Admissions Prerequisites and Recommended Courses &ndash Mathematical Finance at Rutgers

Admissions Prerequisites and Recommended Courses

Prospective students with any undergraduate major are welcome to apply if they will have completed the minimum prerequisites prior to entering the program, which include individual one-semester courses on

Multivariable calculus
Linear algebra
Ordinary differential equations
Partial differential equations
Probability (calculus-based)
Computer programming

Advice for Prospective Applicants

Applicants can strengthen their application by taking one or more of the recommended additional courses prior to entering the program; transcripts should indicate registration even if final grades are unknown at application time.
Applicants with a strong overall record but who are missing a prerequisite course may be admitted, but must complete the course with a grade B or better before September of the admission year; if such a course is not completed with a satisfactory grade, an offer of admission may be revoked.
Prior financial industry experience is not required.
If you have taken all the prequisite courses but it has been more than two (2) years since your undergraduate degree, we recommend that you retake one or more prerequisite or recommended courses to refresh your knowledge.
Domestic applicants and international applicants residing in the United States with prior visa authorization to take classes can take prerequisite courses at Rutgers as non-degree ("non-matriculated") undergraduate students. Please consult the separate application and tuition information.
Undergraduate courses in Economics, Engineering, or Physics with significant mathematics or statistics content can also indicate useful preparation. Examples of such courses include Econometrics, Signal Processing or Control Theory, Electrodynamics, Thermodynamics, or Statistical Mechanics.
Prerequisite courses can be taken at Rutgers or a local university, but it is the responsibility of the applicant to ensure that courses taken elsewhere are equivalent to Rutgers courses. For courses taken in New Jersey, applicants may consult the equivalency chart, Courses Approved for Transfer Credit, provided by our Mathematics Undergraduate Office.
Prerequisite courses may only be taken in a regular classroom setting; online or Internet courses are not accepted.
For further advice and information about undergraduate prerequisite courses, please contact the appropriate office:
1. Undergraduate Mathematics Advisor:
  For domestic applicants and international applicants with prior visa authorization to take individual courses at Rutgers and who have questions about our undergraduate mathematics courses.
2. Mathematical Finance Program Director:
  For international applicants residing outside the United States or without prior visa authorization to take courses at Rutgers and questions from all students about selection of courses to prepare for our program.

Prerequisite Courses

We expect applicants to have a level of knowledge in the prerequisite subjects consistent with the listed Rutgers courses and their accompanying textbooks prior to the start of the program. Brief descriptions of these prerequisite courses can be found in the Rutgers New Brunswick undergraduate course catalog. More detailed descriptions of mathematics courses – including sample syllabi, homework assignments, and exams – are available at the mathematics, electrical & computer engineering, and computer science undergraduate course pages.

Subject	Rutgers Course (Credit Hours)	Course Abstract	Primary Textbook
Calculus I	Math 01:640:151 (4) Calculus I for Mathematical and Physical Sciences	Analytic geometry, differential calculus with applications, logarithmic and exponential functions, introduction to the integral, additional theory and numerical applications.	Calculus Early Transcendentals by Jon Rogawski, Freeman & Co, 2007.
Calculus II	Math 01:640:152 (4) Calculus II for Mathematical and Physical Sciences	Techniques of integration, elementary differential equations, sequences, infinite series, Taylor series, parametric equations, polar coordinates. Prerequisite: Calculus I - Math 01:640:151.	Calculus Early Transcendentals by Jon Rogawski; Freeman & Co, 2007.
Multivariable calculus	Math 01:640:251 (3) Calculus III – Multivariable Calculus	Analytic geometry of three dimensions, partial derivatives, optimization techniques, multiple integrals, vectors in Euclidean space, and vector analysis. Prerequisite: Calculus II - Math 01:640:152.	Calculus Early Transcendentals by Jon Rogawski; Freeman & Co, 2007.
Linear algebra	Math 01:640:250 (3) Introduction to Linear Algebra	Systems of linear equations, Gaussian elimination, matrices and determinants, vectors in two- and three-dimensional Euclidean space, vector spaces, introduction to eigenvalues and eigenvectors. Possible additional topics: systems of linear inequalities and systems of differential equations. Prerequisite: Calculus II - Math 01:640:152.	Elementary Linear Algebra: A Matrix Approach by Spence, Insel, & Friedberg; Prentice-Hall
Ordinary differential equations	Math 01:640:244 (4) Calculus IV – Ordinary Differential Equations for Engineers or	First- and second-order ordinary differential equations; introduction to linear algebra and to systems of ordinary differential equations. Prerequisite: Calculus III - Multivariable Calculus Math 01:640:251.	Elementary Differential Equations by William Boyce & Richard Di Prima; Wiley 2004.
Ordinary differential equations	Math 01:640:252 (3) Elementary Differential Equations	First- and second-order ordinary differential equations; systems of ordinary differential equations. Prerequisites: Calculus III - Multivariable Calculus Math 01:640:251, Introduction to Linear Algebra Math 01:640:250.	Differential Equations by Paul Blanchard, Robert Devaney & Glen Hall; Brooks/Cole, 2006.
Partial differential equations *	Math 01:640:421 (3) Advanced Calculus for Engineering or	Laplace transforms, numerical solution of ordinary differential equations, Fourier series, and separation of variables method applied to the linear partial differential equations of mathematical physics (heat, wave, and Laplace's equation). Prerequisite: Calculus IV - Ordinary Differential Equations for Engineers Math 01:640:244.	Advanced Engineering Mathematics by Dennis Zill & Michael Cullen; Jones & Bartlett, 2006.
Partial differential equations *	Math 01:640:423 (3) Elementary Partial Differential Equations	Linear partial differential equations of mathematical physics (heat, wave, and Laplace's equation), separation of variables, Fourier series. Prerequisite: Calculus IV - Ordinary Differential Equations for Engineers Math 01:640:244.	Partial Differential Equations: An Introduction by Walter Strauss; Wiley, 1992
Probability (calculus-based)	Math 01:640:477 (3) Mathematical Theory of Probability or	Basic probability theory in both discrete and continuous sample spaces, combinations, random variables and their distribution functions, expectations, law of large numbers, central limit theorem. Prerequisite: Calculus III - Multivariable Calculus Math 01:640:251.	A First Course in Probability by Sheldon Ross; Prentice-Hall, 2005
Probability (calculus-based)	Stat 01:960:381 (3) Theory of Probability	Probability distributions; binomial, geometric, exponential, Poisson, normal distributions; moment generating functions; sampling distributions; applications of probability theory. Prerequisite: Calculus III - Multivariable Calculus Math 01:640:251.	N/A
Introduction to computer programming ** (Java, C, or C++)	CS 01:198:111 (4) Introduction to Computer Science (Java) or	Intensive introduction to computer science. Problem solving through decomposition. Writing, debugging, and analyzing programs in Java. Algorithms for sorting and searching. Introduction to data structures, recursion. Prerequisite: any course equal or greater than pre-Calculus II Math 01:640:112.	How To Think Like A Computer Scientist: Java Version by Allen Downey; Green Tea Press, 2003
	ECE 14:332:252 (3) (pdf) Programming Methodology I (C++) (recommended)	Principles of block structured languages and data systems. Syntax, semantics and data types of C programming languages. structured programming. Arrays, structures, lists, queues, stacks, sets and trees. Recursion and pointers. Searching, sorting, and hashing algorithms. Introduction to complexity analysis. Prerequisite: Introduction to Computers for Engineers ECE 14:440:127.	Data Abstraction & Problem Solving with C++ by F. Carrano; Prentice Hall, 2006.
	ECE 14:332:254 (1) (pdf) Programming Methodology I Lab (C++) (recommended)	Laboratory course to go along with Programming Methodologies I. Implementation of basic C++ programs. Prerequisite: Introduction to Computers for Engineers ECE 14:440:127.	C++ How to Program, by Deitel & Deitel; Prentice Hall, 2006.

