MUST MATH courses for phd

[EcoDavid]

Hello all,

 

I notice there are a lot of posts about math, but there is NO one single post clearly states the exact type of math course one must taken in order to do well on phd Mic, Mac and metric courses.

 

Can someone please kindly list ALL the math courses that must be needed in order to be WELL prepared for phd courses. If you can give title and author of the book will be wonderful.

 

Please provide the MUST read/know math inorder to do WELL in phd courses.

 

 

Math books for Microeconomic:

 

 

Math books for Macroeconomic:

 

 

Math books for Econometric:

 

 

Thank you,

David

[SquareSquare]

...but there is NO one single post clearly states the exact type of math course one must taken in order to do well on phd Mic, Mac and metric courses.

 

You're so wrong.

[falco123456]

You're so wrong.

 

Why not point it out to him then? That would be much more constructive.

[Bayern]

econphd.net has a lot of links to different websites which point out the most important courses an individual needs to take to prepare for the graduate schools... as the list of courses are quite similar, i think those links are quite reliable.

[apropos]

Here is the list of math courses that Harvard's professor Mankiw recommends to take:

 

Greg Mankiw's Blog: Which math courses?

 

Don't worry about which books to use because that will be your math professors' decision.

 

Of course, there may be many other preparatory math courses that could potentially become useful along the way in PhD program depending on your field, but those belong to the category of "luxury" courses. That is, they could become useful depending on what you do in the program, but you still should do fine without taking them in advance.

[SquareSquare]

Why not point it out to him then? That would be much more constructive.

 

Maybe it would. And I would. With a more serious question...

[EcoDavid]

"Apropos," thank you for your kind help. The information from the site is very useful, and now I have a clear picture of the type of maths that are needed for phd study.

Btw, what about topology ? The professor at Harvard never mention that ?

 

 

To the rest of the people, if I know the other forums or other sites that provide the information which I need, I won't be seeking help here!!!

 

Thank you

[apropos]

"Apropos," thank you for your kind help. The information from the site is very useful, and now I have a clear picture of the type of maths that are needed for phd study.

Btw, what about topology ? The professor at Harvard never mention that ?

 

 

Thank you

 

 

I think topology is one of those courses that perhaps just might be useful if you're into some deep theory subjects, but it is not necessary at all for admission, and I still would consider taking more advanced real analysis to be more useful that general topology. Anyways, I think people are overestimating the amount of math they need to have to do well in economics.

[asquare]

apropos is right about topology, and about the trend on this forum to overestimate required mathematical preparation. Still, since most undergrad econ programs don't place enough weight on math, this forum probably provides balance ;)

 

The required level of math for the first year varies somewhat by school. In general, higher-ranked school require greater comfort with real analysis and proof-writing. For first year courses in all programs, you must be comfortable with multivariable calculus (especially constrained optimization, but taking derivatives of complicated functions, using the chain rule, should be something you can do in your sleep, be able to use the implicit function theorem), basic linear algebra (matrix manipulation, including multiplying and inverting matrice and other functions, eigenvectors and eigenvalues), and basic differential equations (finding general and particular solutions). You should also know some basics like Taylor series expansions, and be able to work with infinite sums and sequences, and be familiar with expectations (which you might learn in an undergrad probability class).

 

All of this material would be covered by taking typical college level courses in multivariable calculus, real analysis, and differential equations (and the prerequesites for those classes -- specifically single var calculus, of course). I can't give you specific text books because there are many, many books that cover this material at acceptable levels. Just take a look at the syllabi for these courses at your school.

 

You will also have to write basic proofs and understand the logic of some more complicated proofs. This requires two sets of knowledge -- familiarity with basic proof-writing techniques, and knowledge of concepts like continuity, completeness, and convergence. You probably need the latter at most every PhD program; higher ranked programs expect higher degrees of facility with proof writing. You can learn this material by taking undergraduate real analysis, taught at the level of "baby" Rudin.

 

Additional mathematical concepts will come up during first year. Knowing them in advance would only help you, but things you can learn for the first time during first year include basic dynamic programing (Hamiltonians, Bellman's equations, etc.).

 

"Math camps" at most schools provide brief reviews of most/all of these topics. However, it's hard to learn the material for the first time in the fast-moving "math camp" setting, and IMO would be impossible to learn anything without solid grounding in multivariable calc and linear algebra. It is also useful to have prior exposure to the notation of real analysis before starting math camp. You don't want to get bogged down in notation and not understand the concepts.

 

One more thing: it's hard to separate out which math is required for which first year courses. You probably won't use dynamic programing in micro or econometrics, but you will use everything else. You will use everything in macro, since much of modern macro is focused on "micro based models."

[EcoDavid]

APROPOS and ASQUARE, I appreciate very much for you two's kind help. "ASQUARE," your message is clear and sound. Now I know exactly the math courses that I am short of inorder to be well prepared for my phd courses.

THANK YOU for both of you!!!

[nasshi]

I get the feeling that so few people here distinguish between being "well prepared" and "knowing enough so you can learn more along the way". The truth is, you really don't need to know dynamical systems for macro, for example, because you're expected to learn it along the way. The same goes for topology.

 

It seems like many of you suggest knowing 80% of 100% of the material, as opposed to 100% of 80% of the material. From experience, and from what I've been advised, doing the latter is much more preferable.

 

Since the original poster wants to know the "must" courses, based on the idea that many are expected to learn along the way, "must" courses probably really only comprise a rigorous intro the proofs course, the calculus sequence, a rigorous proof based sequence in linear algebra, and ODEs. I think saying that real analysis and topology are "musts" to succeed in a program is just not correct.

 

Feel free to discuss.

