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Academic Preparation

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)
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.


  • 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)
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 provides 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

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++ 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.

Matlab, Mathematica, and Maple

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


As with C++, students who seek positions as quant finance developers or modelers, should be familiar with Unix (editors such as Emacs or VI, the Unix command line, and basic shell scripts)

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Mathematical Finance Master's Program

Department of Mathematics, Hill 348
Hill Center for Mathematical Sciences
Rutgers, The State University of New Jersey
110 Frelinghuysen Road
Piscataway, NJ 08854-8019

Email: finmath (at)
Phone: +1.848.445.3920
Fax: +1.732.445.5530