Mathematics

Contents:

• Fourier Transform
  • Important Examples
  • Duality
  • Operations
  • Convolution: Introduction
  • Convolution: Cooling of a Rod
  • Convolution: Central Limit Theorem
  • Generalized Fourier Transform: Schwartz Space
  • Generalized Fourier Transform: Tempered Distribution
  • Generalized Fourier Transform: Delta Distribution
  • Application One: Diffraction
  • Reference
• Statistical Learning
  • Mean Squared Error Decomposition
  • Bayes Theorem
  • Bayes Example: Biased Coin
  • Bayes Example: Classification
  • Multivariate Gaussian Distribution
  • LDA: Classification
  • LDA: Dimensionality Reduction
  • Quadratic Discriminant Analysis
  • Linear Regression: Formula Derivation
  • Linear Regression: Signal-to-Noise Ratio (SNR)
  • Linear Regression: Ordinary Least Squares
  • Linear Regression: OLS Formula
  • Linear Regression: Ridge Regression
  • SVM: Kernel Method
  • Gradient in Backpropagation
  • Gradient Descent
  • Policy Gradient
  • Appendix A: Setup R Environment
  • Appendix B: Setup Jupyter Lab Environment
• Miscellaneous
  • Multiplying Positives Makes a Positive
  • Calculus of Variations: Circle Minimizing Arc Length
  • KKT Example: Spacecraft Landing Problem

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