Single Variable Calculus[3-1-0-4]

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Convergence of sequences and series of real numbers; Limits, 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.

Texts:

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

References: 

• R. G. Bartle and D. R. Sherbert, Introduction to Real Analysis, Wiley India, 4th Edition, 2014.
• S. R. Ghorpade and B. V. Limaye, A Course in Calculus and Real Analysis, Springer India, 2006.

Multi Variable Calculus[3-1-0-4]

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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:

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

References:

• S. R. Ghorpade and B. V. Limaye, A Course in Multivariable Calculus and Analysis, Springer India, 2010.
• T. M. Apostol, Calculus, Volume 2, Wiley India, 2003
• J. E. Marsden, A. J. Tromba and A. Weinstein, Basic Multivariable Calculus, Springer India, 2002.

Basic Inorganic Chemistry[3-0-0-3]

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Basic Organic Chemistry[3-0-0-3]

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Chemistry Lab[0-0-3-3]

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

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Computing Lab[0-0-3-3]

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Engineering Mechanics[2-1-0-6]

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Introductory Classical Mechanics[2-1-0-3]

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Modern Physics[2-1-0-3]

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Basic Physical Chemistry[3-0-0-3]

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Fundamentals of Data Science[3-0-0-3]

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Electric Circuits[3-0-0-3]

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Digital and Analog Electronics[3-0-0-3]

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Basic Electronics Lab[0-0-3-3]

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Linear Algebra[3-1-0-4]

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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.

Texts:

• D. Poole, Linear Algebra: A Modern Introduction, Cengage Learning India Private Limited, Fourth Edition, 2015.

References:

• G. Strang, Linear Algebra and Its Applications, Cengage Learning, Fourth Edition, 2006
• . Gilbert and L. Gilbert, Linear Algebra and Matrix Theory, Academic Press, 1995.
• K. Hoffman and R. Kunze, Linear Algebra, Pearson India, Second Edition, 2015.

Complex Analysis[3-1-0-4]

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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, 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,  Applications of Residues; Conformal mappings, Mobius transformations.

Texts:

• J. W. Brown and R. V. Churchill, Complex Variables and Applications, Seventh Edition, McGraw Hill, 2004.

 

References:

• J. H. Mathews and R. W. Howell, Complex Analysis for Mathematics and Engineering, Third Edition, Narosa,1998.
• S. Ponnusamy, Foundation of Complex Analysis, Narosa, 2011.

Discrete Mathematics / Probability and Random Processes[3-0-0-6]

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The batch joind in July 2025 will do MA2151 Probability and Random Processes (3-1-0-8) in place of MA1221 Discrete Mathematics (3-0-0-6)

MA1221 Discrete Mathematics

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 graphs, planar graphs, graph colouring, trees, matching.

Texts:

• J. P. Tremblay and R. Manohar, Discrete Mathematics with Applications to Computer Science, Tata McGraw-Hill, 1997
• K. H. Rosen, Discrete Mathematics & its Applications, Sixth Edition, Tata McGraw-Hill, 2007.

 

References:

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

 

MA2151 Probability and Random Processes

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:

• P. G. Hoel, S. C. Port and C. J. Stone, Introduction to Probability Theory, Universal Book Stall, 2000.
• G. R. Grimmett and D. R. Stirzaker, Probability and Random Processes, Fourth Edition, Oxford University Press, 2020.

 

References:

• S. M. Ross, Introduction to Probability Models, Thirteenth Edition, Academic Press, 2023.
• H. Pishro-Nik, Introduction to Probability, Statistics, and Random Processes, Available at https://www.probabilitycourse.com, Kappa Research LLC, 2014.
• J. Medhi, Stochastic Processes, Third Edition, New Age International, 2009.
• W. Feller, An Introduction to Probability Theory and its Applications, Volume I, Third Edition, Wiley, 1968.
• K. S. Trivedi, Probability and Statistics with Reliability, Queuing, and Computer Science Applications, Second Edition, Wiley, 2001.
• C. M. Grinstead and J. L. Snell, Introduction to Probability, Second Edition, Universities Press India, 2009.

