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 the sections within that topic should be studied in order.
Related Material
- If you have watched the Several Variables Calculus videos below and want to see more videos to better understand the material, you can see Chapter 14 of our course MATH 251: Several Variables Calculus. Note these MATH 251 videos are outside the scope of this mini-course and not required viewing.
- If you have watched the Differential Equations videos below and want to see more videos to better understand the material, you can see Chapter 2, Section 3.6, and Chapter 7 of our course MATH 308: Differential Equations. Note these MATH 308 videos are outside the scope of this mini-course and not required viewing.
Summary
Review of several variable calculus, differential equations, and probabillity
Skills
Applications of derivatives for functions with several variablesSolving Differential EquationsCalculating probabilities
Target Audience
For students starting a Master of Science degree in Quantitative Finance
Sections
Module 1: 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
Module 2: Differential Equations
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
Module 3: Mathematical Probability
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 Distributions
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