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