Tools and Techniques¶

This section of the course contains foundational mathematical and statistical tools and techniques

Lectures¶

• Geometric Series for Elementary Economics
  • Overview
  • Key Formulas
  • Example: The Money Multiplier in Fractional Reserve Banking
  • Example: The Keynesian Multiplier
  • Example: Interest Rates and Present Values
  • Back to the Keynesian Multiplier
• Multivariate Hypergeometric Distribution
  • Overview
  • The Administrator’s Problem
  • Usage
• Modeling COVID 19
  • Overview
  • The SIR Model
  • Implementation
  • Experiments
  • Ending Lockdown
• Linear Algebra
  • Overview
  • Vectors
  • Matrices
  • Solving Systems of Equations
  • Eigenvalues and Eigenvectors
  • Further Topics
  • Exercises
  • Solutions
• Complex Numbers and Trigonometry
  • Overview
  • De Moivre’s Theorem
  • Applications of de Moivre’s Theorem
• LLN and CLT
  • Overview
  • Relationships
  • LLN
  • CLT
  • Exercises
  • Solutions
• Heavy-Tailed Distributions
  • Overview
  • Visual Comparisons
  • Failure of the LLN
  • Classifying Tail Properties
  • Exercises
  • Solutions
• Multivariate Normal Distribution
  • Overview
  • The Multivariate Normal Distribution
  • Bivariate Example
  • Trivariate Example
  • One Dimensional Intelligence (IQ)
  • Another representation
  • Magic of the Cholesky factorization
  • Math and Verbal Components of Intelligence
  • Univariate Time Series Analysis
  • Classic Factor Analysis Model
  • PCA as Approximation to Factor Analytic Model
  • Stochastic Difference Equation
  • Application to Stock Price Model
  • Filtering Foundations
• Univariate Time Series with Matrix Algebra
  • Overview
  • Samuelson’s model
  • Adding a random term
  • A forward looking model