A few days back I posted a thread asking for opinions regarding the value of various pure math topics, toward Ph.D. level study in economics. It looks like nobody thought those topics are of much direct value. Fair enough.

I might have the option of taking a year-long sequence in Numerical Analysis, offered in the math department. It is based on the text by Burden and Faires. It's offered in the same timeslot as the abstract algebra sequence, so I'd have to decide before it begins which one to attend. My current math background is unbalanced such that I am better at pure math than applied math. So, numerical analysis might be a beneficial exercise, even though abstract algebra would probably be easier for me. It also would force me to practice Matlab, which I have never used, but am trying to learn how to use this summer.

If anyone here thinks a yearlong sequence in numerical analysis is valuable toward Ph.D. level study in economics, please say so. Especially if you have been in an economics Ph.D. program for some length of time.

The second question is about the value of undergraduate econometrics courses. At how great a disadvantage is a student if he's never taken a course in econometrics, either for admissions, or for the program itself? I've taken 3 courses in the probability/statistics department. They have some material in common with the econometrics sequence. But, the courses I've taken did not discuss regressions at all, and they weren't taught in the economics department by economics professors/grad students.

The econometrics sequence is scheduled such that it covers two other timeslots. The other options offered in those timeslots are potentially valuable or interesting. They include courses in time series analysis, topology, geometry, and differential equations. My single best math performance ever was in a topology course, and I wouldn't mind taking another course in topology.

Any thoughts about what is above, feel free to express.

applicant12 · 2009 July 5th, 05:40 AM

I don't have much knowledge but I can say these

1. I don't really know if those courses are good for admission or useful for PhD study in econ. You may want to ask your professors directly and seek advice from them. Another thing you can do is look at those people who were admitted to your intended school and see what math courses they took

2. I think econometrics is better. It is required by some programs too I guess. I would go ahead and take the econometrics course

Hope these help

Tenhik · 2009 July 5th, 05:45 AM

We're lucky to have advanced courses in time series and cross section metrics at W&M, and everybody I've asked about taking these courses has said the same thing; the more econometrics you take, the better. Given that you've never had a course in regression analysis, the marginal benefit of such a class would likely outweigh that of any other classes besides the requisite courses for admissions. While you'll learn the material again in graduate school at an advanced level, I think being exposed to it early on is important.

unitroot · 2009 July 5th, 06:04 AM

I think having been exposed to econometrics at undergraduate level is a valuable experience, specially if the course also uses matrix algebra.

Regarding abstract algebra vs numerical analysis, I think numerical analysis is hands down a more useful course. In a year-long course you will probably learn how to solve systems of linear and non-linear equations, numeric matrix factorizations, numeric integration, solutions of differential equations, asymptotic expansions, etc None of these is a "must-have" knowledge for an average econ PhD student. Most of this is already implemented as canned functions in Matlab. Nonetheless, understanding how to use these methods can be valuable knowledge if you're facing a computationally intensive econometrics problem. Computation is a huge aspect of modern econometrics, even though practical computational methods are rarely taught or explained well in a typical econometrics course. A side effect of taking this course would be learning matlab well, which is again very useful in econometrics.

Granted, a general course in numerical analysis does not make as its goal to address the needs of econometricians or statisticians. Some of the better statistics departments have dedicated courses in numerical analysis for statisticians, and that would be far more useful for economists. For example, a standard course in numerical analysis rarely discusses numerical optimization which is central to most of statistical estimation methods. The statistics department course in computational statistics might also consider topics like EM-type algorithms or MCMC which are apparently becoming popular in some areas of econometrics.

NB888 · 2009 July 6th, 08:37 AM

Although I like algebra and topology, I can't disagree with the answers here. I'm thinking I should aim to have, within the next year, some rudimentary proficiency with all four of these:

1. Basic economic concepts, articulated in words and simple diagrams
2. Deductive analysis, i.e. definitions, theorems, proofs
3. Applied Math, i.e. numerical methods, simple computation and programs
4. Econometric and statistical analysis

Those four things are not competitors; they feed off what has been learned from the other three. The contribution of all four of them to economics is real, and is irreversible. People who are hoping one or more of them will be removed from economics should just give up now and go home; their dreams will not come true.

