Chemistry [3-1-0-8]

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Chemistry Laboratory [0-0-3-3]

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Basic Electrinics [3-1-0-8]

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Workshop/Physics Laboratory [0-0-3-3]

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Engineering Drawing [2-0-3-7]

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Physics - I [2-1-0 -6]

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English Communication [2-0-2-0]

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Mathematics-I [3-1-0-8]

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Single variable calculus: Convergence of sequences and series of real numbers; Continuity of functions; Differentiability, Rolle's theorem, mean value theorem, Taylor's theorem; Power series; Riemann integration, fundamental theorem of calculus, improper integrals; Application to length, area, volume and surface area of revolution.

Multivariable calculus: Vector functions of one variable - continuity and differentiability; Scalar valued functions of several variables, continuity, partial derivatives, directional derivatives, gradient, differentiability, chain rule; Tangent planes and normals, maxima and minima, Lagrange multiplier method; Repeated and multiple integrals with applications to volume, surface area; Change of variables; Vector fields, line and surface integrals; Green’s, Gauss’ and Stokes’ theorems and their applications.

Texts:

1. G. B. Thomas, Jr. and R. L. Finney, Calculus and Analytic Geometry, Pearson India, 9_th Edition, 2006

References:

1. R. G. Bartle and D. R. Sherbert, Introduction to Real Analysis, Wiley India, 4th Edition, 2014.
2. S. R. Ghorpade and B. V. Limaye, An Introduction to Calculus and Real Analysis, Springer India, 2006.
3. T. M. Apostol, Calculus, Volume-2, Wiley India, 2003.
4. J. E. Marsden, A. J. Tromba and A. Weinstein, Basic Multivariable Calculus, Springer India, 2002.

Introductory Biology [3-0-0 -6]

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Introduction to Computing [3-0-0-6]

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Computing Laboratory [0-0-3-3]

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Basic Electronics Laboratory [0-0-3-3]

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Engineering Mechanics [3-1-0-8]

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Physics - II [2-1-0-6]

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Physics Laboratory/Workshop [0-0-3-3]

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Students Activity Course - I [0-0-2-0]

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Mathematics-II [3-1-0-8]

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Linear algebra: Systems of linear equations, matrices, Gaussian elimination, echelon form, column space, null space, rank of a matrix, inverse and determinant; Vector spaces (over the field of real and complex numbers), subspaces, spanning set, linear independence, basis and dimension; Linear transformations, rank-nullity theorem, matrix of a linear transformation, change of basis and similarity; Eigenvalues and eigenvectors, algebraic and geometric multiplicity, diagonalization by similarity; Inner-product spaces, Gram-Schmidt process, orthonormal basis; Orthogonal, Hermitian and symmetric matrices, spectral theorem for real symmetric matrices

Ordinary differential equations: First order differential equations – exact differential equations, integrating factors, Bernoulli equations, existence and uniqueness theorem, applications; Higher-order linear differential equations – solutions of homogeneous and nonhomogeneous equations, method of variation of parameters, operator method; Series solutions of linear differential equations, Legendre equation and Legendre polynomials, Bessel equation and Bessel functions of first and second kinds; Systems of first-order equations, phase plane, critical points, stability.

Texts:

1. D. Poole, Linear Algebra: A Modern Introduction, Cengage Learning India Private Limited, 4th Edition, 2015.
2. S. L. Ross, Differential Equations, Wiley India, 3rd Edition, 2004.

References:

1. G. Strang, Linear Algebra and Its Applications, Cengage Learning, 4th Edition, 2006.
2. J. Gilbert and L. Gilbert, Linear Algebra and Matrix Theory, Academic Press, 1995.
3. K. Hoffman and R. Kunze, Linear Algebra, Pearson India, 2nd Edition, 2015.
4. E. A. Coddington, An Introduction to Ordinary Differential Equations, Dover Publications, 1989.
5. E. L. Ince, Ordinary Differential Equations, Dover Publications, 1958.
6. T. M. Apostol, Calculus, Volume-2, Wiley India, 2003.
7. W. E. Boyce and R. C. DiPrima, Elementary Differential Equations, Wiley India, 9th Edition, 2008.

