**NOTE**: Course marked ^{###} are Hard Core courses for M.Tech. Students.

**DS 391 (Jan-Apr) 3:0 Data Assimilation to Dynamical Systems**

*Raha *

Quick introduction to nonlinear dynamics: bifurcations, unstable manifolds and attractors, Lyapunov exponents, sensitivity to initial conditions and concept of predictability. Markov chains, evolution of probabilities (Fokker-Planck equation), state estimation problems. An introduction to the problem of data assimilation (with examples) Bayesian viewpoint, discrete and continuous time cases Kalman filter (linear estimation theory) Least squares formulation (possibly PDE examples) Nonlinear Filtering: Particle filtering and MCMC sampling methods. Introduction to Advanced topics (as and when time permits): Parameter estimation, Relations to control theory, Relations to synchronization.

Prerequisites: Permission from the Instructor(s).

Texts and References

- Edward Ott, Chaos in Dynamical Systems, Camridge press, 2nd Edition, 2002.(or one of the many excellent books on dynamical systems)
- Van Leeuwen, Peter Jan, Cheng, Yuan, Reich, Sebastian, Nonlinear Data Assimilation, Springer Verlag, July 2015.
- Sebastian Reich, Colin Cotter, Probabilistic Forecasting and Bayesian Data Assimilation, Cambridge University Press, August 2015
- Law, Kody, and Stuart, Andrew, and Zygalakis, Konstantinos, Data Assimilation, A Mathematical Introduction, Springer Texts in Applied Mathematics, September 2015.

[First part of the book is available at http://arxiv.org/abs/1506.07825]

**DS 291 (JAN) 3:1 Finite Elements: Theory and Algorithms**

*Sashikumaar Ganesan*

Generalized (weak) derivatives, Sobolev norms and associated spaces, inner-product spaces, Hilbert spaces, construction of finite element spaces, mapped finite elements, two- and three-dimensional finite elements, Interpolation and discretization error, variational formulation of second order elliptic boundary value problems, finite element algorithms and implementation for linear elasticity, Mindlin-Reissner plate problem, systems in fluid mechanics.

Prerequisites: Good knowledge of numerical analysis and/or consent from the instructor.

Course Material

- Sashikumaar Ganesan, Lutz Tobiska: Finite elements: Theory and Algorithms, Cambridge-IISc Series, Cambridge University Press, 2017
- Dietrich Braess, Finite Elements: Theory, Fast Solvers, and Applications in Solid Mechanics, Cambridge University Press, 3rd ed., 2007
- Susanne C. Brenner, Ridgway Scott, The Mathematical Theory of Finite Element Methods, Springer-Verlag, 3rd ed., 2008
- Current literature

**DS 250 (AUG) 3:1 Multigrid Methods**

*Sashikumaar Ganesan *

Classical iterative methods, convergence of classical iterative methods, Richardson iteration method, Krylov subspace methods: Generalized minimal residual (GMRES), Conjugate Gradient (CG), Bi-CG method. Geometric Multigrid Method: Grid transfer, Prolongation and restriction operators, two-level method, Convergence of coarse grid approximation, Smoothing analysis. Multigrid Cycles: Vcycle, W-cycle, F-cycle, convergence of multigrid cycles, remarks on computational complexity. Algebraic Multigrid Method: Hierarchy of levels, Algebraic smoother, Coarsening, Interpolation, remarks on parallel implementation.

Prerequisites: Good knowledge of Linear Algebra and/or consent from the instructor.

Course Material

- Pieter Wesseling, An Introduction to Multigrid Methods, R.T. Edwards, Inc., 2004.
- William L. Briggs, Van Emden Henson and Steve F. McCormick, A Multigrid Tutorial, SIAM, 2nd edition, 2000.

