MA615 Programming and Data Structures [3-0-2-8] Prerequisite: Nil
Programming and Data Structures and Algorithms Flowcharts, C Programming: basic features, arrays and pointers, recursion, records (structures), memory management, files, input/output, Asymptotic complexity, heap sort, quick sort, sorting in linear time, elementary data structures, hash tables, binary search trees, Red-Black trees.
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MA618 Mathematics for Computer Science L-T-P-C [3-0-0-6]
Review of sets, functions, relations; Logic: formulae, interpretations, methods of proof in propositional and predicate logic; Number theory: division algorithm, Euclid's algorithm, fundamental theorem of arithmetic, Chinese remainder theorem; Combinatorics: permutations, combinations, partitions, recurrences, generating functions; Graph Theory: isomorphism, complete graphs, bipartite graphs, matchings, colourability, planarity; Probability: conditional probability, random variables, probability distributions, tail inequalities.
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MA625 Linear Algebra - 1 [3-1-0-8] Prerequisite: Nil
Vector spaces: subspaces, sums and direct sums; Finite dimensional vector spaces: bases and dimensions; Linear maps: null-spaces and range, invertibility; Polynomials with real and complex coefficients; Eigenvalues and eigenvectors: triangularization and diagonalization of operators on finite dimensional vector spaces; Inner-product spaces: orthonormal bases, linear functional and adjoins; Operators on inner-product spaces: self-adjoint and normal operators, minimal polynomial, Jordan form; Traces and determinants of operators and matrices.
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MA662 Differential Equations [3-1-0-8] Prerequisite: Nil
Existence and Uniqueness of Initial Value Problems: Picard's and Peano's Theorems, Gronwall's inequality, continuous dependence, maximal interval of existence. Second and Higher Order Linear Equations: Fundamental solutions, Wronskian, variation of constants, behaviour of solutions. Power series method with properties of Legendre polynomials and Bessel functions. Linear Systems: Autonomous Systems and Phase Space Analysis, matrix exponential solution, critical points, proper and improper nodes, spiral points and saddle points.
First Order Partial Differential Equations: Classification, Method of characteristics for quasi-linear and nonlinear equations, Cauchy's problem, Cauchy-Kowalewski's Theorem. Second-Order Partial Differential Equations: Classification, normal forms and characteristics, Well-posed problem, Stability theory, energy conservation, and dispersion, Adjoint differential operators. Laplace Equation: Maximum and Minimum principle, Green's identity and uniqueness by energy methods, Fundamental solution, Poisson's integral formula, Mean value property, Green's function. Heat Equation: Maximum and Minimum Principle, Duhamel's principle. Wave equation: D'Alembert solution, method of spherical means and Duhamel's principle. The Method of separation of variables for heat, Laplace and wave equations.
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MA684 ADVANCED PROBABILITY L-T-P-C [3-0-0-6] Pre requisites: MA 590 or equivalent
Measure theoretic formulation of probability; Random variables, Distributions, Expectations, Modes of convergence; Laws of large numbers:the weak and strong laws; Characteristic functions, Convergence in distribution, Central limit theorems; Markov chains, Random walks, Poisson process; Conditional expectations; Discrete parameter martingales,Convergence theorems for martingales; Brownian motion, Strong Markov property, Introduction to sample path properties.
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MA721 Introduction to Analytic Number Theory and Algebraic Number Fields [4-0-0-8] Prerequisites: MA521 Modern Algebra
Arithmetic functions, Elementary theorems on distribution of prime numbers, Dirichlet's Theorem on primes in arithmetic progressions, Dirichlet series and Euler products, Zeta functions, Prime number theorem.
Number fields and Number rings, Prime decomposition in number rings, The ideal class group and the unit group, Dedekind zeta function and the class number formula, The distribution of primes and class field theory.
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MA723 Permutation Groups and Group Actions [4-0-0-8] Prerequisites: MA547 Complex Analysis.
Group actions, Orbits and Stabilizer, Transitivity, Primitivity, Suborbits and Orbits, Linear groups, Wreath products, Structure of primitive groups and symmetric groups, Groups acting on trees, Jordan groups.
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MA725 Non-Negative Matrix Theory [4-0-0-8] Prerequisites: MA5XX Linear Algebra
Cones, Spectral properties of matrices which leave a cone invariant, Cone primitivity, Irreducible matrices, Reducible matrices, Primitive matrices, Stochastic matrices, Algebraic semigroups, Nonnegative idempotents, The semigroup $N_n$, The semigroup $D_n$, Inverse eigenvalue problems, Nonnegative matrices with given sums.