Digital Design [3-0-0-6]

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Students Activity Course - II[0-0-2-0]

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[-]

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Mathematics-III[3-1-0-8]

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Complex analysis: Complex numbers and elementary properties; Complex functions - limits, continuity and differentiation, Cauchy-Riemann equations, analytic and harmonic functions, elementary analytic functions, anti-derivatives and line (contour) integrals, Cauchy-Goursat theorem, Cauchy's integral formula, Morera's theorem, Liouville's theorem, Fundamental theorem of algebra and maximum modulus principle; Power series, Taylor series, zeros of analytic functions, singularities and Laurent series, Rouche's theorem and argument principle, residues, Cauchy's Residue theorem and applications, Mobius transformations and applications.

Partial differential equations: Fourier series, half-range Fourier series, Fourier transforms, finite sine and cosine transforms; First order partial differential equations, solutions of linear and quasilinear first order PDEs, method of characteristics; Classification of second-order PDEs, canonical form; Initial and boundary value problems involving wave equation and heat conduction equation, boundary value problems involving Laplace equation and solutions by method of separation of variables; Initial-boundary value problems in non-rectangular coordinates.

Laplace and inverse Laplace transforms, properties, convolutions; Solution of ODEs and PDEs by Laplace transform; Solution of PDEs by Fourier transform.

Texts:

1. J. W. Brown and R. V. Churchill, Complex Variables and Applications, 7th Ed., Mc-Graw Hill, 2004.
2. I. N. Sneddon, Elements of Partial Differential Equations, McGraw Hill, 1957.
3. E. Kreyszig, Advanced Engineering Mathematics, 10th Ed., Wiley, 2015.

References:

1. J. H. Mathews and R. W. Howell, Complex Analysis for Mathematics and Engineering, 3rd Ed., Narosa,1998.
2. S. J. Farlow, Partial Differential Equations for Scientists and Engineers, Dover Publications, 1993.
3. K. Sankara Rao, Introduction to Partial Differential Equations, 3rd Ed., Prentice Hall of India, 2011

Discrete Mathematics[3-0-0-6]

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Set theory: Sets, relations, equivalence relations, partially ordered sets, functions, countability, lattices and Boolean algebras. Logic: Well-formed formula, interpretations, propositional logic, predicate logic, theory of inference for propositional logic and predicate logic. Combinatorics: Permutations, combinations, recurrences, generating functions, partitions, special numbers like Fibonacci, Stirling and Catalan numbers. Graph Theory: Graphs and digraphs, special types of graphs, isomorphism, connectedness, Euler and Hamilton paths, planar graphs, graph colouring, trees, matching.

Texts:

1. J. P. Tremblay and R. Manohar, Discrete Mathematics with Applications to Computer Science, Tata McGraw-Hill, 1997.
2. K. H. Rosen, Discrete Mathematics & its Applications, 6th Ed., Tata McGraw-Hill, 2007.

References:

1. A. Shen and N. K. Vereshchagin, Basic Set Theory, American Mathematical Society, 2002.
2. A. Kumar, S. Kumaresan and B. K. Sarma, A Foundation Course in Mathematics, Narosa, 2018.
3. M. Huth and M. Ryan, Logic in Computer Science, Cambridge University Press, 2004.
4. V. K. Balakrishnan, Theory and Problems of Combinatorics, Schaum's Series, McGraw-Hill, 1995.
5. R. L. Graham, D. E. Knuth and O. Patashnik, Concrete Mathematics, 2nd Ed., Addison-Wesley, 1994.
6. A. Tucker, Applied Combinatorics, 6th Ed., Wiley, 2012.
7. R. Balakrishnan and K. Ranganathan, A Text Book of Graph Theory, Springer, 2000.