**DS 252 (JAN) 3:1 Introduction to Cloud Computing**

*Yogesh Simmhan*

(*) Context: Taxonomy of parallel and distributed computing; shared/distributed memory, and data/task parallel computing; Role of Cloud computing. (*) Technology: Cloud Virtualization, Elastic computing; Infrastructure/Platform/Software as a Service (IaaS/PaaS/SaaS); Public/Private Clouds; Service oriented architectures. (*) Design Patterns: Design of task/data parallel distributed algorithms; Cloud applications; Task graphs and Map-Reduce model; Amdahl’s law, data locality, speedup of Cloud applications. (*) Execution Models: Synchronous/asynchronous execution patterns; Scale up/Scale out on VMs; Data marshalling/unmarshalling; Asynchronous coordination of concurrent tasks on VMs; NoSQL Cloud storage. (*) Evaluation: Load balancing of stateful/stateless applications; Performance metrics for evaluating Cloud applications; Consistency, Availability and Partitioning (CAP theorem). (*) Programming project using public Cloud infrastructure e.g. Amazon AWS, Microsoft Azure Cloud resources provided.

Prerequisites: Data Structures, Programming and Algorithm concepts. Programming experience.

Course Material

- Distributed and Cloud Computing: From Parallel Processing to the Internet of Things, Kai Hwang, Jack Dongarra and Geoffrey Fox, Morgan Kaufmann, 2011
- Current literature.
- Webpage

**DS 256 (JAN) 2:1 Scalable Systems for Data Science**

*Yogesh Simmhan and Partha Talukdar*

This course will introduce the fundamental systems aspects of big data platforms, and how these platforms can be used to build large-scale data intensive applications. It will cover topics on: Why Big Data platforms are necessary? How they are designed? What are the programming abstractions (e.g. MapReduce) that are used to compose data science applications? How the programming models are translated to scalable runtime execution on clusters and Clouds (e.g. Hadoop)? How do you design algorithms for analyzing large datasets? and How do you map them to Big Data platforms? A project will be a key part of this course.

Prerequisites: Data Structures, Programming and Algorithm concepts. Programming experience.

Course Material

- Select chapters from Mining of Massive Datasets, Jure Leskovec, Anand Rajaraman and Jeff Ullman, 2nd Edition (v2.1), 2014.
- Lecture notes.
- Webpage

**DS 260 (JAN) 3:0 Medical Imaging**

*Phaneendra K Yalavarthy*

X-ray Physics, interaction of radiation with matter, X-ray production, X-ray tubes, dose, exposure, screen-film radiography, digital radiography, X-ray mammography, X-ray Computed Tomography (CT). Basic principles of CT, single and multi-slice CT. Tomographic image reconstruction, filtering, image quality, contrast resolution, CT artifacts. Magnetic Resonance Imaging (MRI): brief history, MRI major components. Nuclear Magnetic Resonance: basics, localization of MR signal, gradient selection, encoding of MR signal, T1 and T2 relaxation, k-space filling, MR artifacts. Ultrasound basics, interaction of ultrasound with matter, generation and detection of ultrasound, resolution. Doppler ultrasound, nuclear medicine (PET/SPECT), multi-modal imaging, PET/CT, SPECT/CT, oncological imaging, medical image processing and analysis, image fusion, contouring, segmentation, and registration.

Prerequisites: Basic knowledge of system theory and Consent from the instructor.

Course Material:

- Bushberg, J.T., Seibert, J.A., Leidholdt, E.M. Jr., and Boone, J.M., The Essential Physics of Medical Imaging, Second Edn, Lippincott Williams and Wilkins Publishers, Philiadelphia, 2002.
- Wolbarst, A.B., Physics of Radiology, Second Edn, Medical Physics Publishing, Madison, WI, 2005.
- Current Literature

#### DS 263 (AUG) 3:1 Video Analytics

**R. Venkatesh Babu**

Introduction to Digital Image and Video Processing, Background Modeling, Shadow Removal, Invariant Image Representation, Object Detection and Recognition, Image and Motion Features, Multi Object Tracking, Trajectory Analysis, Recognition of Human Biometrics, Activities and Events, Anomaly Detection, Compressed Domain Video Analytics, Multi Camera Surveillance, Camera Coordination, Distributed Multi-Sensor Surveillance, Video Indexing, Mining and Retrieval.

