Syllabus
Vectors Spaces: Vector spaces, basis and dimension, change of basis, orthogonality, and the Gram–Schmidt process. Fundamental Subspaces: Column space, null space, row space, and left null space. Matrix Decompositions and Applications: Projections, least squares, and linear regression; eigenvalue decomposition and diagonalization; special matrices, similarity transformations, algorithms, and singular value decomposition (SVD).
Probability Theory: Probability models and axioms, conditional probability, independence, and Bayes’ rule. Random Variables: Discrete random variables, probability mass functions (PMFs), expectations, and joint PMFs; continuous random variables, probability density functions (PDFs), expectations, joint PDFs, and continuous Bayes’ rule. Probability Distributions: Binomial, Poisson, geometric, exponential, uniform, and normal distributions. Statistical Concepts: Derived distributions, convolution, covariance, correlation, the weak law of large numbers, and the central limit theorem.
Statistical Inference: Parameter estimation, hypothesis testing, and applications of hypothesis testing through case studies. Regression and Analysis: Regression analysis and analysis of variance (ANOVA). Non-Parametric Methods and Experimental Design: Non-Parametric hypothesis tests and design of experiments.