Multivariable Math for Machine Learning

Syllabus

Primary Text: Mathematics for Machine Learning

Secondary Linear Ref.: Linear Algebra by Jim Hefferon

Secondary Calc III Ref: Calculus Volume 3 from Openstax, Strang and Herman

Calendar

There is a proposed calendar on the syllabus, but here I will record what we actually get through in each class.

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Unit 1: Linear Algebra Review and Applications

Slides

Assignments

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Exam Topics

For the exam you should be able to demonstrate facility with or knowledge of the following:

  • Diagonalization of Matrices and Eigenvalues/Eigenvectors
  • Inner Products
  • Gram-Schmidt Orthogonalization Process
  • Orthogonal Projections
  • Least-Squares Regression with Matrices
  • Symmetric Matrices
  • Quadratic Forms and Constrained Optimization
  • Principal Component Analysis
  • Matrix Decompositions:
    • LU – Decomposition
    • Eigendecomposition
    • QR – Decomposition
    • Cholesky Decomposition
    • Singular Value Decomposition

Unit 2: Multivariable Calculus

Slides

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Assignments

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Exam Topics

For the exam you should be able to demonstrate facility with or knowledge of the following:

  • Partial Differentiation
  • Optimizations with Analytic Techniques and Lagrange Multipliers
  • Gradients, Directional Derivatives, and Gradient Descent
  • Backpropagation and Automatic Differentiation (lots of chain rule)
  • Jacobians and Hessians
  • Linear and Quadratic Approximations

Final Exam

For the exam you should study the topics previously listed in units 1 and 2.