Elementary Number Theory and Algebra[3-0-0-6]

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Number theory: Well ordering principle, principle of mathematical induction; Division algorithm, GCD and LCM, Euclidean algorithm, linear Diophantine equation; Primes, the fundamental theorem of arithmetic; Properties of congruences, linear congruences, chinese remainder theorem; Fermat's little theorem; Arithmetic functions, Mobius inversion formula, Euler's theorem; Primitive roots; Introduction to cryptography, RSA cryptosystem, distribution of primes.

Algebra: Groups, subgroups, cyclic groups, permutation groups, Cayley's theorem, cosets and Lagrange's theorem, normal subgroups, quotient groups, homomorphisms and isomorphism theorems; Rings, integral domains, ideals, quotient rings, prime and maximal ideals, ring homomorphisms, field of quotients, polynomial rings, factorization in polynomial rings, fields, characteristic of a field, field extensions, splitting fields, finite fields.

Texts:

1. D. M. Burton, Elementary Number Theory, 7th Ed., McGraw Hill, 2017.
2. J. A. Gallian, Contemporary Abstract Algebra, 4th Ed., Narosa, 1998.

References:

1. I. Niven, S. Zuckerman and H. L. Montgomery, An Introduction to the Theory of Numbers, 5th Ed., Wiley-India, 1991.
2. G. A. Jones and J. M. Jones, Elementary Number Theory, Springer, 1998
3. K. H. Rosen, Elementary Number Theory and its Applications, Pearson, 2015
4. I. N. Herstein, Topics in Algebra, Wiley, 2004.
5. J. B. Fraleigh, A First Course in Abstract Algebra, Addison Wesley, 2002.

Probability Theory and Random Processes[3-1-0-8]

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Probability spaces, independence, conditional probability, and basic formulae; Random variables, distribution functions, probability mass/density functions, functions of random variables; Standard univariate discrete and continuous distributions and their properties; Mathematical expectations, moments, moment generating functions, characteristic functions; Random vectors, multivariate distributions, marginal and conditional distributions, conditional expectations; Modes of convergence of sequences of random variables, laws of large numbers, central limit theorem; Definition and classification of random processes, discrete-time Markov chains, classification of states, limiting and stationary distributions, Poisson process, continuous-time Markov chains.

Texts:

1. P. G. Hoel, S. C. Port and C. J. Stone, Introduction to Probability Theory, Universal Book Stall, 2000.
2. G. R. Grimmett and D. R. Stirzaker, Probability and Random Processes, 3rd Ed., Oxford University Press, 2001.

References:

1. S. M. Ross, Introduction to Probability Models, 11th Ed., Academic Press, 2014.
2. J. Medhi, Stochastic Processes, 3rd Ed., New Age International, 2009.
3. W. Feller, An Introduction to Probability Theory and its Applications, Vol. 1, 3rd Ed., Wiley, 1968.
4. K. S. Trivedi, Probability and Statistics with Reliability, Queuing, and Computer Science Applications, 2nd Ed., Wiley, 2001.
5. C. M. Grinstead and J. L. Snell, Introduction to Probability, 2nd Ed., Universities Press India, 2009

Data Structures[2-0-2-6]

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Prerequistes: CS101 or equivalent

Asymptotic notation, space and time complexity; Abstract data types, arrays, stacks, queues, linked lists, matrices, binary trees, tree traversals, heaps; Sorting - mergesort, quicksort, heapsort; Graph representations, breadth first search, depth first search; Hashing; Searching - linear search, binary search, binary search trees, AVL trees, red-black trees, B-trees.

Texts:

1. T. H. Cormen, C. E. Leiserson, R. L. Rivest and C. Stein, Introduction to Algorithms, Prentice-Hall of India, 2009.
2. E. Horowitz, S. Sahani and D. Mehta, Fundamentals of Data Structures in C++, University Press, 2008.

References:

1. A. V. Aho, J. E. Hopcroft and J. D. Ullman, Data Structures and Algorithms, Pearson Education, 2006.
2. A. M. Tannenbaum, Y. Langsam and M. J. Augenstein, Data Structures Using C++, Prentice-Hall of India, 1996.
3. M. A. Weiss, Data Structures and Problem Solving Using Java, Addison-Wesley, 1997.

