#### Undergraduate Pre-Requisite Course Completion

The*Master of Science Degree in Mathematics, with Option in Mathematical Finance*, is an intensive program. You will experience success in the program only if you know the required prerequisite material thoroughly. While all the prerequisite and recommended undergraduate courses are important, we advise that you pay particular attention to the following topics:

- Probability.
*Recommended text*: Sheldon Ross,*A First Course in Probability*, Prentice Hall, 7th edition, 2005 - Statistics.
*Recommended text*: Morris DeGroot,*Probability and Statistics*, Addison Wesley, 4th edition, 2011 - Ordinary differential equations
- Partial differential equations
- Computer programming (C++, Matlab, Excel/Visual Basic)

#### English as a Second Language

Fluency and skill in English communication is a requirement for all students, both to succeed in the program and also, because finance is a global field and English the common language, to secure summer internships or permanent positions upon graduation.#### Graduate Course Pre-Reading

If your knowledge of the prerequisite courses is already strong, we advise you to do pre-reading in the areas listed below. Your pre-program study will enhance your learning during the first semester and help prepare you for Summer 2007 internship interviews, which are typically held in January, February, and March.

- Mathematics
- Mathematical Finance
- Probability Theory
- Statistics
- Numerical methods
- Computer programming skills
- Excel and Visual Basic for Applications (VBA)
- C++
- Matlab, Mathematica, and Maple
- Unix/Linux

#### Mathematics

- Multivariable, especially differential, calculus
- Lebesgue integration
- Linear algebra
- Complex analysis
- Laplace and Fourier transforms
- Heat equation and its solution by analytical and numerical means (1 and 2 space dimensions)

#### Mathematical Finance

- Discrete-time (binomial) model
- Derivative securities
- Brownian motion, Poisson process
- Continuous-time models and stochastic calculus

#### Probability theory and stochastic processes

- Probability theory, including sigma algebras and conditional expectations
- Multivariate distribution and density functions
- Stochastic processes

#### Statistics

#### Numerical methods

- Linear algebra
- Equation solving and root finding
- Ordinary differential equations
- Finite-difference solution of partial differential equations
- Numerical integration
- Fast-Fourier transform
- Monte Carlo integration
- Monte Carlo solution of stochastic differential equations

#### Computer programming skills

The O'Reilly series provides solid reference texts for Visual Basic, C++, and Linux/Unix. Numerical recipes in C++ by Press is a convenient survey of numerical methods and their C++ implementation.#### Excel and Visual Basic for Applications (VBA)

Excel, especially when coupled with Visual Basic (part of Microsoft Visual Studio), can be used to implement many of the simpler numerical analysis routines and financial models.Your ability to secure a summer internship and then a permanent position after graduation will be significantly enhanced if you know Excel/VBA and especially C++ well.

#### C++

C++ is the industry standard for programming option pricing models and numerical methods at investment banks and hedge funds worldwide. A C++ test is a common component of the screening process for quants at financial institutions.An open source Gnu C++ compiler is included in most linux distributions and Cygwin, an open source Unix platform for Windows. A C++ compiler is part of the Microsoft Visual Studio Package.