Prerequisites: Basic knowledge of Image Processing.

Course Material:

- Richard Szeliski, Computer Vision: Algorithms and Applications, Springer 2010
- Forsyth, D.A., and Ponce, J., Computer Vision: A Modern Approach, Pearson Education, 2003.
- Omar Javed, Mubarak Shah, Automated Multi-Camera Surveillance: Algorithms and Practice, Springer, 2008.
- Current Literature

#### DS 284 (AUG) 2:1 Numerical Linear Algebra ^{###}

**Sivaram Ambikasaran**

Matrix and vector norms, floating points arithmetic, forward and backward stability of algorithms, conditioning of a problem, perturbation analysis, algorithmic efficiency, Structured matrices, Solving linear systems, Gaussian elimination, LU factorization, Pivoting, Cholesky decomposition, Iterative refinement, QR factorization, Gram-Schmidt orthogonalization, Projections, Householder reflectors, Givens rotation, Singular Value Decomposition, Rank and matrix approximations, image compression using SVD, Least squares and least norm solution of linear systems, pseudoinverse, normal equations, Eigenvalue problems, Gershgorin theorem, Similarity transform, Eigenvalue & eigenvector computations and sensitivity, Power method, Schur decomposition, Jordan canonical form, QR iteration with & without shifts, Hessenberg transformation, Rayleigh quotient, Symmetric eigenvalue problem, Jacobi method, Divide and Conquer, Computing the Singular Value Decomposition, Golub-Kahan-Reinsch algorithm, Chan SVD algorithm, Generalized SVD, Generalized and Quadratic eigenvalue problems, generalized Schur decomposition (QZ decomposition), Iterative methods for large linear systems: Jacobi, Gauss-Seidel and SOR, convergence of iterative algorithms, Krylov subspace methods: Lanczos, Arnoldi, MINRES, GMRES, Conjugate Gradient and QMR, Pre-conditioners, Approximating eigenvalues and eigenvectors.

Course Material:

- Biswa Nath Datta, Numerical Linear Algebra and Applications, 2nd Edition,
- Lloyd N. Trefethen and David Bau, III, Numerical linear algebra, SIAM, 1997.
- C. G. Cullen, An Introduction to numerical linear algebra, Charles PWS Publishing, 1994.
- David C. Lay, Linear Algebra and its Applications, Pearson, 2013.
- Golub, G., Van Loan C.F., Matrix Computation, John Hopkins, 1996.
- Saad, Y., Iterative Methods for Sparse Linear Systems, Second Edition, SIAM, 2003
- Webpage

#### DS 286 (AUG) 2:1 Data Structures and Programming ^{###}

**Yogesh Simmhan**

Review of Programming with introduction to OOP with C++, time and space complexity. Elementary data structures: Arrays, Stack, Queues, Heaps, Priority Queues, Vectors and Sparse Matrices and related algorithms. Usage and concepts of frequently used sorting, searching, merging, Hashing Techniques. Introductory graph algorithms, trees including AVL, B+, Red-Black Trees, Tries and Suffix trees: usage and application, Usage/Application of String Algorithms. Introduction to Greedy Algorithms, introduction to Spatial Data Structures.Course Material:

Course Material:

- Cormen, T.H., Leiserson, C.E., and Rivest, R.L., Introduction to Algorithms, The MIT Press and McGraw-Hill Book Company. (Indian Edition Available)
- Stroustrup, B., C++ Programming Language, Addison Wesley. (Indian Edition Available)
- Sahni Sartaj K., Data Structures, Algorithms, and Applications in C++, McGraw Hill.
- Kruse, R.L., and Tondo, C.L., Data Structures and Program Design, Prentice Hall of India 1997.
- Aho, A.V. Hopcroft and Ulman, J.D., Data Structurs and Algorithms.
- Heilerman, G.L., Data Structures, Algorithms and Object oriented Programming, McGraw-Hill Intl Edn, 1996.
- Samet Hanan, The Quadtree and Related Hierarchical Data Structures, ACM Computing Surveys, Vol.16-2, pp.187-229, 1986.