I am now worse at #3 and #4 than at #1 and #2. I should choose some of my courses so as to help address #3 and #4.

There's an essay I just read that might interest people about #2 and #3:
http://bucky.stanford.edu/papers/scekey.pdf
If you like Deirdre McCloskey's writings about underemphasis on quantitative and overemphasis on qualitative analysis, you might find that essay interesting.

walt526 · 2009 July 9th, 10:22 AM

I took an Intro to Numerical Analysis course this past spring and will take Numerical Analysis of Differential Equations this fall. I'm currently registered for Modern Algebra, but am leaning toward dropping it.

I think that NA was extremely helpful for future study (especially the exposure to MATLAB), but I don't know how much it really improved my applicant profile. The problem with Applied Math courses is that there is such a wide range in rigor not only across various universities, but even within departments. My impression is that a lot of Math departments put a lot of emphasis on creating uniform standards on core pure math sequences (Algebra, Calc, RA), but Applied Math courses are usually upper-division electives that are not as well regulated. Since adcoms are aware of this, they put less emphasis on a grades in non-core electives.

So basically I think the decision of whether to take NA or Algebra rests on whether you want to take a course that will provide you with more useful background (NA) or send a stronger signal to adcoms that you are comfortable in abstract math (Algebra). Without knowing your complete profile, it's impossible to say (and even then it's just an educated guess at best). For me, I felt that taking Axiomatic Set Theory to bolster my pure math credentials and then focusing more on Applied Math electives was a better use of my time than Algebra.

Algebra isn't without its uses, but honestly unless you want to go into pure game theory (as opposed to applied game theory) I'm not sure if it's really necessary. You could always take Modern Algebra once you're in the program if it became absolutely necessary. But if you've got the capacity to be a pure game theorist, then something like Modern Algebra should be incredibly easy and intuitive for you. If it's not, then you're probably among the 99.9% of Economists who should just stay in the shallower waters of applied game theory lest they lose their sanity.

unitroot · 2009 July 9th, 03:24 PM

Actually, the undergraduate numerical analysis courses are more or less standardized across universities. At least, the book by Burden and Faires mentioned above is often used at undergraduate level and is usually considered the least common denominator for such courses. A typical NA course will at least cover some material on iterative methods for solving equations, interpolation and extrapolation, numerical integration and ODEs, some matrix algebra, etc, but with a varying amount of rigor. Generally, you can expect an undergraduate NA course to be more computational and less rigorous than abstract algebra, but that generally varies by professor. You can think of it as a continuation of the sophomore level calculus and matrix algebra rather than being in the same league with courses like real analysis.

walt526 · 2009 July 10th, 12:57 AM

No, I don't think that's accurate. It's a topic that I've talked about with a number of students from other universities that I met through SIAM.

B&F is popular, but Sauer is gaining popularity and less rigorous programs use something like Atkinson and Han. Some NA courses require in-class exams on the theory, others just have computer labs with varying levels of difficulty. Also prereqs can vary: many require LA and DE and some programming language, but it's not uncommon for the only prereq to be Calc II. As such, both the rigor and the scope can vary. A majority are offered by Math Departments, but it's not uncommon for Engineering departments to offer their own, in which case the background and research interests of the instructor and his relative emphasis on theory vs applications varies.

In short, there's nothing close to universally recognized standards for the typical undergraduate NA course and unless one reviews the quality of work of a student's final project it would be impossible for an adcom to gauge exactly how proficient a skillset a student gained from the course. And the grading standards in applied math are generally much looser than they are for the department's core courses in MA and RA--just as an Econ department focuses on maintaining uniform standards for the Intermediate Macro and Micro theory, but scope and difficulty of upper-division electives depend largely on the instructor.

