Basics of Topology; complexes on data; homology; topological Persistence; computing Betti numbers; reconstruction from data; topology inference from data; computing optimized homology cycles; reeb graphs from data; topology of Laplace operators, spectra approximation.

Greedy and dynamic programming algorithms; Kruskals algorithm for minimum spanning trees; the folklore algorithm for the longest common subsequence of two strings; Dijstras algorithm and other algorithms for the shortest path problem; divide-and-conqueror and checkpoint algorithms; the Hirshbergs algorithm for aligning sequences in linear space; quick sorting; the Knuth-Morrison-Pratt algorithm; suffix trees; data structures: chained lists, reference lists, hash- ing; the Chomsky-hierarchy of grammars; parsing algorithms; connections to the automaton theory; Turing-machines; complexity and

The reinforcement learning problem; tabular & approximate solution methods: dynamic programming, Monto-Carlo Methods, temporal difference learning, eligibility traces; planning and learning; dimensions of reinforcement learning.

Graphical Models: Basic graph concepts; Bayesian Networks; conditional independence; Markov Networks; Inference: variable elimination, belief propagation, max-product, junction trees, loopy belief propogation, expectation propogation, sampling; structure learning; learning with missing data.

Deep Learning: recurrent networks; probabilistic neural nets; Boltzmann machines; RBMs; sigmoid belief nets; CNN; autoencoders; deep reinforcement learning; generative adversarial net- works; structured deep learning; applications.

Image Formation Models, Monocular imaging system, Orthographic & Perspective Projection ,
Camera model and Camera calibration , Binocular imaging systems Image Processing and Feature
Extraction , Image representations (continuous and discrete), Edge detection, Motion Estimation ,
Regularization theory, Optical computation , Stereo Vision , Motion estimation , Structure from
motion Shape Representation and Segmentation , Deformable curves and surfaces , Snakes and
active contours , Level set representations , Fourier and wavelet descriptors

Unconstrained Optimization: line search method: Wolf condition, Goldstein condition, sufficient decrease and backtracking, Newtons method and Quazi Newton method; trust region method: the Cauchy point, algorithm based on Cauchy point, improving on the Cauchy point, the Dog- leg method, two-dimensional subspace reduction; nonlinear conjugate gradient method: the Fletcher Reeves method.

Theory of reproducing kernel Hilbert space, support vector machines, kernel ridge regession, kernel feature extraction, kernel online learning, Bayesian kernel methods, graph kernels, kernels for text, kernels for structured data.

Human visual system and image perception; monochrome and colour vision models; image
digitization, display and storage; 2 ‐ D signals and systems; image transforms ‐ 2D DFT, DCT, KLT,
Harr transform and discrete wavelet transform; image enhancement: histogram processing, spatial ‐
filtering, frequency ‐ domain filtering; image restoration: linear degradation model, inverse filtering,
Wiener filtering; image compression: lossy and lossless compression, image compression standards,

Basic counting principle: Pigeonhole principle, inclusion - exclusion principle, recurrence relations, generating functions. Fundamentals of logic, set theory, language, and finite state machines.

Undirected and direct graphs, modelling with graphs, trial and cycle- Eulerian trial and Hamilton cycle, connectivity and trees. Graph algorithms: BFS, DFS, shortest path, optimal spanning trees, matching, job assignment problem, optimal transportation through flows in networks

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