Various Statistical Measures:
basic probability, sample space, events, axioms of probability conditional probability, independent events. Random variables, continuous/Discrete random variables, exception, valance, Convenience, conditional distributions, moment generating functions.
Multiple regressions:
Distributions, Bernoulli, Binomial, Poisson, Uniform, Normal, Exponential, Chi-square T and F.
Sample statistics, empirical distributions, and goodness of fit, sampling from normal populations.
Parameter estimation:
moment method, maximum likelihood, interval estimated. Hypothesis Testing, Significance Intervals.
Basics:
Summary of basic concepts from Linear algebra and numerical analysis, Matrices, Operation counts, Matrix Norms, Type of Errors in Numerical computation.
Matrix Factorization and Linear System:
Cholesky Factorization, QR factorization by House holder matrices Lu-factorization and Gaussian elimination, partial pivoting, error Analysis (statement of result) soling triangular system by substitution, solving full systems by factorization. Lu-factorization for banded and sparse matrices, storage schemes, Iterative Methods, Jacobi, Gauss – Seidal and SOR Iterations, Conjugate gradient method, preconditioning.