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MA727 Modern Algebra and Number Theory [4-0-0-8] Prerequisites: Nil
Modern Algebra: Group theory - normal series, solvable groups, nilpotent groups; Ring theory - rings and modules, prime ideals, nil and Jacobson radicals, finitely generated modules, exact sequences, tensor products, primary decomposition, Noetherian rings, Artin rings; Field theory - field extensions, automorphism groups, Galois theory.
Number Theory: congruences, residue systems, Chinese remainder theorem; quadratic residues, reciprocity law; arithmetic functions-Euler function, Mobius function; continued fractions; quadratic forms; Diophantine equations; partitions; Riemann zeta function.
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MA731 Functional Analysis L-T-P-C [4-0-0-8]
Prerequisites: Nil
Review of normed spaces and Banach spaces; Bounded linear operators, Hahn-Banach theorem, Dual spaces, Open mapping theorem, Closed graph theorem, Uniform boundedness principle; Weak and weak* topologies, Alaoglu theorem; Compact operators, Riesz theory for compact operators; Spectra of bounded linear operators, Gelfand-Mazur Theorem.
Review of inner product spaces and Hilbert spaces; Orthonormal bases, Riesz representation theorem; Adjoint of a bounded linear operator, Self-adjoint, normal and unitary operators; Spectral theorem of compact self-adjoint/normal operators.
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MA733 Spectral perturbation theory for matrices and matrix pencils L-T-P-C [4-0-0-8]
Prerequisites: Nil
Matrix valued analytic functions, projections. Invariant subspaces and spectral decompositions, singular value decompositions, pairs of projections. Matrix norms, unitarily invariant norms, gap between subspaces. General perturbation theory for matrices, Bauer-Fike and Henrici theorems, Hoffman-Wielandt theorem, analytic perturbation theory for eigenvalues. Invariant subspaces, Sylvester operator, perturbation of spectral subspaces. Matrix pencils, eigenvalues and eigenvectors of regular pencils, triangular and Weierstrass forms, Kronecker canonical form, deflating subspaces, definite pencils, perturbation of eigenvalues of regular pencils.
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MA742 Iteration Theory [4-0-0-8] Prerequisites: Nil
Chordal and spherical metrics, Normal families, Iteration of polynomials and rational functions, Periodic points and orbits, Singular values, Julia and Fatou sets and their characterizations, Mandelbrot set, Dynamics of transcendental entire functions, Bifurcation and Chaotic burst in the dynamics, Iteration of certain meromorphic functions, Julia sets and Fractals, Self-similarity and Fractal dimensions.
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MA746 Fourier Analysis [4-0-0-8] Prerequisites: Nil
Orthogonal systems, Trigonometric system, Fourier series in these systems, Uniqueness and convergence, Fourier series of continuous and smooth functions, $L^2$ theory of Fourier series - inversion formula and the Parseval identity, Fourier analysis and complex function theory, Paley Wiener's theorem, Tauberian theorem, Dirichlet problem, Bessel functions, Orthogonal polynomials, Fourier analysis and filters, Fourier transforms and distributions.
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MA748 Advanced Complex Analysis [4-0-0-8] Prerequisites: MA547 Complex Analysis
Complex Differential Equations, Special functions, Normal families and applications, Reimann Mapping theorem, Fundementals of Univalent functions and Entire functions, Phragmen-Lindelof theorems, Gamma, Riemann-zeta functions, Harmonic functions, Dirichlet problem for disc, Analytic continuation, Runge's theorem.
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MA752 Theory of Partial Differential Equations L-T-P-C [4-0-0-8]
Review of Sobolev spaces. weak solutions, eigenvalues and eigenfunctions of symmetric and non-symmetric elliptic operators. evolution equations, existence of weak solutions, maximum principle, interior and boundary regularities. Nonlinear elliptic equations: Nonlinear variational problems. first and second variations, existence of minimizers, nonlinear eigenvalue problems. Nonvariational techniques: monotonicity methods, fixed point methods, Nemytskii and pseudo-nRinotone operators. geometric properties of solutions. radial symmetry. Hamilton Jacobi equations: viscosity solutions, uniqueness, control theory, Hamilton-Jacobi-Bellman equations. Semigroup methods: Strongly continuous semigroups, infinitesimal generator, Hille-Yosida theorem, applications to wave and Schrodinger equations, analytic semigroups and their generators. Energy methods for evolution problems. System of conservation laws: Riemann's problem: simple waves, rarefraction waves, shock waves, contact discontinuities, local solution of Riemann's problem, vanishing viscosity, traveling waves, entropy/entropy-flux pairs.