[asquare]

nasshi, I agree in principle that there are a lot of things you can learn along the way (and dynamic programming was an explicit example of that in my last post). However, I think there is more flexibility in preparation than you suggest.

 

For example, you need an introduction to proofs. That can come in many ways; it does not need to be through a "proof based sequence in linear algebra." It would be just as possible to take a basic linear algebra course, and a separate course in intro to proofs or real analysis.

 

Also, I think it's more important to focus on knowledge/topics than specific courses. Courses have different names at different schools (for example, "intro to proofs" can come in Calc III, real analysis, or a separate course in proof-writing) and courses with the same name can be taught at deceptively different levels of difficulty (again, "real analysis" at one school may cover basic proof writing and, say, the first 6 chapters of baby Rudin, while at another school it is a much more advanced syllabus).

 

I see your point about knowing things in depth, rather than scratching the surface. But I think the real key is to know enough before starting the PhD that you have the tools to learn more while in the PhD. You need to be really solid with calculus and linear algebra, for example, to be able to learn the concepts that are presented as well as the new math tools. But there are other cases where knowing a little bit will take you a long way. This is especially true for things like notation, especially notation used in proofs ("there exists," "for all," set opperators, etc.) If you get bogged down in unfamiliar notation, you won't be able to learn the concepts as they are taught. So in some cases, I think that even if you can't learn material really thoroughly before starting, a brief introduction is better than no introduction at all.

[Aeshma]

dynamic programming is actually needed for micro-econometrics. alot of work in labor and io requires the use of dynamic models in estimation.

[asquare]

Yes, but the labor search models that use dynamic programming are often considered "macro-labor" type models ;) Since the question was about math needed for first year courses, I think it's fair to say that you don't use dynamic programming much in first year micro theory.

[Karina 07]

I see your point about knowing things in depth, rather than scratching the surface. But I think the real key is to know enough before starting the PhD that you have the tools to learn more while in the PhD. You need to be really solid with calculus and linear algebra, for example, to be able to learn the concepts that are presented as well as the new math tools. But there are other cases where knowing a little bit will take you a long way. This is especially true for things like notation, especially notation used in proofs ("there exists," "for all," set opperators, etc.) If you get bogged down in unfamiliar notation, you won't be able to learn the concepts as they are taught. So in some cases, I think that even if you can't learn material really thoroughly before starting, a brief introduction is better than no introduction at all.

 

I will return to this thread after a term or two to comment, as I covered the required math courses but many years before I realized I would ever want to do anything with them again, and so I didn't put much effort into them.

 

So far, during the past 3 weeks of math camp, it's been alright. It would probably have been *better* for me to know 80% of the material 100% well, but knowing 100% (well, less than that) 80% well (well, less than *that*, too) is still sufficient -- thus far. Never had a full analysis course, but I was a philo major and so was familiar with the general idea of proofs, so notationally and "idea of proofs"-wise everything's been comfortable.

 

Anyway, as I say, I'll return to comment more later when I see how it feels further into the actual program; but my hunch is that a wide variety of backgrounds can "make it", and it whether or not someone *can* do well with less depends on the individual's general math ability and effort.

[Aeshma]

oh ok, i thought u were talking in general. and when i mentioned micro-econometrics, i meant io, not labor. sorry.

[asianeconomist]

For the OP:

 

Check out the recommended Math courses by T.Sargent:

 

Tom Sargent: Research Articles

 

I believe that he over-does it a bit!

[SquareSquare]

I believe that he over-does it a bit!

 

Maybe he intended to give a 'shopping list' a la pick any 8 classes (honouring the requirements).

 

Just as in jogging, I recommend not overdoing it. Rather, find a pace that you can sustain throughout your years here. You will find that taking these courses doesn't really cost time, because of your improved efficiency in doing economics.

[good_tea]

Asquare's post in the first page was extremely useful, thank you for that.

 

I had a question which is somewhat related to this thread. Can someone hazard a geuss on the relevance of an "Advanced Calculus" course using the textbook "Advanced Calculus" by Kaplan? I understand that Advanced Calculus can mean a lot of different things.

 

Thanks.

[EcoDavid]

DO YOU REALLY NEED ALL THESE MATH COURSES FOR PHD ECONOMICS ? IT LOOKS LIKE YOU NEED TO HAVE A MATH DEGREE FIRST.

 

 

Math Department

 

Math 103, 104, Linear algebra

 

Math 113, 114 Linear algebra and matrix theory

 

Math 106, Introduction to functions of a complex variable (especially useful for econometrics and time series analysis)

 

Math 124, Introduction to stochastic processes

 

Math 130, Ordinary differential equations

 

Math 131, Partial differential equations

 

Math 175, Functional analysis

 

Math 205A, B, C, Real analysis and functional analysis

 

Math 230A, B, C, Theory of Probability

 

Math 236, Introduction to stochastic differential equations

 

 

Engineering Economic Systems and Operations Research

 

EESOR 313, Vector Space Optimization. This course is taught from `the Bible' by the author (Luenberger). The book is wonderful and widely cited by economists

 

EESOR 322, Stochastic calculus and control

 

 

Statistics

 

Stat 215-217, Stochastic processes (Cover)

 

Stat 218, Modern Markov chains (Diaconis)

 

Stat 310 A, B, Theory of probability (Dembo)

 

 

These are very useful courses for applied work in econometrics, macroeconomic theory, and applied industrial organization. They describe the foundations of methods used to specify and estimate dynamic competitive models.

Just as in jogging, I recommend not overdoing it. Rather, find a pace that you can sustain throughout your years here. You will find that taking these courses doesn't really cost time, because of your improved efficiency in doing economics.

There are many other courses that are interesting and useful. The most important thing is just to get started acquiring the tools and habits these courses will convey.