Introductory Electromagnetics[2-1-0-3]

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Introductory Quantum Mechanics[2-1-0-3]

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Physics Lab[0-0-3-3]

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

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Minor Discipline Course-I[3-0-0-6]

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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:

• D. M. Burton, Elementary Number Theory, Seventh Edition, McGraw Hill, 2017.
• J. A. Gallian, Contemporary Abstract Algebra, Fourth Edition, Narosa, 1998.

 

References:

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

Probability and Random Processes / Discrete Mathematics[3-1-0-8]

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The batch joind in July 2025 will do MA1221 Discrete Mathematics (3-0-0-6) in place of MA2151 Probability and Random Processes (3-1-0-8)

MA1221 Discrete Mathematics

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 graphs, planar graphs, graph colouring, trees, matching.

Texts:

• J. P. Tremblay and R. Manohar, Discrete Mathematics with Applications to Computer Science, Tata McGraw-Hill, 1997
• K. H. Rosen, Discrete Mathematics & its Applications, Sixth Edition, Tata McGraw-Hill, 2007.

 

References:

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

 

MA2151 Probability and Random Processes

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:

• P. G. Hoel, S. C. Port and C. J. Stone, Introduction to Probability Theory, Universal Book Stall, 2000.
• G. R. Grimmett and D. R. Stirzaker, Probability and Random Processes, Fourth Edition, Oxford University Press, 2020.

 

References:

• S. M. Ross, Introduction to Probability Models, Thirteenth Edition, Academic Press, 2023.
• H. Pishro-Nik, Introduction to Probability, Statistics, and Random Processes, Available at https://www.probabilitycourse.com, Kappa Research LLC, 2014.
• J. Medhi, Stochastic Processes, Third Edition, New Age International, 2009.
• W. Feller, An Introduction to Probability Theory and its Applications, Volume I, Third Edition, Wiley, 1968.
• K. S. Trivedi, Probability and Statistics with Reliability, Queuing, and Computer Science Applications, Second Edition, Wiley, 2001.
• C. M. Grinstead and J. L. Snell, Introduction to Probability, Second Edition, Universities Press India, 2009.

Digital Logic and Computer Architecture[3-0-0-6]

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Boolean Algebra Minimisation and realisation of switching circuits Basic building blocks of combinational circuits: Multiplexer, De-multiplexer, Encoder, Decoder, Adder, Subtracter Design of synchronous sequential circuits: Flip-flops, Registers, Counters, Finite State Machines, State tables and diagrams, Excitation functions of memory elements.Instruction sets with various addressing modes Memory organisation: ROM, Cache, Main Memory CPU design: ALU, Control unit design: hardwired and microprogrammed I/O transfer: Program controlled, Interrupt controlled and DMA.

Texts:

• M. Morris Mano, Digital Design, 3^rd Edition, Pearson Education, 2007.
• William Stallings, Computer Organization and Architecture: Designing for Performance, 8^th Edition, Pearson Education India. 2010.

 

References:

• A. P. Malvino, D. K. Leach and G. Saha, Digital Principles and Applications, Sixth Edition, McGraw Hill, 2006.
• V. C. Hamacher, Z. G. Vranesic and S. G. Zaky, Computer Organization, Fifth Edition, McGraw Hill, 2002.
• D. A. Patterson and J. L. Hennessy, Computer Organization and Design, Third Edition, Morgan Kaufmann, 2006.
• Barry B. Brey, The INTEL Microprocessors, Eighth Edition, Prentice Hall, 2008.

 

Data Structures with Object Oriented Programming[3-0-2-8]

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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.

Classes and objects, Inheritance, polymorphism, Exceptions handling.

Texts:

• T. H. Cormen, C. E. Leiserson, R. L. Rivest and C. Stein, Introduction to Algorithms, Prentice-Hall of India, 2009.
• E. Horowitz, S. Sahani and D. Mehta, Fundamentals of Data Structures in C++, University Press, 2008.
• Herbert Schildt, Java - The Complete Reference, Ninth Edition, McGraw Hill Education, 2017.

