Complex integration: Cauchy-Goursat Theorem (for convex region), Cauchy's integral formula, Higher order derivatives, Morera's Theorem, Cauchy's inequality and Liouville's theorem, Fundamental theorem of algebra, Maximum modulus principle, Taylor’s theorem, Schwarz lemma. Laurent's series, Isolated singularities, Meromorphic functions, Rouche's theorem, Residues, Cauchy's residue theorem, Evaluation of integrals, Riemann surfaces.

Introduction and fundamentals of machine learning: Basics of supervised/unsupervised/reinforcement learning, Revision of probability and statistics revision, Revision of linear algebra, Fundamentals of numerical optimization, Machine learning for wireless communications, Machine learning for physical layer design Linear Modeling: A Least Squares Approach, Linear modeling Generalization and over fitting, Regularized least squares Wireless application - MIMO zero-forcing receiver design Linear Modeling: A Maximum Likelihood Approach, Errors as noise– thinking generatively, Maximum likelihood,

Linear Prediction and its application - Modelling Time Series Data, Sigma-Delta Modulation, LPC in Speech Processing, Wireless Channel Prediction for Feedback Communication. Applications of Kalman Filter: OFDM Channel estimation, tracking a moving/Flying object using Radar, Lidar data and optical images, alpha-beta and alpha-beta-gamma trackers, State of Charge estimation of a Li-Ion Battery. Sensor fusion.

Applications of Wiener and Adaptive Filters: Deconvolution problem, Noise cancellation, System Identification.

Introduction: Introduction and overview of Wireless Mesh Networks, Evolution of Wireless Mesh Networks, Pros and Cons of WMNs, Architectural issues in Wireless Mesh Networks, Capacity of Wireless Mesh Networks, Layer-wise Protocol, Propagation models for WMNs, and Design issues in Wireless Mesh Networks.

Introduction to Graphs and their applications. Finite and infinite graphs. History of graph theory. Paths and Circuits. Isomorphism, sub graphs. Walks, paths, and circuits. Hamiltonian paths and circuits. Trees and Fundamental Circuits. Cut-Sets and Cut-Vertices. Connected and disconnected graphs and components. Directed Graphs. Euler graphs. Operations on graphs. Graph-Theoretic Algorithms and Computer Programs. Applications of Graph theory in operations research. Distributed graph algorithms for computer networks. Complex networks.

Graph Theory Preliminaries. Introduction to Complex Networks. Centrality Metrics. Community Detection in Complex Networks. Random Networks. E-R random networks. Properties of Random Network. Real- world examples of random networks. Small- World Networks. Creation of Deterministic Small- World Networks. Anchor Points in a String Topology Small- world Network. Routing in Small-World Networks. The capacity of small-world Networks. Scale-Free Networks. Characteristics of Scale-Free Networks. Real- world examples of Scale-free networks. Preferential Attachment-based Scale-Free Network Creation.

Evolution of the Internet and Big Data. Introduction to the Internet of Things (IoT). The Internet protocol stack. IPv4 and IPv6. TCP and UDP. DNS and the IoT Protocol stack, Layers in the Internet of Things. Sensing and Actuator Layer, Network Layer, and Application Layer. Wireless Sensor Networks. Communication Technologies for the Internet of Things. CoAP, MQTT and HTTP Protocols for IoT. Data aggregation and fusion. Operating Systems for IoT. Contiki OS, Tiny OS, and other IoT OSs. Databases for the Internet of things. Data mining for the Internet of Things.

The need for Software radios and its definition, Characteristics and benefits of Software radio, Design principles of a software radio. Radio Frequency Implementation Issues: Purpose of RF front–end, Dynamic range, RF receiver front –end topologies, Enhanced flexibility of the RF chain with software radios, Importance of the components to overall performance, Transmitter architectures and their issues, Noise and distortion in the RF chain, ADC & DAC distortion, Pre-distortion, Flexible RF systems using micro-electro mechanical systems.

Review of Correlation matrix and its properties, its physical significance. Eigen analysis of matrix, structure of matrix and relation with its Eigen values and Eigen vectors. Spectral decomposition of correlation matrix, positive definite matrices and their properties and physical significance. Complex Gaussian processes.