Real analysis

[econyun]

So, I would like to ask what level does the following course belong to? It is a course of one semester long.

Real Analysis
Functions of several variables, implicit and inverse function theorem, uniform convergence measure and integral on the real line.

[paradox3696]

Real Analysis does NOT come into play when you do your Phd program in economics. In most likelihood, you wont be asked to do any proofing like what u did in the Math Real Analysis. I dont understand why Real Analysis has been such a big fuzz from this forum. If you have done standard cal 1-3, Linear and Matrix Algebra, differential equation, Probability and STats (ideally, econometrics as well), you are all GOOD for the math rigor. Perhaps, a course in Advanced Claculus and/or elementary proofing in logic and set wouldnt hurt. DONT read too much into Real Analysis when you actually do your doctoral program in econ.

[asianeconomist]

Originally Posted by paradox3696

Real Analysis does NOT come into play when you do your Phd program in economics. In most likelihood, you wont be asked to do any proofing like what u did in the Math Real Analysis. I dont understand why Real Analysis has been such a big fuzz from this forum. If you have done standard cal 1-3, Linear and Matrix Algebra, differential equation, Probability and STats (ideally, econometrics as well), you are all GOOD for the math rigor. Perhaps, a course in Advanced Claculus and/or elementary proofing in logic and set wouldnt hurt. DONT read too much into Real Analysis when you actually do your doctoral program in econ.

I would beg to differ. IMHO, the real benefit of real analysis lies not in what it teaches, but rather in the mathematical sophistication that it instills.

[paradox3696]

Originally Posted by asianeconomist

I would beg to differ. IMHO, the real benefit of real analysis lies not in what it teaches, but rather in the mathematical sophistication that it instills.

Then you might as well add Abstract/Modern Algebra into your reasoning. yeah lets talk about group and ring theories as they apply to Economics. It would be real interesting! wouldnt it not?

[asianeconomist]

Originally Posted by paradox3696

Then you might as well add Abstract/Modern Algebra into your reasoning. yeah lets talk about group and ring theories as they apply to Economics. It would be real interesting! wouldnt it not?

In fact, I did consider Abstract Algebra to be an useful course. Anyway, the point is that RA does indeed have some elements that'll be helpful to Econ Grad students (FPEs, Continuity, Convergence) whereas a course like abstract algebra aids in developing your mathematical maturity, but doesn't teach you a lot of things that you can apply back in economics. Therefore, my both the application + sophistication counts, RA dominates nearly all other advanced math courses (except topology I guess).

[paradox3696]

Originally Posted by asianeconomist

Anyway, the point is that RA does indeed have some elements that'll be helpful to Econ Grad students (FPEs, Continuity, Convergence)

Yes I totally agree with you mate. My initial intention was to let the readers to be aware that you wont be doing much proofing if any at all in the econ phd program as you do with Math RA. And a course in any mathematical proof-based course would be suffice for the math rigor. ie, RA is NOT a necessary condition. FYI, Advanced Calculus does cover extensively the topics u mentioned above in term of proofing, and providing examples and counter-examples.

[econyun]

Originally Posted by asianeconomist

RA dominates nearly all other advanced math courses (except topology I guess).

serious? When should we stop taking it?? like the marginal benefit is not higher than taking other maths courses..

what about Ad. Probability, Graduate stochastic process..etc.

Some of them are proof-oriented and most of the materials in these courses are of uses.
Am I wrong?

[asianeconomist]

Originally Posted by econyun

serious? When should we stop taking it?? like the marginal benefit is not higher than taking other maths courses..

what about Ad. Probability, Graduate stochastic process..etc.

Some of them are proof-oriented and most of the materials in these courses are of uses.
Am I wrong?

You are quite correct. In fact, I guess I was just comparing between RA and Abstract algebra in the back of my mind when I was writing it. The courses that you mention might just be as useful (or even more useful) as a RA course.

[italos]

Btw in my university calculus was called Mathematical Multivariable Analysis and Real Analysis was called Real Mathematical Analysis.Can the difference be understood from an Adcom?

[econyun]

cool names