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MA754 Homogenization L-T-P-C [4-0-0-8]
Elliptic operators, Dirichlet and periodic boundary conditions, asymptotic expansion using multiple scales, energy proof of the homogenization formula (Tartar's method of oscillating test functions), classical correctors, Bloch waves, Bloch expansion theorem, Bloch approximation function, homogenization of elliptic systems, composite materials containing high-modulus reinforcement, boundary layer theory in composite materials, asymptotic methods and spectral problems in fluid-solid structures, multiphase flows (solid-fluid mixture).
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MA617 Design and Analysis of Algorithms L-T-P-C [3-0-0-6]
Models of Computation: space and time complexity measures, lower and upper bounds; Design techniques: greedy method, divide-and-conquer, dynamic programming; Amortized analysis: basic techniques, analysis of Fibonacci heap and disjoint-set forest; Graph algorithms: connectivity, topological sort, minimum spanning trees, shortest paths, network flow; String matching; Average-case analysis; NP-completeness.
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MA619 Data Structures Lab L-T-P-C [0-2-2-6]
Assignments are designed to provide hands-on experience in programming the following data structures and algorithms using the C programming language. Elementary data structures: arrays, matrices, linked lists, stacks, queues, binary trees, tree traversals; Balanced binary search trees: red-black trees, B-trees; Priority queues: binary heap; Sorting and searching: bubble, insertion, merge, quick sort, heap sort, binary search; Hashing; Strings: tries, suffix arrays, suffix trees; Sets: linked-list, disjoint-set forest; Graphs: adjacency list, adjacency matrix, depth first search, breadth first search.
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MA642 Real Analysis - 1 [3-1-0-8] Prerequisite: Nil
Completeness properties of real numbers, countable and uncountable sets, cardinality. Norms and metrics: Metric spaces, convergence of sequences, completeness, connectedness and sequential compactness; Continuity and uniform continuity; sequences and series of functions, uniform convergence, equicontinuity, Ascoli's theorem, Weierstrass approximation theorem, power series. Calculus of functions of a real variable: Differentiability, Mean value theorems, Taylor's theorem. Calculus of functions of several real variables: Partial and directional derivatives, differentiability, Chain Rule, Taylor's theorem, Maxima and Minima, Lagrange multipliers, Inverse function theorem, Implicit function theorem. Multiple Integration: Fubini's Theorem, Line integrals, Surface integrals, Green, Gauss and Stokes theorems.
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MA683 Probability Theory [3-1-0-8] Prerequisite: Nil
Probability spaces, probability measures on countable and uncountable spaces, conditional probability, independence; Random variables and vectors, distribution functions, functions of random vectors, standard univariate and multivariate discrete and continuous distributions and their properties; Mathematical expectations, moments, moment generating functions, characteristic functions, inequalities, conditional expectations, covariance, correlation; Modes of convergence of sequences of random variables, weak and strong laws of large numbers, central limit theorems; Introduction to stochastic processes, definitions and examples, Markov chains, Poisson processes, Brownian motion.
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MA719 Linear Algebra - II [4-0-0-8] Prerequisites: Nil
Eigenvalues and eigenvectors, Schur's theorem - real and complex versions, Spectral theorems for normal and Hermitian matrices - real and complex versions. Gerschgorin discs with associated perturbation theorems and inclusion results. Jordan canonical forms with application, minimal polynomials, companion matrices. Functions of matrices via spectral decompositions. Variational characterizations of eigenvalues of Hermitian matrices, Rayleigh-Ritz theorem, Courant-Fischer theorem, Weyl theorem, Cauchy interlacing theorem, Inertia and congruence, Sylvester's law of inertia. Matrix norms, spectral radius formula, relationships between matrix norms. Singular value decomposition, polar decomposition. Positive definite matrices, characterizations of definiteness, polar form and singular value decompositions, congruence and simultaneous diagonalization.
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MA722 Topological Groups and Advanced Algebra [4-0-0-8] Prerequisites: MA521 Modern Algebra.
Basic notions from point-set-topology, Direct product and inverse limits, Topological groups, completions, inverse system of finite groups, Profinite groups.
