Hi Everybody,
I'm preparing to apply to PhD programs in Economics for Fall 2013. I have basic calculus as an undergraduate and an MA in Development Economics from an Italian University, both good GPAs. In order to beef up my math credentials I took a 9 credit course at an Italian University called "mathematical economics" which covered the following topics:
(translated w/ google, sorry for some awkwardness)
"Linear Algebra. Vector spaces, norm and inner product in n-dimensional spaces, linear dependence and independence, dimension, bases, rank, matrices, matrix algebra, inverse matrix, symmetric matrix, determinant, characteristic or rank of a matrix, systems of linear equations; solutions, homogeneous systems, eigenvalues, eigenvectors, eigenspace, the power of a matrix, diagonalization of matrices, eigenvalues of symmetric matrices, the property 'of the eigenvalues.
Basic topology, defined functions between Euclidean spaces, graphs, contour lines, linear functions, quadratic functions, continuous functions, concave functions and convex functions.
Multivariate calculus. Partial derivatives, differential derivative along a curve, directional derivative and gradient, higher order derivatives, the Hessian matrix, Schwartz theorem.
Implicit functions. Definitions, comparative statics, inverse function theorem
Quadratic forms. Definitions, a sign of quadratic forms, principal minors of a matrix.
Free and constrained optimization. Definitions, conditions of the first order, second-order conditions, equality constraints, inequality constraints, method of substitution, the Lagrange method, conditions of the second order optimization for convex functions.
Ordinary differential equations. Definitions and examples; exact differential equations with separable variables, exact equations, homogeneous equations, Malthusian growth model, a model of logistic growth, second-order linear equations (homogeneous or not); general theorem of existence and uniqueness' of the solution; field of directions.
Systems of differential equations: generalities; two-dimensional systems, linear systems: eigenvalues through decisive method, method of substitution, stationary states and their stability"
This was a beast of a course, and I got an 87%. It's sort of mixed bag of topics from Cal II-III, Linear Algebra, and ODE courses. I also have a perfect score from an econometrics class during the MA. How do you think this will look to admission offices and is it sufficient for survival?
Thanks,
Michael
