Recommended Additional Courses
Completion of one or more of the courses in this section is recommended prior to program start, but not required for admission.
Subject  Rutgers Course  Course Abstract  Pimary Textbook 

Introduction to numerical analysis I (strongly recommended) 
Math 01:640:373 (3) Numerical Analysis I 
Analysis of numerical methods for the solution of linear and nonlinear equations, approximation of functions, numerical differentiation and integration, and the numerical solution of initial and boundary value problems for ordinary differential equations.  Numerical Analysis by R.Burden & J.Faires; Brooks/Cole, 2005 
Introduction to theory of functions of complex variables  Math 01:640:403 (3) Introductory Theory of Functions of a Complex Variable 
First course in the theory of a complex variable. Cauchy's integral theorem and its applications. Taylor and Laurent expansions, singularities, conformal mapping.  Complex Variables by Stephen Fisher, Dover, 1999 
Stochastic processes  Math 01:640:424 (3) Stochastic Models for Operations Research 
Introduction to stochastic processes and their applications to problems in operations research: Poisson processes, birthdeath processes, exponential models, continuoustime Markov chains, queuing theory, computer simulation of queuing models, and related topics in operations research.  Introduction to Stochastic Modeling, H. Taylor & S. Karlin, Academic Press 
Introduction to probability II (strongly recommended) 
Math 01:640:478 (3) Probability II or

Sums of independent random variables, moments and moment generating functions, characteristic functions, uniqueness and continuity theorems, law of large numbers, conditional expectations, Markov chains, random walks..  Introduction to Probability Models by Sheldon Ross; Academic Press, 2006. 
Stat 01:960:582 (3) Introduction to Theory and Methods of Probability 
Emphasis on methods and problem solving. Topics include probability spaces, basic distributions, random variables, expectations, distribution functions, conditional probability and independence, sampling distributions  Probability and Statistics by M. DeGroot & M. Schervish,; Adison/Wesley, 2001.  
Statistics  Math 01:640:481 (3) Mathematical Theory of Statistics or 
Fundamental principles of mathematical statistics, sampling distributions, estimation, testing hypotheses, correlation analysis, regression, analysis of variance, nonparametric methods.  John E. Freund's Mathematical Statistics with Applications by Irwin Miller & Marylees Miller; PrenticeHall, 2004 
Stat 01:960:382 (3) Theory of Statistics 
Statistical inference methods, point and interval estimation, maximum likelihood estimates, information inequality, hypothesis testing, NeymanPearson lemma, linear models.  Mathematical Statistics with Applications by Wackerly, Mendenhall, & Scheaffer; 2001.  
Introduction to financial mathematics (strongly recommended) 
Math 01:640:495 (3) Selected Topics in Mathematics – Financial Mathematics 
Mathematical techniques used to model and analyze financial derivatives such as options. Topics covered are hedging, arbitrage and the fundamental theorem of asset pricing; pricing options with binomial tree models; risk neutral probabilities and martingales applied to pricing; Brownian motion, geometric Brownian motion and the BlackScholes formula; partial differential equations for pricing. As time permits, interest rate derivatives and term structure models.  The Mathematics of Finance: Modeling and Hedging by V. Goodman and J. Stampfli; Brooks/Cole, 2000. 
Basic computer programming (MATLAB, Maple, Mathematica, or Python)  CS 01:198:107 (3) Computing for Math and Physical Science (or similar mathematics or engineering course employing MATLAB) 
This course is designed to introduce the student to computers, programming, and some of the key ideas on which the field of computer science is based. The primary vehicle for doing so is the computer language MATLAB. The use of a program like Maple to manipulate symbolic equations is also covered. This course is aimed at students majoring in math or in a physical science.  Introduction to Scientific Computation and Programming by Daniel Kaplan; Brooks/Cole, 2003 
Advanced computer programming (Java, C, C++) (strongly recommended) 
ECE 01:332:351 (3, pdf) Programming Methodology II (C++) (recommended) or

Indepth analysis of algorithms using object oriented techniques. Comparative algorithm analysis, sorting, graphs, NPCompleteness. Emphasis is on programming and practical applications in Electrical and Computer Engineering. Introduction to parallel programming. Programming Project.  Data Abstraction & Problem Solving with C++ by F. Carrano; Prentice Hall, 2006 
CS 01:198:113 (4) Introduction to Software Methodology 
Essential principles, techniques and tools used to develop large software programs in Java, and going "under the hood" with memory addressing and management in C.  ObjectOriented Design and Patterns, by Cay Horstmann; Wiley  
Economics and Finance  No specific course recommendations. Students should consult their undergraduate or graduate advisors for Economics or Finance for suitable courses in economic theory and quantitative finance, after explaining their interest in mathematical finance to their advisors. 