 

References:

• A. V. Aho, J. E. Hopcroft and J. D. Ullman, Data Structures and Algorithms, Pearson Education, 2006.
• A. M. Tannenbaum, Y. Langsam and M. J. Augenstein, Data Structures Using C++, Prentice-Hall of India, 1996
• M. A. Weiss, Data Structures and Problem Solving Using Java, Addison-Wesley, 1997.
• Robert Lafore, Object Oriented Programming in C++, Fourth Edition, Sams, 2001.

Ordinary Differential Equations[3-1-0-4]

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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 undetermined coefficients, 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:

• S. L. Ross, Differential Equations, Wiley India, Third Edition, 2004.

 

References:

• E. A. Coddington, An Introduction to Ordinary Differential Equations, Dover Publications, 1989.
• G.  Simmons and S. Krantz, Differential Equations: Theory, Technique and Practice, McGraw Hill Educations, 2006.
• W. E. Boyce and R. C. DiPrima, Elementary Differential Equations, Wiley India, Ninth Edition, 2008.
• E. L. Ince, Ordinary Differential Equations, Dover Publications, 1958.

Partial Differential Equations[3-1-0-4]

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Fourier series, half-range Fourier series, Fourier transforms, finite sine and cosine transforms. Laplace and inverse Laplace transforms, properties, convolutions.

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. Solution of PDEs by Laplace transform and Fourier transform.

Texts:

• K. Sankara Rao, Introduction to Partial Differential Equations, Third Edition, Prentice Hall of India, 2011.

 

References:

• I. N. Sneddon, Elements of Partial Differential Equations, McGraw Hill, 1957.
• S. J. Farlow, Partial Differential Equations for Scientists and Engineers, Dover Publications, 1993.
• E. Kreyszig, Advanced Engineering Mathematics, Tenth Edition, Wiley, 2015.

 

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

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

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Minor Discipline Course-II[3-0-0-6]

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HSS Elective - II[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:

• J. E. Marsden and M. J. Hoffman, Elementary Classical Analysis, Second Edition, W. H. Freeman, 1993.
• M. Capinski and E. Kopp, Measure, Integral and Probability, Second Edition, Springer, 2004.

 

References:

• N. L. Carothers, Real Analysis, Cambridge University Press, 2000.
• G. de Barra, Measure Theory and Integration, New Age International, 1981
• R. C. Buck, Advanced Calculus, Third Edition, Waveland Press Incorporated, 2004.

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:

• D. Kincaid and W. Cheney, Numerical Analysis: Mathematics of Scientific Computing, Third Edition, American Mathematical Society, 2009.
• G. D. Smith, Numerical Solutions of Partial Differential Equations, Third Edition, Clarendon Press, 1986.

 

References:

• K. E. Atkinson, An Introduction to Numerical Analysis, Second Edition, Wiley, 1989.
• S. D. Conte and C. de Boor, Elementary Numerical Analysis - An Algorithmic Approach, McGraw Hill, 1981.
• R. Mitchell and S. D. F. Griffiths, The Finite Difference Methods in Partial Differential Equations, John Wiley, 1980.
• Richard L. Burden, J. Douglas Faires and Annette M. Burden, Numerical Analysis, Tenth Edition, Cengage Learning, 2015.

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

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Overview of financial engineering, financial markets and financial instruments; Interest rates, present and future values of cash flow streams; Risk free 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:

• M. Capinski and T. Zastawniak, Mathematics for Finance: An Introduction to Financial Engineering, Second Edition, Springer, 2010.
• S. Shreve, Stochastic Calculus for Finance, Volume I, Springer, 2004.

 

References:

• J. C. Hull, Options, Futures and Other Derivatives, Eleventh Edition, Pearson, 2021.
• J. Cvitanic and F. Zapatero, Introduction to the Economics and Mathematics of Financial Markets, Prentice Hall of India, 2007.
• S. Roman, Introduction to the Mathematics of Finance: From Risk Management to Options Pricing, Springer, 2004.
• D. G. Luenberger, Investment Science, Second Edition, Oxford University Press, 2013.
• N. J. Cutland and A. Roux, Derivative Pricing in Discrete Time, Springer, 2012.