First Level HSS Elective - I [3-0-0-6]

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Real Analysis[3-0-0-6]

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Metrics and norms - metric spaces, normed vector spaces, convergence in metric spaces, completeness, compactness; Functions of several variables - differentiability, chain rule, Taylor's theorem, inverse function theorem, implicit function theorem; Lebesgue measure and integral - sigma-algebra of sets, measure space, Lebesgue measure, measurable functions, Lebesgue integral, Fatou’s lemma, dominated convergence theorem, monotone convergence theorem, L^p spaces.

Texts:

1. J. E. Marsden and M. J. Hoffman, Elementary Classical Analysis, 2nd Ed., W. H. Freeman, 1993.
2. M. Capinski and E. Kopp, Measure, Integral and Probability, 2nd Ed., Springer, 2007.

References:

1. N. L. Carothers, Real Analysis, Cambridge University Press, 2000.
2. G. de Barra, Measure Theory and Integration, New Age International, 1981.
3. R. C. Buck, Advanced Calculus, Waveland Press Incorporated, 2003.

Design and Analysis of Algorithms[3-0-0-6]

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Prerequistes: MA 221 or MA251 or equivalent.

Sorting and order statistics - linear time sorting, randomize quicksort, lower bounds for sorting, median and order statistics, randomized selection; Design and analysis techniques - greedy method, divide-and-conquer, dynamic programming, amortized analysis; Graph algorithms - properties of BFS and DFS, connected components, topological sort, minimum spanning trees, shortest paths, maximum flow; NP-completeness; Approximation algorithms.

Texts:

1. T. H. Cormen, C. E. Leiserson, R. L. Rivest and C. Stein, Introduction to Algorithms, Prentice-Hall of India, 2009

References:

1. A. V. Aho, J. E. Hopcroft and J. D. Ullman, The Design and Analysis of Computer Algorithms, Pearson Education, 2006.
2. J. Kleinberg and E. Tardos, Algorithm Design, Pearson Education, 2006.
3. E. Horowitz and S. Sahni, Fundamentals of Computer Algorithms, Galgotia Publishers, 1984.
4. M. T. Goodrich and R. Tamassia, Algorithm Design: Foundations, Analysis and Internet Examples, John Wiley, 2001.
5. H. Papadimitriou and K. Steiglitz, Combinatorial Optimization: Algorithms and Complexity, Prentice Hall of India, 1992.

Financial Engineering - I[3-0-0-6]

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Prerequistes: MA 225 or equivalent.

Overview of financial engineering, financial markets and financial instruments; Interest rates, present and future values of cash flow streams; Riskfree assets, bonds and bond pricing, yield, duration and convexity, term structure of interest rates, spot and forward rates; Risky assets, risk-reward analysis, Markowitz’s mean-variance portfolio optimization model and efficient frontier, CAPM; No-arbitrage principle; Derivative securities, forward and futures contracts and their pricing, hedging strategies using futures, interest rate and index futures, swaps; General properties of options, trading strategies involving options; Discrete time financial market model, Cox-Ross-Rubinstein binomial asset pricing model, pricing of European derivative securities by replication; Countable probability spaces, filtrations, conditional expectations and their properties, martingales, Markov processes; Risk-neutral pricing of European and American derivate securities.

Texts:

1. M. Capinski and T. Zastawniak, Mathematics for Finance: An Introduction to Financial Engineering, 2nd Ed., Springer, 2010.
2. S. Shreve, Stochastic Calculus for Finance, Vol. I, Springer, 2004.

