Löb'sTheorem

Hi all, I'm presently a math major at an unknown school, but I've taken a pretty absurd number of math courses. My overall GPA is 3.4, but there were several semesters where my schedule consisted of 5-6 math courses. Here is the list of relevant classes: First year : Calc I B Calc 2 B Calc 3 B Intro Stats/prob. C+ Linear Algebra A MAthematical Programming A Abstract Algebra I A Intro to higher math A Number Theory A Abstract Algebra 2 A Diff eq B Numerical Analysis C+ AI programming in OCAML B+ Discrete Mathematics A Real Variables (under grad real analysis) A- Real Variables 2 B Complex Variables C+ Theory of Computation A Graduate Complexity theory seminar B+ Graduate Formal Methods in Prog. A Graduate Mathematical Logic I B+ Graduate MAthematical Logic 2 B+ Applied Algebra A Intro to Alg. Geometry A Cryptology B Relevant work experience: One summer working as a research fellow on Algebraic cryptanalysis Two years as a calculus tutor Presently have a job for an academically oriented non-profit formatting papers for publication (latex/typsetting work) and doing background research GRE: 790Q/660V/4.5AW GRE MAth Subj.: 30%ile (retaking, hope to get to at least 50%ile) Psych Subject GRE: 50%ile (75%ile on experimental psych subsection) - Note: I have taken no psychology courses, but I have a strong interest in neuroeconomics and behavioral economics. A particular interes here is in searching for invariants in neuroeconomic models of choice and asking how they may be applied within other economic models (prospect theory and behavioral economics are more broadly, interests of mine). Concerns: No economics experience on paper, no coursework. My university is very iffy, and most of my graduate work was done at a nearby larger university. Also, I may take either graduate real analysis or topology in the fall, along with a course on experimental methods and another probability course. Interests: The school that I would most like to attend is NYU, for their strong neuroeconomics program. I'm also interested in Duke for the same reason, (also I'm a fan of Robin Hanson). Aside from neuroeconomics my interests lie in modelling bounded rationality, applications of game theoretic analysis to economics, and applications of machine learning and Bayesian statistics to econometric analysis. I'm also interested in the application of Judea Pearl's Structural Models to policy analysis. Also, information/prediction markets (and analyzing information inefficiencies and methods for intervention more generally) are an interest. I have a very wide range of interests outside of economics, though I'm not sure if that is of any consequence (positive or negative) to schools. School List Recap: NYU CMU Duke U Chicago (of course) Cal Tech U Rochester UC San Diego Ohio State (relatively close to me, seems to have a strong mathematical economics faculty) Pending any feedback I get here, I'll adjust my list. Currently I feel that it is too skewed towards the top schools, but this just happens to be the list of schools that are of the greatest interest to me presently.

I recall seeing that having taken a graduate course in complex analysis as an undergraduate and done well is a particularly good indicator that you will do well in a graduate program and sticks out; more so than other graduate courses. I'm not sure if this is true, and it doesn't totally seem sensible to me, so can anyone tell me whether this is or is not the case?

Ok, that sounds like solid advice; I could definitely write quite a bit on my research, and it is fairly closely related to my interests. So 90% on ideas from that research (which will be invariant program to program) and then talk about other interests and faculty that interest me, to be tailored for each program. I'm glad to hear that a good SoP can make a difference, my GPA (~3.5) is fairly solid but not quite up to snuff, and my institution is very small (though I've taken graduate courses at a neighboring institution starting my third year; however, they unfortunately limit the number of courses I can take as if they were from my home institution, hence if I wanted to take as many as I could have handled it would have been quite costly). Unfortunately, I won't have any publications as of the time I apply (though I'm continuing my research this year, so I may acquire one on the way out, but that will be no help on my applications).

I'll be applying to graduate schools this fall, and I've been doing quite a bit of research into my various options (of course I've been looking into grad schools for the duration of my undergraduate degree, but now I need to actually fill in the minutia and avoid making any gaffs that hurt my chances, if possible); in any event, I'm a bit unsure of (a) How much weight (if much at all) is given to the statement of purpose (b How much detail should be included in the way of interests, interest in faculty research specialties etc. My primary concern is with length, and due to the breadth of my interests I can only include so much. To give you an idea, my primary areas of interests are Algebraic Areas: algebraic geometry (I'm presently part way through Eisenbud, and Atiyah McDonald, and I've covered a significant amount of material in the book Ideals Varieties and Algorithms and have had an independent study in the basics of the area), algebraic cryptanalysis (I've done some research in this), arithmetic geometry, category theory (specifically categorical logic and the application of category theory to cognitive science, though there are only a few researchers looking into the latter), Geometric complexity theory is super fascinating to me Logic Areas: Game semantics in proof theory, Girard's linear logic and "Ludics" programme and Japaridze's work in computability logic, constructive mathematics and Martin-Löf type theory (a large part of this is due to the work by Voevodsky and Awodey in homotopy type theory, which seems very interesting to me), applications of model theory to algebraic geometry and tropical geometry, reverse mathematics (I've been reading Simpson's book on subsystems of second order arithmetic and it is fascinating to me) Applied Areas: Machine learning, specifically reinforcement learning and Bayesian methodologies in pattern recognition (I've been reading Barto and Sutton as well as Bishop), Computational cognitive science and computational neuroscience, specifically representational learning Some of these areas are more recent interests and some are surely irrelevant to certain departments, so I would probably not include my interest in linear logic or machine learning in the case of a school that has no researchers doing anything related to either area. So now that I've blasted you with a wall of boring self indulgence, can anyone tell me whether I should include as many interersts as possible, if the school has people working in a lot of them? Or should I totally avoid doing that? Basically, I need to know how to write a statement of purpose.