Linear Algebra
Matrices: Definition of matrix, different types of matrices, algebra of matrices, adjoint and inverse of a matrix, rank and elementary transformations of matrices.
Linear equation: Linear equation, system of linear equations, solution of system of linear equations, homogeneous and non-homogenous equations, consistent and inconsistent system of linear equations, unique solution and general solution.
Vector spaces: Vector addition and scalar multiplication, vector spaces and subspaces; linear combination and linear spans. Row space of matrix. Basis and dimensions, linear dependence and independence, Basis and dimensions.
Linear mapping, eigenvalue and eigenvector: Mappings, linear mappings, linear operators, Kernel and image linear mapping, Polynomials of matrix and linear operator, eigenvalues and eigenvectors, diagonalizability, characteristic polynomial, Caley-Hamilton theorem.
Fundamentals of Statistics
Probability & Random variables: Probability, sample space, random variables (discrete and continuous)
Probability distributions: Binomial distributions, Poisson, uniform, normal, exponential; expected values.
Introduction to Statistics: Frequency distribution. Mean, median, mode and other measures of central tendency, Standard deviation.
Sample distribution & test of hypothesis: Confidence limits, estimation and hypothesis testing, chi-square distribution; Regression analysis.