caltech math suggestions for other schools

Colleges and Universities A-Z California Institute of Technology
1

<p>hi! i will be a freshman at princeton this upcoming year. i want to be an economics major, but i know that, at princeton, the "requirements" for an economics degree are not very rigorous. therefore, i want to ask the people on the cal-tech board...can you help me make a "plan of mathematics study" assuming that i can only take two math courses a year (and two economics courses a year)? here is what i have completed in high school (through local state univ).</p>

<p>multivariable calculus
linear algebra
intro to microeconomics
intro to macroeconomics
rigorous statistics (introductory, but for math majors)</p>

<p>suggestions would be helpful to me, and to anyone else who is not going to as "math-rigorous" a school as caltech.</p>

2

<p>Yay! My plan in life is to do economics theory (which involves a lot of math, of course) so I can suggest some courses for you to take. (NQO, our resident economics professor, will offer corrections, I hope, if I say something silly.)</p>

<p>I recommend these courses, in order. You will probably be able to take one a semester at first, and then two per semester as you get past freshman year. Star means extra important for economics.</p>

<p>*MAT 215 -- single variable analysis with proofs.</p>

<p>(optional) MAT 217 -- Honors Linear Algebra -- linear algebra with proofs and lots of abstract theory, taught by a Fields medalist (Charles Fefferman). You've had linear algebra, but probably not like this.</p>

<p>*MAT 218 -- Analysis in Several Variables </p>

<p>MAT 306 Introduction to Graph Theory -- important if you want to study social networks and the like.</p>

<p>*** MAT 308 -- Theory of Games -- enough said</p>

<ul>
<li>MAT 309 -- Probability and Stochastic Systems (see ORF 309)</li>
</ul>

<p>** MAT 310 -- Mathematical Statistics (goes together well with econometrics)</p>

<ul>
<li><p>MAT 314 -- Introduction to Real Analysis </p></li>
<li><p>MAT 390 -- Probability Theory </p></li>
<li><p>MAT 391 -- Random Processes</p></li>
</ul>

<p>309 vs. 390-391 are probably kind of interchangeable.</p>

<p>I know that seems like a lot, but if you take the biggest subset of these courses you can manage, you will be set to be a very competent economist.</p>

3

<p>In two words: </p>

<p>Thank you!</p>

<p>My parents are encouraging me NOT to follow economics, and to instead try to get into a good Ph.D. program for Finance after college...do you plan to do an Econ. Ph.D? Right now an Econ PhD seems more interesting than Finance/Accounting, but my parents are worried about job prospects.</p>

4

<p>PS Im taking 215 next semester hopefully.</p>

5

<p>Ben's got it right. I would only add that Real Analysis may be more important than some of the stats though it's a tossup.</p>

<p>Since you're at Princeton, make sure you get to know one or more of your professors well and try to do some serious research as an undergrad. Once you've taken some game theory/real analysis/stats serious undergrad research is the other factor that's likely to make or break your application to good schools.</p>

<p>If you don't end up in Math Econ, applied econometrics is generally more useful than graph theory or higher math. I would also try to take the first sem grad micro class at Princeton if you can hack it.</p>

<p>It's "almost" true that the ideal grad student doesn't need to take the first year Phd courses and THEN the schools force you take them again.</p>

<p>I am not entirely happy about this, but that is the way of the world.</p>

6

<p>Yes, I agree that the graph theory business is a point of taste and only useful if you want to do some kinds of trendy theory (which may not be trendy at all by the time you get out of school.) It goes without saying that the above math program should be supplemented by a steady dose of economics courses, including econometrics and the standard micro/macro sequences, adjusted slightly depending on your interests.</p>

<p>As for the finance/accounting vs. economics. First, anyone with a sufficiently good background to get into a top Econ PhD program would not typically have difficulty getting into top Finance/Accounting programs, which value math just as much or more. (If anything, the right path in this case would be to lean more on the math, while still taking the harder econ courses -- game theory, econometrics, etc.) So you can calm your parents and tell them that this is not a choice that is important to make now.</p>

<p>Personally, I think I would be unhappy doing straight finance -- I like the broader and more general approach of economics. So the right choice for me is pretty clear. I think you will also be much closer to being able to make an informed decision after four more years of learning about the world and about yourself. So for now, just relax, learn as much of the fundamentals (i.e. math) as you can, and the right decision will become apparent soon enough.</p>