References:

1. J. C. Hull, Options, Futures and Other Derivatives, 10th Ed., Pearson, 2018.
2. J. Cvitanic and F. Zapatero, Introduction to the Economics and Mathematics of Financial Markets, Prentice-Hall of India, 2007.
3. S. Roman, Introduction to the Mathematics of Finance: From Risk Management to Options Pricing, Springer, 2004.
4. D. G. Luenberger, Investment Science, 2nd Ed., Oxford University Press, 2013.
5. N. J. Cutland and A. Roux, Derivative Pricing in Discrete Time, Springer, 2012

Computer Organization and Architecture [3-0-0-6]

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Database Management Systems[3-0-0-6]

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Database Management Systems Lab [0-0-4-4]

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Students' Activity Course - III [0-0-2-0]

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Course-2[3-0-0-6]

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First Level HSS Elective - II[3-0-0-6]

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Optimization[3-0-0-6]

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Classification and general theory of optimization; Linear programming (LP) - formulation and geometric ideas, simplex and revised simplex methods, duality and sensitivity, transportation, assignment, and integer programming problems; Nonlinear optimization, method of Lagrange multipliers, Karush-Kuhn-Tucker theory, convex optimization; Numerical methods for unconstrained and constrained optimization (gradient method, Newton’s and quasi-Newton methods, penalty and barrier methods).

Texts:

1. M. S. Bazaraa, J. J. Jarvis and H. D. Sherali, Linear Programming and Network Flows, 4th Ed., Wiley, 2011.
2. N. S. Kambo, Mathematical Programming Techniques, Revised Ed., Affiliated East-West Press, 2008.

References:

1. E. K. P. Chong and S. H. Zak, An Introduction to Optimization, 4th Ed., Wiley, 2013.
2. M. S. Bazaraa, H. D. Sherali and C. M. Shetty, Nonlinear Programming: Theory and Algorithms, 3rd Ed., Wiley, 2013.
3. D. G. Luenberger and Y. Ye, Linear and Nonlinear Programming, 4th Ed., Springer, 2016.
4. K. G. Murty, Linear Programming, Wiley, 1983.
5. D. Gale, The Theory of Linear Economic Models, The University of Chicago Press, 1989

Minte Carlo Simulation[0-1-2-4]

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Prerequisites: MA225 or Equivalent

Principles of Monte Carlo; Generation of random numbers from a uniform distribution - linear congruential generators and its variations; Generation of discrete and continuous random variables - inverse transform and acceptance-rejection method; Simulation of univariate normally distributed random variables - Box-Muller and Marsaglia methods; Generation of multivariate normally distributed random variables - Cholesky factorization; Generation of geometric Brownian motion and jump-diffusion sample paths; Variance reduction techniques; Quasi Monte Carlo - general principles and low discrepancy sequences.

Texts:

1. P. Glasserman, Monte Carlo Methods in Financial Engineering, Springer, 2004.
2. R. U. Seydel, Tools for Computational Finance, 5th Ed., Springer, 2012.

Stochastic Calculus for Finance[3-0-0-6]

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Prerequisites: MA224 or equivalent and MA271 or equivalent

General probability spaces, filtrations, conditional expectations, martingales and stopping times, Markov processes; Random walks, Brownian motion and its properties; Itô integral and its properties, Itô processes, Itô-Doeblin formula; Derivation of the Black-Scholes-Merton equation, Black-Scholes-Merton formula, multi-variable stochastic calculus; Risk-neutral valuation, risk-neutral measure, Girsanov's theorem for change of measure, martingale representation theorem, fundamental theorems of asset pricing; Stochastic differential equations and their solutions, Feynman-Kac theorem and its applications

Texts:

1. S. Shreve, Stochastic Calculus for Finance, Vol. II, Springer, 2004.

References:

1. F. C. Klebaner, Introduction to Stochastic Calculus with Applications, 3rd Ed., Imperial College Press, 2012.
2. S. Shreve, Stochastic Calculus for Finance, Vol. I, Springer, 2004.
3. M. Baxter and A. Rennie, Financial Calculus, Cambridge University Press, 1996.
4. A. Etheridge, A Course in Financial Calculus, Cambridge University Press, 2003.
5. R. J. Elliott and P. E. Kopp, Mathematics of Financial Markets, Springer, 1999.

