Applicants are expected to have extensive exposure to mathematics, probability theory, statistics and programming at the undergraduate level. You will be asked to highlight your relevant coursework within the online application.

We expect applicants to be thoroughly familiar with the following:

**Calculus**: Topics covered in the standard 3-course calculus sequence, including: limits, differential and integral calculus, optimization, implicit functions, transcendental and trigonometric functions, sequences and series, methods of integration, vectors, lines, and planes, multiple integration, cylindrical and spherical coordinates, directional derivatives, scalar and vector fields, the gradient, potentials, approximation, Stokes’, and related theorems.**Linear Algebra**: Vector and matrix arithmetic, linear independence, solutions of linear systems, Gaussian elimination, row-echelon form, vector spaces, bases and norms, spectral and canonical decomposition.**Differential Equations**: First-order equations, second-order equations, systems of differential equations, linearization, Laplace transforms, Liapunov functions.**Probability Theory:**Combinatorial analysis, conditional probability and independence, joint distributions of random variables, moments and moment generating functions, limit theorems, conditional expectation and martingales, Markov chains, simulation**Statistics**: Sampling, statistical inference, prior and posterior distributions, maximum likelihood, sampling distributions of estimators, linear statistical models and the method of least squares**Computer Programming:**Basics of R and Python programming, including data types, data structures, manipulation of vectors and arrays, reading data from files, and graphical procedures.

#### Mathematics and Statistics Review (QSTMF600)

Mathematical Finance as a discipline borrows concepts from probability theory, statistics, linear algebra, calculus and optimization, ordinary and partial differential equations, computer science and financial economics. This course reviews the essential prerequisites in mathematics, probability and statistics to prepare students for the MS in Mathematical Finance program. The course begins with a review of probability and the fundamentals of stochastic processes. Following this, statistical inference and linear algebra are reviewed. A review of comparative statics, optimization theory and dynamics, beginning with a review of integration, and continuing with first- and higher- order differential equations concludes the course.