Credits: 3 (3-0-0)
Overlaps with: MTL101, MTL104, MTL103, MTL106, MTL108, MTL265, MTL502, MTL508, MTL601, MTL628, MCL261, MCL761, ELL701, ELL780, COL756, MSL719
Description
Vector space, dimension, basis, matrix rank & nullity, system of linear equations, eigenvalues and properties for some special matrices, diagonalization. Normed linear space, matrix norm, closed sets, sequence, convergence, Banach space, Hahn Banach Theorem (without proof), Inner product space, orthonormal basis, Gram Schmidt process, Hilbert space, adjoint operator, SVD. Nonlinear programming, linearizing cone, KKT optimality, convex function and its properties, Lagrange function, Lagrange dual. Steepest decent method for unconstrained problem, momentum gradient and stochastic gradient method, empirical risk, shattering, VC dimension, Mercer theorem, reproducing Kernel. Probability, Bayes theorem, pdf and cdf, moment generating function, some discrete and continuous distributions, transformation of variables, t-test, chi-square test, F-test, random sampling, central limit theorem, maximum likelihood estimator, hypothesis testing (without proof but the concept building)