Nilpotent and Solvable groups, Frattini subgroups, Chief factors, Free groups, Presentations, Matrix groups and their properties, Profinite and Pro-p-groups.
The topology of pointwise convergence.
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MA724 Combinatorial Group Theory[4-0-0-8] Prerequisites: MA521 Modern Algebra
Generators and Relations, Free groups, Subgroups of a free group, Presentation of groups, Dehn's fundamental problems, Tietze transformations, Cayley graph of a group, Free products, Generalized free products, HNN extensions, Wreath Products, Commutator calculus, Residual Properties.
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MA726 Number Theory L-T-P-C [4-0-0-8]
Congruences: linear and polynomial congruences; prime numbers: counting primes, numbers of special forms, pseudo-primes and primality testing; factorization: factorization algorithms; arithmetic functions: multiplicative and additive functions, Euler's phi function, sum and number of divisors functions, the Mobius function and other important arithmetic functions, Dirichlet products; primitive roots and quadratic residues: primitive roots, index arithmetic, quadratic residues, modular square roots; Diophantine equations: linear Diophantine equations, Pythagorean triples, Fermat's last theorem, Tell's, Bachet's and Catalan's equations, sums of squares and Waring's problem; Diophantine approximations: continued fractions, convergent, approximation theorems; quadratic fields: primes and unique factorization.
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MA728 Universal Algebra
Complete lattices, equivalence relations, algebras, subalgebras, homomorphism theorems, products, congruences, free algebras, term algebras, identities, subdirect products, subdirectly irreducible algebras, class operators, varieties, Birkhoff's variety theorem, congruence varieties, equational logic, equational theories, bases of varieties, many-sorted algebras.
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MA732 Spectral perturbation theory for bounded linear operators L-T-P-C [4-0-0-8]
Prerequisites: Nil
Banach space valued analytic functions, bounded linear operators in Banach spaces, adjoint operators, projection operators. Resolvent and spectra of bounded linear operators, isolated spectral values, spectral projections and spectral decompositions, spectra of adjoint operators. Linear and analytic perturbation theory for discrete spectra, continuity and analyticity of the resolvent operators, perturbation of the spectral projections, perturbation series for spectral projections and eigenvalues, a theorem of Motzkin-Taussky.
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MA741 Complex Analysis L-T-P-C [4-0-0-8]
Prerequisites: Nil
Analytic functions, properties of elementary analytic functions. Complex integration, Cauchy's theorem, Liouville's theorem, power series representation, open mapping theorem, calculus of residues. Harmonic functions, Poisson integral, Harnack's theorem, Schwarz reflection principle. Maximum modulus principle, Schwarz lemma, Phragmen-Lindelof method. Runge's theorem, Mittag-Leffler theorem, Weierstrass theorem, Jensen's formula, Hadamard's theorem. Analytic continuation, monodromy theorem. Equicontinuous, Normal families, Arzela's theorem, Riemann mapping theorem and its consequences.
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MA745 Theory of Distribution and Sobolev Spaces [4-0-0-8] Prerequisites: Nil
Test Function and distribution: Definition, operations with distributions, convolution of distributions, Fourier transform of tempered distributions.
Sobolev spaces: Definition and properties, extension theorem, imbedding and completeness theorem, fractional order Sobolev spaces, trace theory. Application to Elliptic Problems: Weak solution of elliptic boundary value problem (BVP), regularity of weak solutions, maximum principle, eigenvalue problems, fixed point theorems and their application in semilinear elliptic BVP.
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MA747 Measure Theory L-T-P-C [4-0-0-8]
Fields and a-fields, generators; Borel a-field on Euclidean, metric and general topological spaces. Monotone classes, monotone class theorem. Finitely additive measures. Measures, finite and a-finite measures. Borel measures, regularity. Outer measures; Caratheodory's extension theorem. Lebesgue measure in Euclidean spaces. Distribution functions. Measurable functions and their properties. Induced measures. a-fields generated by classes of functions; Monotone class theorem for functions. Integrability of functions. Lebesgue integrals and their properties. Fatou's lemma, monotone convergence theorem, dominated convergence theorem. Finite-dimensional product measurable spaces and measures on them. Product measures. Fubini's Theorem. Holder's. Minkowski's and Jensen 's inequalities. LP spaces; Characterizations of compact, precompact sets in LP spaces. Complex-valued measurable and integrable functions. Fourier transforms of finite measures on the real line and inversion formulae. Signed and complex-valued measures. Absolute continuity and singularity of measures. Lebesgue's differentiation theorem. Hahn decomposition theorem. Radon-Nikodym Theorem. Lebesgue decomposition theorem. Spaces of measures. Weak convergence. Helly's Theorem. Measures on locally compact spaces. Radon measures; Riesz representation theorem.
