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:

## Undergraduate Pre-Requisite Course Completion

- 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)

Please see our prerequisites page for the complete list of prerequisite courses and textbooks.

## 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

## Mathematics

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

Applied linear algebra texts [Strang] will cover the required linear algebra at an appropriate level. Advanced engineering math texts [Kreysig] will cover the required complex analysis, transform, and PDE theory at about the right level. Multivariable calculus is well covered in Thomas & Finney and many similar texts.

## Mathematical Finance

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

Good introductory texts include Shreve (Volume 1) for the binomial model, Hull for descriptions of financial instruments, and Luenberger for introductory stochastic calculus.

## Probability theory and stochastic processes

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

Papoulis covers the above topics, though with an emphasis on electrical engineering. Ross is a more basic introduction, concentrating on probability theory. Karlin and Taylor provide a good introduction to stochastic processes.

## 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: C++,Python,Matlab

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.

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.

These packages are commonly used in Rutgers courses as they provide a powerful to quickly means to quickly implement numerical analysis routines.