# Math for Quantitative Finance

### A mini-course of Mathematics to prepare for Quantitative Finance

This online workshop reviews topics to help students prepare for a Master of Science in Quantitative Finance.

For more information on the program, please consult the program page.

This course is a collaboration between the Math Learning Center, the Department of Mathematics, and the Adam C. Sinn '00 Department of Finance.

Format

- The videos for this mini-course are broken into three main topics: Several Variable Calculus, Differential Equations, and Mathematical Probability.
- The three topics are independent of each other and can be studied in any order.
- Each topic covers the listed sections, and these sections should be studied in order.

## Course Content

View Topic: Several Variables Calculus- Section 1: Functions of Several Variables
- Section 2: Limits and Continuity
- Section 3: Partial Derivatives
- Section 4: Tangent Planes and Linear Approximations
- Section 5: The Chain Rule
- Section 6: Directional Derivatives and The Gradient Vector
- Section 7: Maximum and Minimum Values
- Section 8: Lagrange Multipliers

- Section 1: Integrating Factor
- Section 2: Separable Equations
- Section 3: Compound Interest
- Section 4 : Variation of Parameters
- Section 5: Systems of Ordinary Differential Equations
- Section 6: Matrices
- Section 7: Systems of Equations, Linear Independence, and Eigenvalues & Eigenvectors
- Section 8: Homogeneous Linear Systems with Constant Coefficients
- Section 9: Complex Eigenvalues
- Section 10: Fundamental Matrices
- Section 11: Repeated Eigenvalues
- Section 12: Nonhomogeneous Linear Systems

- Section 1: Probabilistic Models and Probability Laws
- Section 2: Conditional Probability, Bayes’ Rule, and Independence
- Section 3: Discrete Random Variable, Probability Mass Function, and Cumulative Distribution Function
- Section 4: Expectation, Variance, and Continuous Random Variables
- Section 5: Discrete Distributions
- Section 6: Continuous Distribution
- Section 7: Joint Distribution Function, Marginal Probability Mass Function, and Uniform Distribution
- Section 8: Independence of Two Random Variables, Covariance, and Correlation
- Section 9: Conditional Distribution and Conditional Expectation
- Section 10: Moment Generating Function
- Section 11: Markov’s Inequality, Chebyshev’s Inequality, and Weak Law of Large Numbers
- Section 12: Convergence and the Central Limit Theorem