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CS 501: Mathematical Foundations of Data Science

This course focuses on fundamental mathematical ideas and topics that you should know and be familiar with when pursuing careers in data science and machine learning. The three rough areas we will cover are as follows:

  • Linear Algebra: Understanding vectors and matrices as mathematical tools for representing and analyzing data, and the computational and algorithmic aspects therein. Applications including principle component analysis and matrix factorization.
  • Probability and Statistics: Representing and dealing with uncertain knowledge. How to turn data into some representation of knowledge or understanding.  Applications including estimation, simulation theory, Kalman filtering, hypothesis testing.
  •  Optimization: Algorithmic approaches to finding good models or hypotheses, the classic example being of course Gradient Descent, but we will also look at constrained and unconstrained optimization.
Notes:
  • Linear Algebra – Vectors, Linear Transformations, Geometry, Linear Systems ( Coming Soon )
  • Linear Algebra – Bases, Eigenvalues and Vectors, Similarity and Diagonalization ( Coming Soon )
  • Optimization and Optimization in ML ( Coming Soon )
  • Probability ( Coming Soon )
  • Statistics and Statistical Inference ( Coming Soon )
  • Commentary on Noisy Gradient Descent ( Coming Soon )