MathResources.md

These are math video resources from youtube. The videos in bold are essential videos. Please watch the linear algebra and regression essential videos before the class, if you have not already studied it. This list is pulled from here if you want to see the notes for the videos.

• Calculus (1st semester mostly, for those who need a refresher)

  • limits
  • derivatives
  • differentiability
  • chain rule
  • minima, maxima, and critical pts; and testing critical pts
  • fundamental theorem of calculus and integration: part1, part2
  • vector fields and visualizations (up to time 2:14) (watch before class)
  • partial derivatives (watch before class)
  • gradients; gradient graphs; and contour maps
  • intro to lagrange multipliers; constrained optimization with lagrange multipliers; and an example

• Linear algebra

  • vector intro
  • real coordinate spaces
  • linear combinations, span, and basis vectors
  • linear transformations and matrices
  • matrix multiplication as composition
  • determinant
  • inverse matrices, column space and null space
  • big picture of linear algebra
  • change of basis

• Linear regression

  • linear regression overview
  • least squares + ridge regression

• Advanced: eigenvalues and PCA

  • eigenvalues and eigenvectors
  • matrix diagonalization
  • linear systems of differential equations (only for those interested in diff-eq)
  • similar matrices
  • abstract vector spaces
  • positive semi-definite matrices
  • PCA derivation (first part of video)
  • SVD derivation

Resources

• MIT online course taught by Prof. Gilbert Strang
• BOOK: LINEAR ALGEBRA AND ITS APPLICATIONS by Prof. Gilbert Strang
• Khan Academy linear algebra online course
• MIT diffeq notes (page 61 has linear ODEs)
• first order ODEs
• nice PCA blog post
• PCA chapter from PRML by Bishop
• khan academy stats
• nice interactive stats resources
• Intro and Prob chapter from PRML by Bishop (includes ML)