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MA751 Differential Equations and Boundary-Value Problems [4-0-0-8]
Existence and uniqueness of solutions of ODEs, power series solution, singular points, some special functions. Nonlinear system of ODE : Preliminary concepts and definitions, the fundamental existence-uniqueness results, dependence on initial conditions and parameters, the maximum interval of existence, linearlization, stability and Liapunov functions, saddle, nodes, foci and centers, normal form theory and Hamiltonian systems. Boundary value problems : Green's function method, Sturm-Liouville problem.
First-order PDEs, Cauchy problem, method of characteristics, Second-order PDEs, classification, characteristics and canonical forms. Elliptic boundary value problems : Maximum principle, Green's function, Sobolev spaces, variational formulations, weak solutions, Lax-Milgram theorem, trace theorem, Poincarénequality, energy estimates, Fredholm alternative, regularity estimates, system of conservation laws, entropy criteria.
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MA753 Perturbation Techniques L-T-P-C [4-0-0-8]
Asymptotic expansion and approximation, asymptotic solution of algebraic and transcendental equations, regular and singular perturbations for first and second-order ordinary differential equations, physical examples, initial-value problems, multiple scales, two-scale asymptotic approximation, averaging technique, composite asymptotic expansions, initial layers - matching by Van Dyke rules. Two-point boundary-value problems: Boundary layers -exponential and cusp layers, matched asymptotic expansions, composite asymptotic expansions, WKB (Wentzel, Kramers, Brillouin) expansion method, conditions for validity of the WKB approximation, patched asymptotic approximations, WKB solution of inhomogeneous ordinary differential equations. Perturbation methods for linear eigenvalue problems, Rayleigh-Schrodinger theory, singularity structure of eigenvalues as functions of complex perturbing parameter, level crossing. Nonlinear eigenvalue problems, direct error estimation, oscillatory phenomena - free conservative and free self-sustained oscillations, harmonic resonance, shock and transition layers.
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MA761 Advanced Fluid Dynamics [4-0-0-8]
Prerequisites: MA561 Fluid Dynamics
Review of Equations of Motion, Fundamentals of compressible flow, Boundary layer theory, Stability of laminar flows, Introduction to transition and turbulent flows.
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MA763 Introduction to Environmental Diffusion [4-0-0-8] Prerequisites: MA561 Fluid Dynamics
Fick's law. Diffusion of finite size cloud. Reflection at boundary. Diffusion through random movements, diffusion with stationary velocities, dispersion of Brownian particles, reflecting and absorbing barriers. Statistical approach environmental diffusion. Lagrangian properties of turbulence. Apparent eddy diffusivity. Application to atmospheric diffusion. Experimental basis, probability distributions of particle displacements. History of a concentrated sewage plumes. Properties of planetary boundary layer, particle displacements in a wall layer, continuous line and point sources at ground level. Elevated sources, dispersion natural streams.
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MA765 Wave Structure Interaction [4-0-0-8]
Prerequisites: MA561 Fluid Dynamics, MA762 Potential Flow of Fluids and water-Wave Theory
Wave forces on structures, Morison equation, Froude-Krylov theory, Diffraction Theory, Perturbation method of solutions. Radiation. Dynamics of floating structures, damping and added-mass.
Interaction of water waves with spherical and cylindrical objects, hydrodynamic coefficients.
Nonlinear long waves in shallow water, KdV equation. Inverse scattering transforms and the theory of solitons. The Scrodinger equation. Soliton solution of the KdV equation.
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MA771 Advanced Numerical Analysis [4-0-0-8] Prerequisites: MA561 Fluid Dynamics
Iterative methods for linear systems : Classical iterative methods (Jacobi, Gauss-Seidel and successive overrelaxation (SOR) methods), Krylov subspace methods; GMRES, Conjugate-gradient, biconjugate-gradient (BiCG), BiCGStab methods, preconditioning techniques, parallel implementations.
Finite difference method : Explicit and implicit schemes, consistence, stability and convergence, Lax equivalence theorem, numerical solutions to elliptic, parabolic and hyperbolic partial differential equations.
