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rcwlhk
02-19-2008, 12:00 PM
Hey guys,

Are number theory and/or linear programming useful in economics and/or finance? Specifically, I'm wondering whether to take these courses:

MATH 312 Introduction to Number Theory
Euclidean algorithm, congruences, Fermat's theorem, applications. Some diophantine equations. Distribution of the prime numbers.

MATH 340 Introduction to Linear Programming
Linear programming problems, dual problems, the simplex algorithm, solution of primal and dual problems, sensitivity analysis. Additional topics chosen from: Karmarkar's algorithm, non-linear programming, game theory, applications.

Now, the opportunity cost of taking MATH 340 is my chance to take a course in PDE (which I know is useful in Economics and Finance). There's no "real" opportunity cost to taking MATH 312 other than time, tuition and extra studying energy.

Please help out! Thanks again to all the TM'ers out there!

israelecon
02-19-2008, 12:18 PM
i think linear programming may be useful, but my understanding is that it may be a bit old fashioned in economics, but i don't really know.
number theory is not only useless for economics, its useless for anything other than cryptography. I am taking a number theory class (it is required for me as a math major). it is pretty interesting and not as difficult as other math. It may show the adcoms you have good abstract thinking, i don't know. but based on the syllabus you wrote down you don't get very much past the first two chapters in any introductory book on number theory.
in any case there are definitely much more relevant math courses you can take than number theory.

AstralTraveller
02-19-2008, 01:08 PM
MATH 340 Introduction to Linear Programming
Linear programming problems, dual problems, the simplex algorithm, solution of primal and dual problems, sensitivity analysis. Additional topics chosen from: Karmarkar's algorithm, non-linear programming, game theory, applications.

I agree with israelecon about the uselessness of Number Theory for Economists. And about Linear Programming....we learnt nonlinear programming during our first intermediate micro course. Our professor told us that we'd be better off thinking everything as nonlinear programming, as linear programming was simply a particular case of nonlinear. So we obeyed and studied everything as nonlinear programming. Then, linear programming became useless, and, paraphrasing israelecon, old fashioned for economics.

reactor
02-19-2008, 01:12 PM
Yes they can be useful. They will not determine whether or not you survive the first year of the Econ PhD but they have applications in economics and also can serve as foundations to build upon for further mathematics that are used in economics.

econphilomath
02-19-2008, 01:42 PM
When you try programming nonlinear systems, you will generally use techniques that solve a sequence of linear problems to find the nonlinear solution. Linear programing might not be as sexy but it will be useful. I would not take the course however.

buckykatt
02-19-2008, 04:29 PM
My two cents:

Number theory won't improve your economics toolkit except insofar as doing lots of proofs makes you better at formal math. So in the absence of a course like analysis an A in number theory might be a good signal to an adcom and good for your overall math development, but otherwise a waste of time. (Fun, maybe, but not useful.)

Linear programming has more direct relevance. It probably won't make any difference to surviving your first year of grad school, but it may be useful to have an introduction to this "old fashioned" language when reading older work in economics. I also find it useful to have more than one way of approaching a problem. But if the opportunity cost of this class is something like real analysis, probability theory, or even numerical analysis, I'd take those instead.

rcwlhk
02-20-2008, 12:34 AM
Wow thanks guys for the breadth of responses! I really appreciate it.

I guess I'll go on to take Number Theory --- even though I have gathered from you guys and as well as from my own understanding that it is not very applicable in economics, but I'll use it more or less as a "signaling" tool to the adcoms; as mentioned, since I'm doing these courses over the summer, there aren't other "better" choices (i.e. real analysis, numerical analysis, etc) around for me to forgo and I probably should pick up more pure maths.

Thx!

pevdoki1
02-20-2008, 12:35 AM
I had some number theory in my algebra class, and it was great fun! :)