This course is designed specifically for undergraduate Mathematics students. It covers a wide range of topics including Jacobi and Gauss-Seidel methods, various vector and matrix norms, error analysis, approximation theory for orthogonal polynomials, least squares, Chebyshev polynomials, eigenvalue approximation for matrices using power, inverse power, symmetric and Householder methods. In addition to this, the course will also explore numerical solutions to initial and boundary value problems.