Computer Networks[3-0-0-6]

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Computer Networks Lab[0-0-4 -4]

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Operating Systems[3-0-0-6]

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Operating Systems Lab[0-0-4 -4]

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Students' Activity Course - IV [0-0-2-0]

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Course-3[3-0-0-6]

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Department Elective - I[3-0-0-6]

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[-]

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Scientific Computing[3-0-2-8]

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Errors; Numerical methods for solving scalar nonlinear equations; Interpolation and approximations, spline interpolations; Numerical integration based on interpolation, quadrature methods, Gaussian quadrature; Initial value problems for ordinary differential equations - Euler method, Runge-Kutta methods, multi-step methods, predictor-corrector method, stability and convergence analysis; Finite difference schemes for partial differential equations - explicit and implicit schemes; Consistency, stability and convergence; Stability analysis (matrix method and von Neumann method), Lax equivalence theorem; Finite difference schemes for initial and boundary value problems (FTCS, backward Euler and Crank-Nicolson schemes, ADI methods, Lax Wendroff method, upwind scheme).

Texts:

1. D. Kincaid and W. Cheney, Numerical Analysis: Mathematics of Scientific Computing, 3rd Ed., AMS, 2002.
2. G. D. Smith, Numerical Solutions of Partial Differential Equations, 3rd Ed., Calrendorn Press, 1985.

References:

1. K. E. Atkinson, An Introduction to Numerical Analysis, Wiley, 1989.
2. S. D. Conte and C. de Boor, Elementary Numerical Analysis - An Algorithmic Approach, McGraw-Hill, 1981.
3. R. Mitchell and S. D. F. Griffiths, The Finite Difference Methods in Partial Differential Equations, Wiley, 1980.
4. Richard L. Burden and J. Douglas Faires, Numerical analysis, Brooks/Cole, 2001

Statistical Inference and Multivariate Analysis[3-0-0-6]

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Prerequisites: MA225 or Equivalent

Review of different transformation techniques, modes of convergence, law of large numbers, and central limit theorem; Sampling distributions based on normal distributions, multivariate normal distribution; Point estimation: sufficiency, Neymann-Fisher factorization theorem, unbiased estimation, method of moments, maximum likelihood estimation, consistency and asymptotic normality of maximum likelihood estimator; Interval estimation: confidence coefficient and confident level, pivotal method, asymptotic confidence interval, Bootstrap confidence interval; Hypothesis testing: type-I and type-II errors, power function, size and level, test function and randomized test, most powerful test and Neyman-Pearson lemma, likelihood ratio test, p-value; Multiple linear regression: least squares estimation, estimation of variance, tests of significance, interval estimation, multicollinearity, residual analysis, PRESS statistic, detection and treatment of outliers, lack of fit; Multivariate analysis: principle component analysis, factor analysis, canonical correlations, cluster analysis6

Texts:

1. R. V. Hogg, J. W. McKean and A. T. Craig, Introduction to Mathematical Statistics, 7th Ed., Pearson, 2013.
2. D. C. Montgomery, E. A. Peck and G. G. Vining, Introduction to Linear Regression Analysis, 5th Ed., Wiley, 2012.
3. R. A. Johnson and D. W. Wichern, Applied Multivariate Statistical Analysis, 6th Ed., Prentice Hall of India, 2012.

References:

1. V. K. Rohatgi and A. K. Saleh, An Introduction to Probability and Statistics, 3rd Ed., Wiley, 2015.
2. G. Casella and R. L. Berger, Statistical Inference, 2nd Ed., Cengage Learning, 2006.
3. N. R. Draper and H. Smith, Applied Regression Analysis, 3rd Ed., Wiley, 2000.
4. S. Weisberg, Applied Linear Regression, 1st Ed., Wiley, 2005.
5. T. W. Anderson, An Introduction to Multivariate Statistical Analysis, 3rd Ed., Wiley, 2012.
6. W. K. Härdle and L. Simar, Applied Multivariate Statistical Analysis, 3rd Ed., Springer, 2012.

Theory of Computation[4-0-0-8]

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Prerequisites: MA221 or equivalent

Alphabets, languages, grammars; Finite automata, regular languages, regular expressions; Context-free languages, pushdown automata, DCFLs; Context sensitive languages, linear bounded automata; Turing machines, recursively enumerable languages; Operations on formal languages and their properties; Decidability; Undecidability; Cook’s theorem.