2009 July 5th, 04:18 AM	#1 (permalink)
NB888 Within my grasp! Join Date: May 2009 Posts: 108	Value of Numerical Analysis and Econometrics A few days back I posted a thread asking for opinions regarding the value of various pure math topics, toward Ph.D. level study in economics. It looks like nobody thought those topics are of much direct value. Fair enough. I might have the option of taking a year-long sequence in Numerical Analysis, offered in the math department. It is based on the text by Burden and Faires. It's offered in the same timeslot as the abstract algebra sequence, so I'd have to decide before it begins which one to attend. My current math background is unbalanced such that I am better at pure math than applied math. So, numerical analysis might be a beneficial exercise, even though abstract algebra would probably be easier for me. It also would force me to practice Matlab, which I have never used, but am trying to learn how to use this summer. If anyone here thinks a yearlong sequence in numerical analysis is valuable toward Ph.D. level study in economics, please say so. Especially if you have been in an economics Ph.D. program for some length of time. The second question is about the value of undergraduate econometrics courses. At how great a disadvantage is a student if he's never taken a course in econometrics, either for admissions, or for the program itself? I've taken 3 courses in the probability/statistics department. They have some material in common with the econometrics sequence. But, the courses I've taken did not discuss regressions at all, and they weren't taught in the economics department by economics professors/grad students. The econometrics sequence is scheduled such that it covers two other timeslots. The other options offered in those timeslots are potentially valuable or interesting. They include courses in time series analysis, topology, geometry, and differential equations. My single best math performance ever was in a topology course, and I wouldn't mind taking another course in topology. Any thoughts about what is above, feel free to express.

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2009 July 5th, 05:40 AM	#2 (permalink)
applicant12 Within my grasp! Join Date: Jun 2009 Posts: 234	I don't have much knowledge but I can say these 1. I don't really know if those courses are good for admission or useful for PhD study in econ. You may want to ask your professors directly and seek advice from them. Another thing you can do is look at those people who were admitted to your intended school and see what math courses they took 2. I think econometrics is better. It is required by some programs too I guess. I would go ahead and take the econometrics course Hope these help

2009 July 5th, 05:45 AM	#3 (permalink)
Tenhik Eager! Join Date: Mar 2009 Location: Williamsburg, VA Posts: 57	We're lucky to have advanced courses in time series and cross section metrics at W&M, and everybody I've asked about taking these courses has said the same thing; the more econometrics you take, the better. Given that you've never had a course in regression analysis, the marginal benefit of such a class would likely outweigh that of any other classes besides the requisite courses for admissions. While you'll learn the material again in graduate school at an advanced level, I think being exposed to it early on is important.

2009 July 5th, 06:04 AM	#4 (permalink)
unitroot Within my grasp! Join Date: May 2008 Posts: 458	I think having been exposed to econometrics at undergraduate level is a valuable experience, specially if the course also uses matrix algebra. Regarding abstract algebra vs numerical analysis, I think numerical analysis is hands down a more useful course. In a year-long course you will probably learn how to solve systems of linear and non-linear equations, numeric matrix factorizations, numeric integration, solutions of differential equations, asymptotic expansions, etc None of these is a "must-have" knowledge for an average econ PhD student. Most of this is already implemented as canned functions in Matlab. Nonetheless, understanding how to use these methods can be valuable knowledge if you're facing a computationally intensive econometrics problem. Computation is a huge aspect of modern econometrics, even though practical computational methods are rarely taught or explained well in a typical econometrics course. A side effect of taking this course would be learning matlab well, which is again very useful in econometrics. Granted, a general course in numerical analysis does not make as its goal to address the needs of econometricians or statisticians. Some of the better statistics departments have dedicated courses in numerical analysis for statisticians, and that would be far more useful for economists. For example, a standard course in numerical analysis rarely discusses numerical optimization which is central to most of statistical estimation methods. The statistics department course in computational statistics might also consider topics like EM-type algorithms or MCMC which are apparently becoming popular in some areas of econometrics.