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

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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:

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

 

References:

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

Database Management Systems[3-0-3-9]

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Using DBMS as a black box: ER Model, relational model and algebras, SQL, normalization. Internals of relational DBMS: file organizations, indexing (tree, hash, and bitmap), implementation of relational operators. Transaction management: ACID properties, concurrency control, crash recovery. Non-relational DBMS: consistency and availability trade-offs, NoSQL DBMS (key-value, document, and graph).

Practical: Using a relational DBMS: Writing SQL queries, accessing a DBMS from an external application. Implementing of parts of DBMS such as various file organizations, indexing methods (Tree/ Hash/ Bitmap), external sorting algorithms, concurrency control schemes, and crash recovery schemes. Non-relational DBMS; performance comparison of a non-relational DBMS with a relational DBMS for an application.

Texts:

• R. Ramakrishnan, J. Geherke, Database Management Systems, McGraw Hill, 2014.
• P. Sadalage and M. Fowler, NoSQL Distilled: A Brief Guide to the Emerging World of Polyglot Persistence, Addison Wesley, 2012.
• H. Garcia-Molina, J. Ullman, J. Widom, Database System: The Complete Book, Second Edition, Pearson, 2013.

 

References:

• P. Bailis, J. Hellerstein, M. Stonebraker, Readings in Database Systems, Fifth Edition, available under Creative Commons Attribution-NonCommercial-ShareAlike 4.0 license, http://www.redbook.io/pdf/redbook-5th-edition.pdf, 2015.
• J. Groff and P. Weinberg, SQL Complete Reference, McGraw Hill, Third Edition, 2017.

Skill Enhancement and Employability Course[0-0-2-0]

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Minor Discipline Course-III[3-0-0-6]

---

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

---

Matrix Computation[3-0-2-8]

---

Floating point computations, IEEE floating point arithmetic, analysis of round off 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:

• D. S. Watkins, Fundamentals of Matrix Computations, Second Edition, John Wiley, 2002.
• L. N. Trefethen and D. Bau, Numerical Linear Algebra, SIAM, 1997.

 

References:

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

 

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

---

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 analysis.

Texts:

• R. V. Hogg, J. W. McKean and A. T. Craig, Introduction to Mathematical Statistics, Eighth Edition, Pearson, 2020.
• D. C. Montgomery, E. A. Peck and G. G. Vining, Introduction to Linear Regression Analysis, Sixth Edition, Wiley, 2021.
• R. A. Johnson and D. W. Wichern, Applied Multivariate Statistical Analysis, Sixth Edition, Prentice Hall of India, 2015.

 

References:

• V. K. Rohatgi and A. K. Saleh, An Introduction to Probability and Statistics, Third Edition, Wiley, 2015.
• G. Casella and R. L. Berger, Statistical Inference, Second Edition, Cengage Learning, 2006
• N. R. Draper and H. Smith, Applied Regression Analysis, Third Edition, Wiley, 2000.
• S. Weisberg, Applied Linear Regression, First Edition, Wiley, 2005.
• T. W. Anderson, An Introduction to Multivariate Statistical Analysis, Third Edition, Wiley, 2012.
• W. K. Härdle and L. Simar, Applied Multivariate Statistical Analysis, Fifth Edition, Springer, 2019.

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

---

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:

• S. Shreve, Stochastic Calculus for Finance, Volume II, Springer, 2004.

 

References:

• F. C. Klebaner, Introduction to Stochastic Calculus with Applications, Third Edition, Imperial College Press, 2012.
• S. Shreve, Stochastic Calculus for Finance, Volume I, Springer, 2004.
• M. Baxter and A. Rennie, Financial Calculus, Cambridge University Press, 1996.
• A. Etheridge, A Course in Financial Calculus, Cambridge University Press, 2003.
• R. J. Elliott and P. E. Kopp, Mathematics of Financial Markets, Springer, 1999.

