View Full Version : Imperfect Substitutes for Not Having Analysis

GymShorts

02-20-2008, 08:37 PM

Unfortunately, Analysis I and Linear Algebra are scheduled for the same time this fall, and that will be the last semester that I can get in grades before I apply. I'm now looking into taking Linear Algebra over the summer at another university. But if that doesn't work out, I'll take Linear Algebra this fall and some other math classes to prove that I can handle advanced mathematics. I know most of these classes are irrelevant to economics, so they are imperfect substitutes for Analysis I at best--they will only show that I can handle tough math. Other than Analysis and Linear Algebra, I have all the "must" classes. Here are the additional classes I could take:

Complex Variables

Combinatorics

Elementary Number Theory

Abstract Algebra I

Any thoughts of which ones (I might be able to take two) would be best?

Mr.Keen

02-20-2008, 08:41 PM

I would take abstract algebra. Some concepts you learn there are then useful when dealing with measure theory.

Thesus

02-20-2008, 08:56 PM

Don't take combinatorics.

pevdoki1

02-20-2008, 09:01 PM

Another vote for abstract algebra.

Even if you don't use any results in grad school, it's a great signal. In most places, algebra tends to be the class that separates the wheat from the chaff.. Many people stop being math majors after taking it because they realize that they must know how to write serious proofs. At worst, it will teach you how to use the various proof techniques (induction, contradiction etc)

GymShorts

02-20-2008, 09:03 PM

Many people stop being math majors after taking it because they realize that they must know how to write serious proofs. At worst, it will teach you how to use the various proof techniques (induction, contradiction etc)

I should mention that I am currently taking Fundamentals of Advanced Mathematics, which is essentially an intro to mathematical proofs class.

pevdoki1

02-20-2008, 09:04 PM

Well, you can bet on proofs being harder in algebra :p

buckykatt

02-20-2008, 10:25 PM

I agree that algebra is probably your best option. I can't see any way to teach that course without doing lots of proofs, so it should be a clear signal. And it's good background for both linear algebra and real analysis, even though it's not really essential.

I'm not sure what "complex variables" covers, though. I would have thought this would be complex analysis, but if real analysis isn't listed as a pre-requisite then maybe not?

apropos

02-21-2008, 02:49 AM

If your school offers it, consider taking a more advanced course in linear algebra.

GymShorts

02-22-2008, 11:28 PM

I'm not sure what "complex variables" covers, though. I would have thought this would be complex analysis, but if real analysis isn't listed as a pre-requisite then maybe not?

Here's the course description for complex variables. The prerequisite is calc III.

MATH 524: Complex Variables

3.00 Credits

Field of complex numbers. Elementary functions in complex variables: polynomials, rational, trigonometric and exponential functions. Limits and continuity. The complex derivative, Cauchy-Riemann equations. Analytic and harmonic functions. Complex integration, Cauchy's integral formula. Taylor and Laurent series. Residue theory. Uniform convergence. Analytic continuation. Conformal mapping. Prerequisite: 221.

TruDog

02-22-2008, 11:40 PM

That would be quite helpful.

buckykatt

02-23-2008, 12:08 AM

Yeah, that sounds like a good option.

decide_aposteriori

02-23-2008, 12:52 AM

I would take algebra, it's actually fun (if you're into that kinda thing). You'll learn about coloring problems, groups, and rings. I found it to be a great *break* from so much calculus.

wednesday

02-29-2008, 01:31 AM

The above posters may be right that Abstract Algebra is better for signaling purposes, but unless you're doing some pretty serious micro theory, you're never going to need to worry about monoid isomorphisms. On the other hand, there are methods from Complex Analysis that are really useful even on the Real line.

On the third hand, Complex Analysis is usually predicated on some knowledge of Real Analysis...

math2009

02-29-2008, 05:41 AM

complex anlaysis has a very geometric flavour, so it will cover some elementary topology, which I think would be helpful for first year phd micro course. and of course, it covers some elementary theory of functions. Many techniques are similar to analysis on reals.

for other courses you listed ,you wont use any of it in your first year econ classes.

israelecon

02-29-2008, 09:29 AM

The above posters may be right that Abstract Algebra is better for signaling purposes, but unless you're doing some pretty serious micro theory, you're never going to need to worry about monoid isomorphisms. On the other hand, there are methods from Complex Analysis that are really useful even on the Real line.

On the third hand, Complex Analysis is usually predicated on some knowledge of Real Analysis...

complex analysis is a very nice course, and it is useful for many problems involving just real numbers, but i find it hard to believe that an economist will ever run into these problems. Summing series and caculating integrals using complex analysis may be useful in electronics and engineering, but not in economics. i don't think you will find economics articles using complex analysis.

complex analysis is also important for proving many results in "standard" real number math (like in number theory, probability, etc.), but again I don't think this is really relevant for an economist, even the most technical one. its a pretty safe bet, that unless someone in the adcom has a degree in mathematics or engineering, he has no idea what complex analysis is. (he may know that its about functions of a complex variable, but he certainly has no idea about the theory of complex functions). this may be a good thing, because the adcom may think its a more advanced course than real analysis, which it is not even though it sounds like it is.

wednesday

02-29-2008, 06:04 PM

complex analysis is a very nice course, and it is useful for many problems involving just real numbers, but i find it hard to believe that an economist will ever run into these problems. Summing series and caculating integrals using complex analysis may be useful in electronics and engineering, but not in economics. i don't think you will find economics articles using complex analysis.

complex analysis is also important for proving many results in "standard" real number math (like in number theory, probability, etc.), but again I don't think this is really relevant for an economist, even the most technical one. its a pretty safe bet, that unless someone in the adcom has a degree in mathematics or engineering, he has no idea what complex analysis is. (he may know that its about functions of a complex variable, but he certainly has no idea about the theory of complex functions). this may be a good thing, because the adcom may think its a more advanced course than real analysis, which it is not even though it sounds like it is.

I agree with most of what you're saying. A marginal semester of Real Analysis strictly dominates a marginal semester of Complex Analysis, at least for this questioner. However, the methods of Complex Analysis can be useful, even in economics research. I've done proofs (in micro theory) with real functions where the trick was manipulate the function v(x) into Re{u(z)} and then prove a result about u(z).