#### DS 288 (AUG) 3:1 Numerical Methods ^{###}

**Phaneendra K Yalavarthy**

Root finding: Functions and polynomials, zeros of a function, roots of a nonlinear equation, bracketing, bisection, secant, and Newton-Raphson methods. Interpolation, splines, polynomial fits, Chebyshev approximation. Numerical Integration and Differentiation: Evaluation of integrals, elementary analytical methods, trapezoidal and Simpson’s rules, Romberg integration, Gaussian quadrature and orthogonal polynomials, multidimensional integrals, summation of series, Euler-Maclaurin summation formula, numerical differentiation and estimation of errors. Optimization: Extremization of functions, simple search, Nelder-Mead simplex method, Powell’s method, gradient-based methods, simulated annealing. Complex analysis: Complex numbers, functions of a complex variable, analytic functions, conformal mapping, Cauchy’s theorem. Calculus of residues. Fourier and Laplace Transforms, Discrete Fourier Transform, z transform, Fast Fourier Transform (FFT), multidimensional FFT.

Course Material:

- Richard L. Burden and J. Douglas Faires, Numerical Analysis: Theory and Applications, India Edition, Cengage Brooks-Cole Publishers, 2010.
- Press, W.H., Teukolsky, S.A., Vetterling, W.T., and Flannery, B.P., Numerical Recipes in C/FORTRAN, Prentice Hall of India, New Delhi, 1994.
- Krishnamurthy, E.V., and Sen, S.K., Numerical Algorithms, Affiliated East-West Press, New Delhi, 2001.
- Borse, G.J., Numerical Methods with MATLAB: A Resource for Scientists and Engineers, PWS Publishing Co., Boston, 1997.

#### DS 289 (JAN) 3:1 Numerical Solutions of Differential Equations ^{###}

**A Mohanty**

Ordinary differential equations: Lipschitz condition, solutions in closed form, power series method. Numerical methods: error analysis, stability and convergence, Euler and Runge-Kutta methods, multistep methods, Adams-Bashforth and Adams-Moulton methods, Gear’s open and closed methods, predictor-corrector methods. Sturm-Liouville problem: eigenvalue problems, special functions, Legendre, Bessel and Hermite functions. Partial differential equations: classification, elliptic, parabolic and hyperbolic PDEs, Dirichlet, Neumann and mixed boundary value problems, separation of variables, Green’s functions for inhomogeneous problems. Numerical solution of PDEs: relaxation methods for elliptic PDEs, Crank-Nicholson method for parabolic PDEs, Lax-Wendroff method for hyperbolic PDEs. Calculus of variations and variational techniques for PDEs, integral equations. Finite element method and finite difference time domain method, method of weighted residuals, weak and Galerkin forms, ordinary and weighted/general least squares. Fitting models to data, parameter estimation using PDEs.

Course Material:

- Arfken, G.B., and Weber, H.J., Mathematical Methods for Physicists, Sixth Edition, Academic Press, 2005.
- Press, W.H., Teukolsky, S.A., Vetterling, W.T., and Flannery, B.P., Numerical Recipes in C/FORTRAN – The art of Scientific Computing, Second Edn, Cambridge University Press, 1998.
- Lynch, D.R., Numerical Partial Differential Equations for Environmental Scientists and Engineers – A First Practical Course, Springer, New York, 2005.