Approximate method of solution : Galerkin method, properties of Galerkin approximations, Petrov-Galerkin method, generalized Galerkin method.
The finite element method(FEM) : FEM for second order problems, one and two dimensional problems, finite elements(elements with a triangular mesh and a rectangular mesh and three dimensional finite elements), fourth-order problems, Hermite families of elements, isoparametric elements, numerical integration.
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MA773 Finite Element Methods [4-0-0-8]
Prerequisites: MA745 Theory of distribution and Sovolov spaces
Basic concept of the finite element method, Integral formulations and variational methods, The Lax-Milgram theorem, The abstract Galerkin method, Piecewise polynomial approximation in Sobolev spaces, Finite elements, Numerical quadrature, Applications to autonomous and non-autonomous problems, Optical error bounds in energy norms, Variational crimes, Apriori error estimates.
The discontinuous Gaterkin methods, Adaptive finite element, The Autin-Nitscte duality argument, A posteriori error analysis.
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MA782 Lévy Processes L-T-P-C [4-0-0-8]
Poisson random measures and their use in discontinuous martingales and LÉY processes; Brownian motion: Hitting times, maximum process, local times and excursions; Structure of local times and excursions in terms of Poisson random measures; LÉY processes: Structure and general properties, role of Brownian motion and Poisson random measures in the structure of LÉY processes, subordinators, hitting time of subordinators.
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MA793 DATA STRUCTURES AND ALGORITHMS L-T-P-C [3-0-2-8] Pre requisites: Nil
Review of linear and non-linear data structures, dynamic storage allocation techniques; Advanced data structures - B-Trees, Binomial and Fibonacci, set representation and operations; Algorithm analysis - time and space complexities; Sorting and searching algorithms; Algorithm design techniques: divide and conquer, dynalii;c programming, search and traversals, backtracking, branch and bound; Review of graph algorithms; Flow networks, sorting networks, arithmetic circuits, matrix operations, polynomials and FFT, number theoretic algorithms, string matching.
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Probability Theory (MA683) or equivalent
Preamble / Objectives:
Statistical methods play an essential role in designing and analysing modern clinical studies. Multi-stage clinical trials in personalized medicine require advanced statistical methodologies. This course will enable PhD students to learn existing and new methodologies that are used in advanced clinical studies with real examples. The course is designed to prepare Ph.D. students to develop new statistical methodologies for advanced clinical studies/trials.
Course Content/ Syllabus:
Overview of clinical trials: design and analysis of phase-I dose-finding trials, overview of phase-II and phase-III trials. Regulatory affairs: data monitoring and interim analysis. Statistical methods to design and analysis: non-inferiority and equivalence trials, factorial and cross-over trials, cluster randomized trials and stepped wedge trials, sequential, group-sequential and adaptive trials, seamless phase II/III trials. Pharmacovigilance: phase IV trials including spontaneous reporting system. Dynamic treatment regimens: sequential multiple assignment randomized trials (SMART) designs.
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Pre-Requisite: Basic knowledge of Probability and Statistical Distributions
Preamble / Objectives:
Knowledge of statistics is now essential for all academic branches as well as in the industry. This course's objectives are to teach students about different types of data that exist in real life and various statistical methods for them to analyze. This course will enable students to learn the topics in an applied manner so that they can use those methods/techniques in real life using a statistical software (like R).
Course Content/ Syllabus:
Data types: binary, continuous, categorical, ordinal, count, survival, longitudinal with examples. Study types: prospective, retrospective, case-control, cohort, cross-sectional, qualitative studies, randomized controlled trials. Exploratory Data Analysis: data visualization and statistical plots. Statistical Inference: Estimation, Hypothesis testing. Useful Statistical Tests: z-test, t-test, F-test, Chi-Square test, Wilcoxon signed-rank test with applications. Regression: linear regression, logistic regression, count regression. Analysis of Variance (ANOVA): One-way and two-way ANOVA. Bayesian Techniques: Bayes theorem, prior and posterior distributions, Bayesian inference. Survival Analysis: survival function, hazard function, Kaplan–Meier curves, log-rank test, Cox proportional hazards regression. Statistical Learning: clustering and classification. Statistical traps to avoid: correlation vs causation, misuse of p-values and multiple testing, handling outliers, misuse of variable selection, misuse of data visualization, ethical issues in statistics. Case studies with real data.
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