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    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 between the time you submit your application and the time the program begins.

    Computer Programming Experience

    Coursework or experience in computer programming and familiarity with computational and management tools.

    Language/Topic Proficiencies 
    • C++ Programming
    • Advanced Python
    • Advanced R
    • Advanced Machine Learning with Python

    Quantitative Background

    A strong quantitative background including multivariate calculus, linear algebra, partial differential equations, numerical analysis, and advanced statistics and probability.

    Calculus (2 courses suggested)
    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.
    Linear Algebra (1 course suggested)
    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.
    Partial Differential Equations (1 course suggested)
    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.
    Statistics (2 courses suggested - two advanced statistics or econometrics)
    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.
    Numerical Analysis (1 course suggested)
    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.

    Finance (2 courses OR equivalent work experience)
    Examples
    • 131. Corporate Finance and Financial Analysis. This course will cover the principles and practice of business finance. It will focus on project evaluation, capital structure, and corporate governance. Firms' policies toward debt, equity, and dividends are explored. The incentives and conflicts facing managers and owners are also discussed.
    • 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).

    English Writing, English Composition, Speech/Rhetoric (1 course OR equivalent work experience)
    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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