#### DS 290 (AUG) 3:0 Modelling and Simulation^{###}

**S Raha**

Statistical description of data, data-fitting methods, regression analysis, analysis of variance, goodness of fit. Probability and random processes, discrete and continuous distributions, Central Limit theorem, measure of randomness, Monte Carlo methods. Stochastic Processes and Markov Chains, Time Series Models. Modelling and simulation concepts,Discrete-event simulation: Event scheduling/Time advance algorithms verification and validation of simulation models. Continuous Simulation: Modelling with and Simulation of Stochastic Differential Equations

Course Material:

- Banks, J., Carson, J.S., and Nelson, B., Discrete-Event System Simulation, Second Edn, Prentice Hall of India, 1996.
- Francois E. Cellier, Ernesto Kofman, Continuous System Simulation, Springer, 2006, ISBN: 0387261028.
- Peter E. Kloden, Eckhard Platen, Numerical Solutions of Stochastic Differential Equations, Springer, Verlog, 1999.
- Peter E. Kloden, Eckhard Platen, Henri Schurz, Numerical Solution of SDE through Computer Experiments, Springer Verlog, 1994

#### DS 292 (AUG) 3:0 High Performance Computing ^{###}

**Sathish Vadhiyar**

Introduction to Computer Systems: Processors, Memory, I/O Devices; Cost, timing, and scale (size) models. Program Execution: Process, Virtual Memory, System Calls, Dynamic Memory Allocation. Machine-Level View of a Program, typical RISC instruction set and execution, Pipelining. Performance issues and Techniques, Cost and Frequency Models for I/O, paging, and caching. Temporal and spatial locality. Typical Compiler Optimizations. Identifying program bottlenecks – profiling, tracing. Simple high-level language optimizations – locality enhancement, memory disambiguation. Choosing Appropriate Computing Platforms: benchmarking, cost-performance issues, etc. Parallel Computing: Introduction to parallel Architectures and Interconnection Networks, communication latencies. Program parallelization: task partitioning and mapping, data distribution, Message passing, synchronization and deadlocks. Distributed memory programming using MPI/PVM. Shared memory parallel programming. Multithreading.

Course Material:

- Dowd, K., High performance Computing, O’Reilly Series, 1993.
- Culler, D., and Singh, J.P., Parallel Computer Architecture: A Hardware/Software Approach. Morgan Kaufmann Pub., 1999.
- Gropp, W., Lusk, E., and Skjellum, A., Using MPI: Portable Parallel Programming with the Message-passing Interface, MIT Press, 1997.

#### DS 294 (JAN) 3:1 Data Analysis and Visualization ^{###}

**Phaneendra K Yalavarthy**

Data pre-processing, data representation, data reconstruction, visualization pipeline, isosurfaces, volume rendering, vector field visualization, applications to biological and medical data , OpenGL, visualization toolkit, linear models, principal components, clustering, multidimensional scaling, information visualization.

Course Material:

- Hansen, C.D., and Johnson, C.R., Visualization Handbook, Academic Press, 2004.
- Ware, C., Information Visualization: Perception for Design, Morgan Kaufmann, Second Edn, 2004.
- Current literature

#### DS 295 (JAN) 3:1 Parallel Programming ^{###}

**S Vadhiyar**

Introduction: Scope of parallel computing, challenges, performance metrics, parallel architecture models, parallel programming paradigms, algorithm models. Principles of parallel algorithm design: decomposition techniques, data distribution methods, mapping techniques for load balancing. Programming using the message passing paradigm: Principles of message-passing programming, The Message Passing Interface (MPI): MPI-1, Collective communications, MPI-2, Parallel I/O; Shared memory programming: OpenMP; Parallel applications: Laplace equation, molecular dynamics. Parallel dense linear algebra: Gaussian elimination, iterative methods. Parallel sparse linear algebra: Cholesky factorization, graph partitioning, sparse iterative methods, graph coloring and others. Other topics: Parallel FFT. Parallelism in Bioinformatics and other Applications, Scheduling on parallel systems and other advanced topics.

Pre-requisite(s): High Performance Computing and preferably Numerical Linear Algebra and Numerical Methods.

