Math 561 Syllabus

This is a Qualifying Eligible (QE) course for the Math PhD with regular, graded HW and a comprehensive final exam.


The equivalent of Math 212 and 221.  Some coding experience with Matlab/Python/C.


Singular Value Decomposition, Principle Component Analysis, QR Factorization, Least Square Problems, Conditioning and Stability, Direct Method for Linear Systems – Gaussian Elimination, Cholesky Factorization, Iterative Methods for Linear Systems – Conjugate Gradients, GMRES, Preconditioning,  Eigenvalue Problem – Power Method, Rayleigh Quotient, Inverse Iteration, QR Algorithms, Newton Method for Nonlinear Equation, Multigrid Method and Fast Fourier Transform.


  • Numerical Linear Algebra, by Lloyd Trefethen and David Bau
  • Matrix Computations, by Gene H. Golub and Charles F. Van Loan
  • Applied Numerical Linear Algebra, by James Demmel
  • Solving Nonlinear Equations with Newton’s Method, by C. T. Kelley