Texts:

1. J. E. Hopcroft and J. D. Ullman, Introduction to Automata Theory, Languages and Computation, Narosa, 1995.
2. H. R. Lewis and C. H. Papadimitriou, Elements of the Theory of Computation, Pearson Education, 1998.

References:

1. M. Sipser, Introduction to the Theory of Computation, Thomson, 2004.
2. P. Linz, An Introduction to Formal Languages and Automata, Narosa, 2007.
3. D. C. Kozen, Automata and Computability, Springer, 1997.

Financial Engineering-II [3-0-0-6]

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Prerequisites: MA372 or equivalent

Continuous time financial market models, Black-Scholes-Merton model, Black-Scholes-Merton equation and formula, dividend paying assets, forwards and futures, risk-neutral valuation of European, American and Exotic derivative securities, change of numeraire, hedging of contingent claims, Greeks, implied volatility, volatility smile; Options on futures; Incomplete markets, stochastic volatility models, pricing and hedging in incomplete markets; Fixed income markets, bonds and interest rates, pricing of fixed income securities, term structure equation; Short rate models, martingale models for short rate (Vasicek, Cox-Ingersoll-Ross, Dothan, Ho-Lee and Hull-White models), multifactor models; Forward rate models, Heath-Jarrow-Morton framework, pricing and hedging under short rate and forward rate models, swaps, caps and floors; LIBOR and swap market models.

Texts:

1. T. Bjork, Arbitrage Theory in Continuous Time, 3rd Ed., Oxford University Press, 2003.
2. S. Shreve, Stochastic Calculus for Finance, Vol. II, Springer, 2004.

References:

1. J. C. Hull, Options, Futures and Other Derivatives, 10th Ed., Pearson, 2018.
2. D. Brigo and F. Mercurio, Interest Rate Models: Theory and Practice, Springer, 2006.
3. N. H. Bingham and R. Kiesel, Risk-Neutral Valuation, 2nd Ed., Springer, 2004.
4. J. Cvitanic and F. Zapatero, Introduction to the Economics and Mathematics of Financial Markets, Prentice-Hall of India, 2007.
5. M. Musiela and M. Rutkwoski, Martingale Method in Financial Modelling, 2nd Ed., Springer, 2005.

Financial Engineering Laboratory[0-0-3-3]

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Prerequisites: MA271 or equivalent

This course will focus on computational aspects of the financial market models studied in MA271 and MA373 such as CAPM, binomial models, Black-Scholes-Merton model, interest rate models and asset pricing based on above models. The implementation will be done using MATLAB/C++/R.

Texts:

1. Y. Lyuu, Financial Engineering and Computation, Cambridge University Press, 2002.
2. D. Higham, Introduction to Financial Option Valuation: Mathematics, Stochastics and Computation, Cambridge University Press, 2004.

References:

1. P. Glasserman, Monte Carlo Methods in Financial Engineering, Springer, 2004

Second Level HSS Elective - I [3-0-0-6]

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Project - I [0-0-6-6]

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[-]

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Matrix Computation[3-0-2-8]

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Floating point computations, IEEE floating point arithmetic, analysis of roundoff errors; Sensitivity analysis and condition numbers; Linear systems, LU decompositions, Gaussian elimination with partial pivoting; Banded systems, positive definite systems, Cholesky decomposition - sensitivity analysis; Gram-Schmidt orthonormal process, Householder transformation, Givens rotations; QR factorization, stability of QR factorization. Solution of linear least squares problems, normal equations, singular value decomposition(SVD), polar decomposition, Moore-Penrose inverse; Rank deficient least-squares problems; Sensitivity analysis of least-squares problems; Review of canonical forms of matrices; Sensitivity of eigenvalues and eigenvectors. Reduction to Hessenberg and tridiagonal forms; Power, inverse power and Rayleigh quotient iterations; Explicit and implicit QR algorithms for symmetric and nonsymmetric matrices; Reduction to bidiagonal form; Golub- Kahan algorithm for computing SVD.