Course Material:

- Grama, Gupta, A., Karypis, G., Kumar, V., Introduction to Parallel Computing, Addison Wesley, 2003. ISBN: 0-201-64865-2
- Dongarra, J., Foster, I., Fox, G., Kennedy, K., White, A., Torczon, L., Gropp, W. (Eds), The Sourcebook of Parallel Computing, Morgan Kaufmann, 2002. ISBN: 1-558-60871-0.
- Dongarra, J., Duff, I., Sorensen, D.C., Van der Vorst, H.A., Numerical Linear algebra for High Performance Computers, 1998. ISBN 0-89871-428-1.

#### DS 297 (JAN) 2:1 Topics in Embedded Computing

**S K Nandy**

Introduction to embedded processing, dataflow architectures, architecture of embedded SoC platforms, dataflow process networks, compiling techniques/optimizations for stream processing, architecture of runtime reconfigurable SoC platforms, simulation, design space exploration and synthesis of applications on runtime reconfigurable SoC platforms, additional topics including but not limited to computation models for coarse grain reconfigurable architectures (CGRA), readings and case study of REDEFINE architecture, compiler back-ends for CGRAs.

Pre-requisites: Basic knowledge of digital electronics, computer organization and design, computer architecture, data structures and algorithms, and consent of instructor.

Course Material:

- Current literature.
- IEEE transactions on VLSI systems.
- IEEE transactions on Multimedia Systems.
- ACM Transactions on embedded computing systems.
- Technical reports and design notes from micro-electronics industries and other academic institutions.

#### DS 299 (AUG) 0:24 Dissertation Project

This includes the analysis, design of hardware/software construction of an apparatus/instruments and testing and evaluation of its performance. The project work is usually based on a scientific/engineering problem of current interest. Every student has to complete the work in the specified period and should submit the Project Report for final evaluation.

#### DS 301 (AUG) 2:0 Bioinformatics

**K Sekar**

Biological Databases: Organisation, searching and retrieval of information, accessing global bioinformatics resources using internet links. Introduction to Unix operating system and network communication. Nucleic acids sequence assembly, restriction mapping, finding simple sites and transcriptional signals, coding region identification, RNA secondary structure prediction. Similarity and Homology, dotmatrix methods, dynamic programming methods, scoring systems, multiple sequence alignments, evolutionary relationships, genome analysis. Protein physical properties, structural properties – secondary structure prediction, hydrophobicity patterns, detection of motifs, structural database (PDB). Genome databases, Cambridge structure database, data mining tools and techniques, Structural Bioinformatics, Topics from the current literature will be discussed.

Hands on experience will be provided.

Course Material:

- Gribkov, M., and Devereux, J. (Eds), Sequence Analysis Primer, Stockton Press, 1991.
- Mount, D.W., Bioinformatics: Sequence and Genome Analysis, Cold. Spring Harbor Laboratory Press, 2001.
- Baxevanis, A.D., and Ouellette, B.F.F. (Eds), Bioinformatics: A practical guide to the analysis of the genes and proteins, Wiley-Interscience, 1998.

#### DS 303 (AUG) 2:0 Chemoinformatics

**Debnath Pal**

Exploring current chemoinformatics resources for synthetic polymers, pigments, pesticides, herbicides, diagnostic markers, biodegradable materials, biomimetics. Primary, secondary and tertiary sources of chemical information. Database search methods: chemical indexing, proximity searching, 2D and 3D structure and substructure searching. Introduction to quantum methods, combinatorial chemistry (library design, synthesis and deconvolution), spectroscopic methods and analytical techniques. Analysis and use of chemical reaction information, chemical property information, spectroscopic information, analytical chemistry information, chemical safety information. Representing intermolecular forces: ab initio potentials, statistical potentials, forcefields, molecular mechanics. Monte Carlo methods, simulated annealing, molecular dynamics. High throughput synthesis of molecules and automated analysis of NMR spectra. Predicting reactivity of biologically important molecules, combining screening and structure ‘SAR by NMR’. Computer storage of chemical information, data formats, OLE, XML, web design and delivery.

