Programming with Python: Introduction to Python, data types, file operations, object oriented programming. Programming with R: Introduction to R, string operations, data visualization.

Machine learning basics: capacity, overfitting and underfitting, hyperparameters and validation sets, bias & variance; PAC model; Rademacher complexity; growth function; VC-dimension; fundamental concepts of artificial neural networks; single layer perceptron classifier; multi-layer feed forward networks; single layer feed-back networks; associative memories; introductory concepts of reinforcement learning, Markhov decision process.

Introduction to fundamental linear algebra problems and their importance, computational difficulties using theoretical linear algebra techniques, review of core linear algebra concepts; introduction to matrix calculus; floating point representation; conditioning of problems and stability of algorithms; singular value decomposition and regularization theory.

Introduction to data mining concepts; linear methods for regression; classification methods: k- nearest neighbourclassifiers, decision tree, logistic regression, naive Bayes, Gaussian discriminant analysis; model evaluation & selection;unsupervised learning: association rules; apriori algorithm, FP tree, cluster analysis, self organizing maps, google page ranking; dimensionality reduction methods: supervised feature selection, principal component analysis; ensemble learning: bagging, boosting, AdaBoost; outlier mining; imbalance problem; multi class classification; evolutionary computat

Optimization: need for unconstrained methods in solving constrained problems, necessary conditions of unconstrained optimization, structure methods, quadratic models, methods of line search, steepest descent method; quasi-Newton methods: DFP, BFGS, conjugate-direction methods: methods for sums of squares and nonlinear equations; linear programming: simplex methods, duality in linear programming, transportation problem; nonlinear programming: Lagrange multiplier, KKT conditions, convex programing

Theoretical Foundations: Macroscopic electrodynamics, wave equations, time harmonic fields, Dyadic Green’s function, Evanescent fields. Propagation and focusing of optical fields – field operators, paraxial approximation of optical fields, polarized electric and magnetic fields, focusing of fields, point spread function, principles of confocal microscopy, near field optical microscopy, scanning near –field optical microscopy

Quantum theory of light: quantization of the electromagnetic field, evolution of the field operators, quantum states of the electromagnetic field. Quantum information processing: quantum information, quantum communication, quantum computation with qubits, quantum computation with continuous variables. Density operators and super operators, fidelity, entropy, information and entanglement measures, correlation functions and interference of light, photon correlation measurements.

Laser for detection and ranging- LIDAR applications-Doppler wind LIDAR, Differential Absorption LIDAR for water vapor monitoring. Laser application in material processing – esp. CO2, YAG , Excimer,Ruby lasers-[material processing, Cutting, Welding, drilling, micro machining] – Interation of laser radiation with matter, Heat Flow Theory, Process characteristics etc. Laser anemometry, Schlieren Techniques for wind tunnels, Holography etc Lasers for metrology – Interferometery for surface characterization, precision length measurement, time standards etc, Medical applications of lasers

Introduction : Fourier Optics, Holography,  Optical thin films and periodical structures Bragg gratings, photonic crystals,  Gaussian beam propagation, ultra fast lasers, Fundamentals of Nonlinear Optics, Quantum optics.

Nonlinear optical susceptibility, wave equation description of nonlinear optical interactions - Sum frequency generation, Difference frequency generation, Second Harmonic generation, Phase matching condition, Optical parametric Oscillators, Quantum mechanical theory of nonlinear optical susceptibility- Schrodinger equation calculation, density matrix calculation.

Introduction to probability theory, properties of probabilities, random variabes and probability distribution, generating functions, examples of probability distributions, Gaussian probability distribution, central limit theorem, multivariate Gaussian distribution. Random processes, statistical ensembles, stationarity and ergodicity, properties of autocorrelation function, spectral properties of stationary random processes, orthogonal representation of a random process, Wiener Khinchine theorem, Karhunen–Loeve expansion.