Prerequisites
Before the program you are applying to is scheduled to begin, you should have taken—or have a plan in place to take—the prerequisite courses listed below for a grade of "B" or higher. You should also plan to take all of the pre-program courses in addition to the prerequisites to reinforce your understanding of the basic concepts.
Prerequisites include:
For students who have not taken a math course in more than 5 years, we do recommend some type of refresher course in order to excel in the program.
Please note that you do not necessarily need to complete all of the prerequisites and coursework prior to submitting your application. However, you do need to have a clear plan in place to complete the coursework if you have not already done so via your prior studies between the time you submit your application and the time the program begins.
More information on Preparation Resources as well as where to take classes can be found in the MFE Preparation Resources.
Computer Programming Experience
- C++ Programming
- Advanced Python
- Hands-on experience, whether through job or academic projects, with a low-level language such as C++, or a high-level language such as Python
- An understanding of data ETL and algorithm design
- Ability to pick-up a programming language is also very helpful, and therefore being comfortable with development tools such as Jupyter Notebooks, GitHub, CLEs goes a long way.
- Hands-on experience with:
- Training/validation/inference of AI/ML models from common open-source libraries
- large data sets management through tools such as (and not limited to): kX (formerly kdb), Spark, Databricks/Snowflake
- In-depth understanding, even experience, with memory management and algorithm optimization (I/O, alternative implementations with trade-offs in average vs worst-case complexity)
Quantitative Background
A strong quantitative background including multivariate calculus, linear algebra, partial differential equations, numerical analysis, and advanced statistics and probability.
Examples
- 1A, 1B. Calculus. (A) An introduction to differential and integral calculus of functions of one variable, with applications and an introduction to transcendental functions. (B) Techniques of integration; applications of integration. Infinite sequences and series. First-order ordinary differential equations. Second-order ordinary differential equations; oscillation and damping; series solutions of ordinary differential equations.
- 53. Multivariable Calculus. Parametric equations and polar coordinates. Vectors in 2- and 3-dimensional Euclidean spaces. Partial derivatives. Multiple integrals. Vector calculus. Theorems of Green, Gauss, and Stokes.
Examples
- 54. Linear Algebra & Differential Equations. Basic linear algebra; matrix arithmetic and determinants. Vector spaces; inner product as spaces. Eigenvalues and eigenvectors; linear transformations. Homogeneous ordinary differential equations; first-order differential equations with constant coefficients. Fourier series and partial differential equations.
- 110. Linear Algebra. Matrices, vector spaces, linear transformations, inner products, determinants. Eigenvectors. QR factorization. Quadratic forms and Rayleigh's principle. Jordan canonical form, applications. Linear functionals.
Examples
- 126. Introduction to Partial Differential Equations. Classification of second order equations, boundary value problems for elliptic and parabolic equations, initial value problems for hyperbolic equations, existence and uniqueness theorems in simple cases, maximum principles, a priori bounds, the Fourier transform.
Examples
- 101. Introduction to the Theory of Probability. Random variables and their distributions, expectation, univariate models, central limit theorem, statistical applications, dependence, multivariate normal distribution, conditioning, simulation, and other computer applications.
- 102. Introduction to the Theory of Statistics. Least squares estimates, t tests, F tests, and the application of these procedures to the design and analysis of experiments. Maximum likelihood estimates, Wald test and likelihood ratio tests in the context of logistic regression and Poisson regression. Computer-based applications.
- 134. Concepts of Probability. An introduction to probability, emphasizing concepts and applications. Conditional expectation, independence, laws of large numbers. Discrete and continuous random variables. Central limit theorem. Selected topics such as the Poisson process, Markov chains, characteristic functions.
- 135. Concepts of Statistics. A comprehensive survey course in statistical theory and methodology. Topics include descriptive statistics, maximum likelihood estimation, goodness-of-fit tests, analysis of variance, and least squares estimation. The laboratory includes computer-based data-analytic applications to science and engineering.
- 140. Economic Statistics and Econometrics. Introduction to problems of observation, estimation, and hypothesis testing in economics. This course covers the linear regression model and its application to empirical problems in economics
- 141. Econometric Analysis. Introduction to problems of observation, estimation, and hypothesis testing in economics. This course covers the statistical theory for the linear regression model and its variants, with examples from empirical economics.
Examples
- 128A. Numerical Analysis. Programming for numerical calculations, round-off error, approximation and interpolation, numerical quadrature, and solution of ordinary differential equations. Practice on the computer.
Training in Finance
Sufficient training to undertake graduate study in the chosen field.
Examples
- 132. Money and Capital Markets. Organization, behavior, and management of financial institutions. Markets for financial assets and the structure of yields, influence of Federal Reserve System and monetary policy on financial assets and institutions.
- 133. Investments. Sources of and demand for investment capital, operations of security markets, determination of investment policy, and procedures for analysis of securities.
- 100B, 101B. Macroeconomics. A study of the factors/theories which determine national income, employment, and price levels, with attention to the effects of monetary and fiscal policy.
Language Skills
Excellent writing, speaking, and presentation skills (in English).
Examples
- 100. Business Communication. Theory and practice of effective communication in a business environment. Students practice what they learn with oral presentations and written assignments that model real-life business situations.
- R1A, R1B. The Craft of Writing. (A) Rhetorical approach to reading and writing argumentative discourse. Close reading of selected texts; written themes developed from class discussion and analysis of rhetorical strategies. (B) Intensive argumentative writing drawn from controversy stimulated through selected readings and class discussion.
- R1A, R1B. Reading and Composition. Instruction in expository writing in conjunction with reading literature.
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