Computational Methods for Data Science, Jan-May 2025

Lecture notes

Reading Materials

• Top 10 algorithms of the \(20^{th}\) century
• Definition of Numerical Analysis
• The \(25\) billion dollar eigenvector: The Linear Algebra behind Google
• The Smart Money's on Numerical Analysts
• Vancouver Stock Exchange crash due to floating point errors
• Some disasters attributable to bad numerical computing
• Numerical Computing with IEEE Floating Point Arithmetic
• What every computational mathematician should know
• Fundamental theorem of polynomial interpolation
• Backward stability of solving triangular linear system
• Backward stability of inner and outer product
• Weierstrass approximation theorem
• Orthogonal polynomials
• Legendre polynomials
• Chebyshev polynomials
• Gershgorin circle theroem

Assignments

• Assignment 1
• Assignment 2
• Assignment 3
• Assignment 4
• Assignment 5
• Assignment 6
• Assignment 7