Application Preparation Course

The Financial Mathematics Preparation Course is designed to provide potential applicants for the Master's Program in Financial Mathematics with the necessary mathematical background. There are no admissions criteria though students should have some college level mathematics to successfully follow the lectures. The course can also be taken remotely through the web.

The course meets every Tuesday 5-7pm in Ryerson Hall Room 251, starting October 6 and runs through July 2010. The cost of the course is $2,500 a quarter or $7,500 for the entire 10 months course

The course does not lead to a degree. Successful completion of the course does not guarantee admission to the Master's program

The lectures alternate between Calculus and Linear Algebra/Economics

Linear Algebra:

Real and complex vector spaces, linear transformations and matrices, change of basis. Determinants, characteristic polynomial and eigen-values. Inner products and orthogonality. Diagonalization of symmetric matrices and the spectral theorem. Matrix decompositions: SVD-decomposition, QR-decomposition and Householder reflectors, LU and Cholesky decomposition.

Applications: principal component analysis, portfolio optimization, single and multi-period market models, stochastic processes, martingale theory.

Calculus

The real and complex numbers, the concepts of convergence and limits. Completeness of the real numbers. Continuous functions, max and min. Integration and differentiation of functions of a single variable. Mean value theorem, the fundamental theorem of calculus. Infinite series, power series and Taylor series, convergence of infinite series. Functions of several variables, partial derivatives. Differentiability of a function of several variables, the chain rule in several variables. Inverse and Implicit function theorems. Optimization, Lagrange multipliers. Multiple integrals, Fubini's theorem. Vector functions, curve and surface integrals, Green's and Stokes' theorems.

Differential equations, existence theorem for first order equations. Techniques for solving low order equations.

Partial differential equations, first order equations, characteristics. Second order linear equations, the heat equation. Fourier and Laplace transform.