Operating Systems[3-0-0-3]

---

Introduction to Operating Systems, process management basics, Processes and threads and their scheduling, synchronization, deadlocks in concurrent processes; Memory management basics, demand paging and virtual memory implementation; File system design and implementation.,

Texts:

• A. Silberschatz, P. B. Galvin and G. Gagne, Operating System Concepts, Tenth Edition, John Wiley, 2019.

 

References:

• W. Stallings, Operating Systems: Internals and Design Principles, Ninth Edition, Pearson, 2018.
• A. S. Tanenbaum and A. S. Woodhull, Operating Systems Design and Implementation, Third Edition, Pearson India, 2015.
• A. S. Tanenbaum and H. Bos, Modern Operating Systems, Fifth Edition, Pearson Education, 2024.

Computer Networks[3-0-0-3]

---

Introduction to computer networks,  OSI and TCP/IP Model; Local area networks: Multiple access techniques – wired and wireless; Concepts of switched networks, Internet addressing and routing algorithms; Transport protocols, UDP, TCP, flow control, congestion control; Application Layer: Client-Server and P2P architecture, API; Application layer protocols such as DNS, SSL, WWW, HTTP.

Texts:

• L. L. Peterson and B. S. Davie, Computer Networks: A Systems Approach, Sixth Edition, Morgan Kaufmann, 2021.
• A. S. Tanenbaum, Computer Networks, Fifth Edition, Pearson India, 2013.

 

References:

• J. F. Kurose and K. W. Ross, Computer Networking: A Top-Down Approach, Eighth Edition, Pearson Education, 2022.
• D. E. Comer, Internetworking with TCP/IP, Volume-1, Sixth Edition, Pearson Education, 2015.
• S. Keshav, An Engineering Approach to Computer Networking, First Edition, Pearson India, 1999.
• B. Forouzan, Data Communications and Networking, Fourth Edition,Tata Mcgraw Hill, 2006.

Machine Learning[3-0-3-9]

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Introduction to learning: supervised and unsupervised, generative and discriminative models, classification and regression problems, performance measures, design of experiments; Feature space and dimensionality reduction: Feature selection, PCA, exploratory factor analysis, LDA, ICA; Unsupervised learning: K-means clustering, hierarchical agglomerative clustering, DBSCAN, MLE, MAP, Bayesian learning, Gaussian Mixture Models; Supervised learning: Bayesian decision theory, Logistic Regression, data balancing, simple perceptron and multi-layer perceptron, Parzen windows, k-nearest neighbor, decision trees, support vector machines; ensemble methods, bagging and boosting; Applications and case studies.

Practical: Sci-kit Learn, NumPy and MatPlotLib; PCA and LDA; K-means Clustering, Hierarchical Agglomerative Clustering and DBSCAN; MLE and Bayesian learning; Linear and Logistic Regression; Perceptron; Data Balancing & Imbalance-Learning; Multi-layer perceptron; k-nearest neighbor, Classification and Regression Trees; Support Vector Machines; Random Forest, AdaBoost.

Texts:

• Ethem Alpaydin, Introduction to Machine Learning, Third Edition, Prentice Hall of India, 2015.
• Tom M. Mitchell, Machine Learning, McGraw Hill Education, 2017

 

References:

• C. M. Bishop, Pattern Recognition and Machine Learning, Second Edition, 2011.
• Miroslav Kubat, An Introduction to Machine Learning, Third Edition, Springer, 2021.
• S. O. Haykin, Neural Networks and Learning Machines, Third Edition, Pearson Education, 2016.

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

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Minor Discipline Course-IV[3-0-0-6]

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

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Numerical Optimization[3-0-2-8]

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Optimization Problems, Convex Sets and Convex Functions, Extremum Points.

Unconstrained Optimization:  Search methods: Powell’s Method, Hooke and Jeeves Method; Steepest Descent Method, Fletcher and Reeves Method, Newton’s Method, Marquardt’s Method, Quasi-Newton Methods, Davidson-Fletcher-Powell Method, Least Square Problems.

Constrained Optimization: Lagrange multiplies, Kuhn-Tucker Conditions, Duality, Simplex Method, Dual methods, Active Set Methods for Convex Quadratic Programming, Gradient Projection Methods, Penalty-Barrier Methods.