Course Material:

- Current Scientific Literature and Web lectures: Lectures posted online.
- Maizell, R.E., How to find Chemical Information: A guide for Practicing Chemists, Educators, and students, John Wiley and Sons, 1998. ISBN 0-471-12579-2.
- Gasteiger, J., and Engel, T., Chemoinformatics. A Textbook, Wiley-VCH, 2003. ISBN: 3-527-30681-1

#### DS 305 (AUG) 3:1 Topics in Web-scale Knowledge Harvesting

**P P Talukdar**

Entity extraction, entity normalization, entity categorization, relation extraction, distant supervision, curriculum learning, knowledge base (KB) inference, open information extraction (OpenIE), temporal inference,ontology evolution, bootstrapped learning, learning from limited supervision in KBs, scalable learning and inference over large datasets for KB construction, recent KB construction systems, multilingual knowledge acquisition, knowledge acquisition from multiple modalities, representation learning for knowledge harvesting.

Pre-requisites: Basic knowledge of machine learning and/or natural languageprocessing will be helpful although not mandatory.

Course Material:

- Current Literature.

#### DS 360 (JAN) 3:0 Topics in Medical Imaging

**Phaneendra K Yalavarthy**

Three-dimensional Medical Image Processing, Medical Image reconstruction using high performance computing, General Purpose Graphics Processing Units (GP-GPU) computing for Medical Image processing, reconstruction, and Analysis, Computer Aided Detection (CAD) systems – Algorithms, Analysis, Medical Image Registration: rigid and non-rigid registration, Volume based image analysis, Medical Image Enhancement: Deblurring techniques, Four-dimensional Medical Imaging, Molecular Imaging, Diffuse Optical Tomography, and Medical Image Informatics.

Pre-requisites: DS 260 or E9 241 or consent from the Instructor.

Course Material:

- Current Literature

#### DS 397 (JAN) 3:1 Topics in Embedded Computing

**S K Nandy**

Introduction to embedded processing, dataflow architectures, architecture of embedded SoC platforms, dataflow process networks, compiling techniques/optimizations for stream processing, architecture of runtime reconfigurable SoC platforms, simulation, design space exploration and synthesis of applications on runtime reconfigurable SoC platforms, additional topics including but not limited to computation models for coarse grain reconfigurable architectures (CGRA), readings and case study of REDEFINE architecture, compiler back-ends for CGRAs.s

Pre-requisites: Basic knowledge of digital electronics, computer organization and design, computer architecture, data structures and algorithms, and consent of instructor.

Course Material:

- Current literature.
- IEEE transactions on VLSI systems.
- IEEE transactions on Multimedia Systems.
- ACM Transactions on embedded computing systems.
- Technical reports and design notes from micro-electronics industries and other academic institutions.

**DS 270 (JAN) 3:1 Constructive Approximation Theory**

*Sivaram Ambikasaran*

The course will focus on constructive approximation of real valued functions by simpler function and numerical quadrature. We will discuss the mathematical theory and computational techniques of such approximations. Rigorous error bounds and convergence of approximations will be discussed. A substantial part of the course will be dedicated to polynomial approximations and quadratures. All the course material (error bounds, convergence, Weierstrass approximation theorem, optimal interpolant, Ramez algorithm) will be discussed and illustrated computationally. The emphasis of the course is on computational assignments, which will be due weekly. The highlight of the course would be how approximations lend themselves in constructing highly accurate fast algorithms. Topics: Approximation by Algebraic Polynomials, Weierstrass Theorem, Muentz-Szasz theorem, Orthogonal polynomials, Optimal interpolation nodes, Optimal interpolant, Lebesgue constants, Fourier series, Gibbs phenomenon, Potential theory and approximation, Spectral methods, Pade approximation, Clenshaw-Curtis and Gaussian quadrature, fast low rank construction of kernel matrices and other fast matrix computations.

NOTE: Course marked ### are Hard Core courses for M.Tech. Students.