Suggested Background Work and Self-Assessment
Suggested Mathematical Background
Listed below is an outline of the mathematical background that we think is desirable to have in order to be successful in the most challenging of courses in the program.
Linear Algebra: Basic topics, including: matrix/vector notation, operations on matrices and vectors, determinants, eigenvalues and eigenvectors, quadratic forms, and systems of linear equations.
Calculus: Multivariable differentiation and integration, series expansions, and function approximation and maximization.
Probability: Sample spaces and random variables, common distributions and densities, moments of distributions, conditional probability and Bayes’ theorem, law of large numbers, central limit theorem, joint distributions, covariance, correlation, and stochastic independence.
Stochastic Processes: Random walks, Bernoulli trials, Markov processes, basic properties of linear time series models, continuous-time processes, and Ito’s lemma.
Statistics/Econometrics: Parameter estimation, confidence intervals, hypothesis tests, linear regression models, ordinary least squares, and likelihood principle.
Computer Literacy: Basic programming experience and readiness to learn new tools and features; for example, familiarity with programming in MATLAB, Python, Java, or C++. Basic experience with Microsoft Office business tools, especially use of Excel for data analysis and presentation.
To assess the adequacy of your mathematical background, please use the following self-assessment test. If you experience difficulties in any particular area, we strongly recommend that you strengthen your skills through self-study or formal coursework prior to enrolling in the MFin program.
Students without this background will enroll in 15.S24 - Fundamentals of Financial Mathematics, which provides an overview of fundamental mathematics essential for the study of modern finance: linear algebra, probability, stochastic processes, statistics, optimization, and programming in MATLAB.
MIT OpenCourseWare provides access to many resources that may be helpful, including lecture videos, lecture notes, problem sets, exams, and solutions.
- 18.02: Multivariable Calculus (as taught in Fall 2007)*
- Lectures 1-4: some vector and matrix properties
- Lectures 8-13: partial derivatives; Lagrange multipliers
- 18.05: Introduction to Probability and Statistics
- 18.06: Linear Algebra (as taught in 2010)*
- 6.041: Probabilistic Systems Analysis and Applied Probability (as taught in 2010)*
- 6.041x: Introduction to Probability — The Science of Uncertainty
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