Texts:

• Jorge Nocedal and Stephen Wright, Numerical Optimization, Second Edition, Springer Verlag, 2006.
• D. P. Bertsekas, Nonlinear Programming, Athena Scientific, 1999.

 

References:

• Suresh Chandra, Jaydeva, Aparna Mehra, Numerical Optimization with Applications, Narosa, 2009.
• S. S. Rao, Optimization: Theory and Applications, Second Edition, Wiley Eastern, 1984
• David Luenberger and Yinyu Ye, Linear and Nonlinear Programming, Fourth Edition, Springer, 2016.
• E. K. P. Chong and S. H. Zak, Introduction to Optimization, Fourth Edition, Wiley India, 2017.
• S. Boyd and L. Vandenberghe, Convex Optimization, Cambridge India, 2016.

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

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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:

• T. Bjork, Arbitrage Theory in Continuous Time, Third Edition, Oxford University Press, 2003.
• S. Shreve, Stochastic Calculus for Finance, Volume II, Springer, 2004.

 

References:

• J. C. Hull, Options, Futures and Other Derivatives, Eleventh Edition, Pearson, 2021.
• D. Brigo and F. Mercurio, Interest Rate Models: Theory and Practice, Springer, 2006.
• N. H. Bingham and R. Kiesel, Risk-Neutral Valuation, Second Edition, Springer, 2004.
• J. Cvitanic and F. Zapatero, Introduction to the Economics and Mathematics of Financial Markets, Prentice Hall of India, 2007.
• M. Musiela and M. Rutkwoski, Martingale Method in Financial Modelling, Second Edition, Springer, 2005.

Financial Engineering Lab[0-0-3-3]

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This course will focus on computational aspects of the financial market models studied mainly in MA2271 Financial Engineering-I and MA3271 Financial Engineering-II 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:

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

 

References:

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

Monte Carlo Methods in Finance[3-0-2-4]

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Principles of Monte-Carlo simulation; Generation of uniform (LCG and its variations), general (inverse transform method, acceptance-rejection method) and normal (Box-Muller method) random variables; Generation of multivariate normal random vectors, Cholesky factorization; Generation of sample paths, Brownian motion, geometric Brownian motion, jump-diffusion process; Monte-Carlo for valuation of European, American and exotic options and Greeks; Gaussian short rate models, forward rate models, LIBOR market model, volatility structure and calibration; Variance reduction techniques, control variates, antithetic variates, stratified sampling, importance sampling; Applications in risk management, Value-at-Risk (VaR), credit risk.

Texts:

• P. Glasserman, Monte Carlo Methods in Financial Engineering, Springer, 2004.
• R. U. Seydel, Tools for Computational Finance, Sixth Edition, Springer, 2017.

 

References:

• R. Korn, E. Korn and G. Kroisandt, Monte Carlo Methods and Models in Finance and Insurance, CRC Press, 2023.
• Desmond J. Higham, An Introduction to Financial Option Valuation: Mathematics, Stochastics and Computation, Cambridge University Press, 2004.

Computational Finance[3-0-2-4]

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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.

Texts:

• R. U. Seydel, Tools for Computational Finance, Fifth Edition, Springer, 2012.
• You-Ian Zhu, X. Wu, I-Liang Chern and Zhi-zong Sun, Derivative Securities and Difference Methods, Second Edition, Springer, 2013.

 

References:

• D. Higham, Introduction to Financial Option Valuation: Mathematics, Stochastics and Computation, Cambridge University Press, 2004.
• P. Wilmott, S. Howison and J. Dewynne, The Mathematics of Financial Derivatives: A Student Introduction, Cambridge University Press, 1997
• Y. Lyuu, Financial Engineering and Computation, Cambridge University Press, 2002.

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

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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:

• J. E. Hopcroft, Rajeev Motwani and  J. D. Ullman, Introduction to Automata Theory, Languages, and Computation, Third Edition,  Pearson Education India, 2008.
• H. R. Lewis and C. H. Papadimitriou, Elements of the Theory of Computation, Pearson Education, 1998.

 

References:

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

Minor Discipline Course-V[3-0-0-6]

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