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:
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.
"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!!!
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.
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."
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