2009 July 6th, 08:37 AM	#5 (permalink)
NB888 Within my grasp! Join Date: May 2009 Posts: 108	Although I like algebra and topology, I can't disagree with the answers here. I'm thinking I should aim to have, within the next year, some rudimentary proficiency with all four of these: 1. Basic economic concepts, articulated in words and simple diagrams 2. Deductive analysis, i.e. definitions, theorems, proofs 3. Applied Math, i.e. numerical methods, simple computation and programs 4. Econometric and statistical analysis Those four things are not competitors; they feed off what has been learned from the other three. The contribution of all four of them to economics is real, and is irreversible. People who are hoping one or more of them will be removed from economics should just give up now and go home; their dreams will not come true. I am now worse at #3 and #4 than at #1 and #2. I should choose some of my courses so as to help address #3 and #4. There's an essay I just read that might interest people about #2 and #3: http://bucky.stanford.edu/papers/scekey.pdf If you like Deirdre McCloskey's writings about underemphasis on quantitative and overemphasis on qualitative analysis, you might find that essay interesting.

2009 July 9th, 10:22 AM	#6 (permalink)
walt526 TestMagic Guru Join Date: Aug 2008 Posts: 1,308	I took an Intro to Numerical Analysis course this past spring and will take Numerical Analysis of Differential Equations this fall. I'm currently registered for Modern Algebra, but am leaning toward dropping it. I think that NA was extremely helpful for future study (especially the exposure to MATLAB), but I don't know how much it really improved my applicant profile. The problem with Applied Math courses is that there is such a wide range in rigor not only across various universities, but even within departments. My impression is that a lot of Math departments put a lot of emphasis on creating uniform standards on core pure math sequences (Algebra, Calc, RA), but Applied Math courses are usually upper-division electives that are not as well regulated. Since adcoms are aware of this, they put less emphasis on a grades in non-core electives. So basically I think the decision of whether to take NA or Algebra rests on whether you want to take a course that will provide you with more useful background (NA) or send a stronger signal to adcoms that you are comfortable in abstract math (Algebra). Without knowing your complete profile, it's impossible to say (and even then it's just an educated guess at best). For me, I felt that taking Axiomatic Set Theory to bolster my pure math credentials and then focusing more on Applied Math electives was a better use of my time than Algebra. Algebra isn't without its uses, but honestly unless you want to go into pure game theory (as opposed to applied game theory) I'm not sure if it's really necessary. You could always take Modern Algebra once you're in the program if it became absolutely necessary. But if you've got the capacity to be a pure game theorist, then something like Modern Algebra should be incredibly easy and intuitive for you. If it's not, then you're probably among the 99.9% of Economists who should just stay in the shallower waters of applied game theory lest they lose their sanity.

2009 July 9th, 03:24 PM	#7 (permalink)
unitroot Within my grasp! Join Date: May 2008 Posts: 458	Actually, the undergraduate numerical analysis courses are more or less standardized across universities. At least, the book by Burden and Faires mentioned above is often used at undergraduate level and is usually considered the least common denominator for such courses. A typical NA course will at least cover some material on iterative methods for solving equations, interpolation and extrapolation, numerical integration and ODEs, some matrix algebra, etc, but with a varying amount of rigor. Generally, you can expect an undergraduate NA course to be more computational and less rigorous than abstract algebra, but that generally varies by professor. You can think of it as a continuation of the sophomore level calculus and matrix algebra rather than being in the same league with courses like real analysis.

2009 July 10th, 12:57 AM	#8 (permalink)
walt526 TestMagic Guru Join Date: Aug 2008 Posts: 1,308	No, I don't think that's accurate. It's a topic that I've talked about with a number of students from other universities that I met through SIAM. B&F is popular, but Sauer is gaining popularity and less rigorous programs use something like Atkinson and Han. Some NA courses require in-class exams on the theory, others just have computer labs with varying levels of difficulty. Also prereqs can vary: many require LA and DE and some programming language, but it's not uncommon for the only prereq to be Calc II. As such, both the rigor and the scope can vary. A majority are offered by Math Departments, but it's not uncommon for Engineering departments to offer their own, in which case the background and research interests of the instructor and his relative emphasis on theory vs applications varies. In short, there's nothing close to universally recognized standards for the typical undergraduate NA course and unless one reviews the quality of work of a student's final project it would be impossible for an adcom to gauge exactly how proficient a skillset a student gained from the course. And the grading standards in applied math are generally much looser than they are for the department's core courses in MA and RA--just as an Econ department focuses on maintaining uniform standards for the Intermediate Macro and Micro theory, but scope and difficulty of upper-division electives depend largely on the instructor.

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