* Another course, such as Real Analysis (Advanced Calculus 01:640:311 (3) or Mathematical Analysis 01:640:411 (3)), Numerical Analysis (01:640:373 (3)), or Complex Variables (01:640:403 (3)) may be accepted, but a course on partial differential equations is preferred.

** Another course, such as Computing for Mathematics & Physical Sciences (MATLAB, Maple, Mathematica, Python, or Visual Basic) (01:198:107), may be accepted instead, but a course on computer programming with C, C++, or Java is preferred. For students who cannot take ECE 14:332:252 & 254 or CS 01:198:111 during the regular Fall or Spring semesters, our program accepts CSC-133 (Introduction to Computer Science with C++) offered in Summer School by Middlesex County College, Edison, NJ.

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, birth-death processes, exponential models, continuous-time 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.
Introduction to probability II (strongly recommended)	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; Prentice-Hall, 2004
Statistics	Stat 01:960:382 (3) Theory of Statistics	Statistical inference methods, point and interval estimation, maximum likelihood estimates, information inequality, hypothesis testing, Neyman-Pearson 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 Black-Scholes 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	In-depth analysis of algorithms using object oriented techniques. Comparative algorithm analysis, sorting, graphs, NP-Completeness. 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.	Object-Oriented 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.

Optional Advanced Mathematics Courses

The courses listed in this section are not required for admission but can provide useful background.

Subject	Rutgers Course	Course Abstract	Primary Textbook
Mathematical reasoning	Math 01:640:300 (3) Introduction to Mathematical Reasoning	Fundamental abstract concepts common to all branches of mathematics. Special emphasis placed on ability to understand and construct rigorous proofs.	A Transition To Advanced Mathematics, by Smith, Eggen, St. Andre
Advanced calculus I	Math 01:640:311 (4) Advanced Calculus I	Introduction to language and fundamental concepts of analysis. The real numbers, sequences, limits, continuity, differentiation in one variable.	Introduction to Analysis by Edward D. Gaughan, 5th edition, Brooks/Cole, 1998
Advanced calculus II	Math 01:640:312 (2) Advanced Calculus II	Continuation of Advanced Calculus I	Advanced Calculus by Patrick Fitzpatrick; Brooks/Cole, 2006
Introduction to numerical analysis II	Math 01:640:374 (3) Numerical Analysis II	Continuation of Numerical Analysis I	Numerical Analysis by R.Burden & J.Faires; Brooks/Cole, 2005
Mathematical analysis I	Math 01:640:411 (3) Mathematical Analysis I	Rigorous analysis of the differential and integral calculus of one and several variables.	Principles of Mathematical Analysis by Walter Rudin, 3rd edition, McGraw-Hill, 1976
Mathematical analysis II	Math 01:640:412 (3) Mathematical Analysis II	Continuation of Mathematical Analysis I	Principles of Mathematical Analysis by Walter Rudin, 3rd edition, McGraw-Hill, 1976
Applied mathematics	Math 01:640:426 (3) Topics in Applied Mathematics	Topics selected from integral transforms, calculus of variations, integral equations, Green's functions; applications to mathematical physics.