Texts:

1. D. S. Watkins, Fundamentals of Matrix Computations, 2nd Ed., John Wiley, 2002.
2. L. N. Trefethen and D. Bau, Numerical Linear Algebra, SIAM, 1997.

References:

1. J. W. Demmel, Applied Numerical Linear Algebra, SIAM, 1997.
2. M. L. Overton, Numerical Computing with IEEE Floating Point Arithmetic, SIAM, 2001.

Computational Finance[3-0-2-8]

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Prerequisites: MA373 or equivalent

Review of financial market models for derivative pricing, interest rate modelling and Black-Scholes PDE; Solutions of pricing PDEs using finite difference methods, American option as free boundary problem, computation of price of American options, pricing of exotic options, upwind scheme and other methods; Monte-Carlo simulation, generating sample paths, discretization of SDE, Monte-Carlo for option valuation and Greeks, Monte-Carlo for American and exotic options; Variance reduction techniques; Monte-Carlo implementation of short rate models, forward rate models and LIBOR market model, volatility structure and calibration.

Texts:

1. R. U. Seydel, Tools for Computational Finance, 5th Ed., Springer, 2012.
2. P. Glasserman, Monte Carlo Methods in Financial Engineering, Springer, 2004.

References:

1. Y.-l. Zhu, X. Wu, I-L. Chern and Z.-z. Sun, Derivative Securities and Difference Methods, 2nd Ed., Springer, 2013.
2. D. Higham, Introduction to Financial Option Valuation: Mathematics, Stochastics and Computation, Cambridge University Press, 2004.
3. P. Wilmott, S. Howison and J. Dewynne, The Mathematics of Financial Derivatives: A Student Introduction, Cambridge University Press, 1997.
4. Y. Lyuu, Financial Engineering and Computation, Cambridge University Press, 2002.

Department Elective - II [3-0-0-6]

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Second Level HSS Elective - II[3-0-0-6]

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Department Elective - III[3-0-0-6]

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Department Elective - IV[3-0-0-6]

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Open Elective - I[3-0-0-6]

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Project - II[0-0-10-10]

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Mathematics - III[3-1-0-8]

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Complex numbers and elementary properties. Complex functions - limits, continuity and differentiation. Cauchy-Riemann equations. Analytic and harmonic functions. Elementary functions. Anti-derivatives and path (contour) integrals. Cauchy-Goursat Theorem. Cauchy's integral formula, Morera's Theorem. Liouville's Theorem, Fundamental Theorem of Algebra and Maximum Modulus Principle. Taylor series. Power series. Singularities and Laurent series. Cauchy's Residue Theorem and applications. Mobius transformations.

First order partial differential equations; solutions of linear and nonlinear first order PDEs; classification of second-order PDEs; method of characteristics; boundary and initial value problems (Dirichlet and Neumann type) involving wave equation, heat conduction equationi, Laplace's equations and solutions by method of separation of variables (Cartesian coordinates); initial boundary value problems in non-rectangular coordinates.

Laplace and inverse Laplace transforms; properties, convolutions; solution of ODE and PDE by Laplace transform; Fourier series, Fourier integrals; Fourier transforms, sine and cosine transforms; solution of PDE by Fourier transform.

Texts:

1. J. W. Brown and R. V. Churchill, Complex Variables and Applications, 7th Ed., Mc-Graw Hill, 2004.
2. I. N. Sneddon, Elements of Partial Differential Equations, McGraw Hill, 1957.
3. S. L. Ross, Differential Equations, 3rd Ed., Wiley India, 1984.

References:

1. T. Needham, Visual Complex Analysis, Oxford University Press, 1999.
2. J. H. Mathews and R. W. Howell, Complex Analysis for Mathematics and Engineering, 3rd Ed., Narosa,1998.
3. S. J. Farlow, Partial Differential Equations for Scientists and Engineers, Dover Publications, 1993.
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