BTech Course Structure and Syllabus for Mathematics & Computing

(to be applicable from 2010 batch onwards)

 

Course No.

Course Name

L

T

P

C

 

Course No.

Course Name

L

T

P

C

Semester - 1

 

Semester -2

CH101

Chemistry

3

1

0

8

 

BT101

Modern Biology

3

0

0

6

CH110

Chemistry Laboratory

0

0

3

3

 

CS 101

Introduction to Computing

3

0

0

6

EE 101

Electrical Sciences

3

1

0

8

 

CS110

Computing Laboratory

0

0

3

3

MA101

Mathematics - I

3

1

0

8

 

EE 102

Basic Electronics Laboratory

0

0

3

3

ME 110/

PH 110

Workshop /Physics Laboratory

0

0

3

3

 

MA102

Mathematics - II

3

1

0

8

ME 111**

Engineering Drawing

0

0

3

3

 

ME101

Engineering Mechanics

3

1

0

8

PH101

Physics - I

2

1

0

6

 

PH102

Physics - II

2

1

0

6

SA 101

Physical Training -I

0

0

2

0

 

PH 110/

ME 110

Physics Laboratory/ Workshop

0

0

3

3

NCC/NSO/NSS

0

0

2

0

 

SA 102

Physical Training -II

0

0

2

0

11

4

9

39

 

 

NCC/NSO/NSS

0

0

2

0

** For 2010 batch the credit structure is 0-0-3-3

 

 

 

14

3

9

43

Semester 3

 

Semester 4

MA 201

Mathematics-III

3

1

0

8

 

MA 224

Real Analysis

3

0

0

6

MA 221

Discrete Mathematics

4

0

0

8

 

MA 226

Monte Carlo Simulation

0

1

2

4

MA 222

Modern Algebra

3

0

0

6

 

CS 222

Computer Organization and Architecture

3

0

0

6

MA 225

Probability Theory and Random Processes

3

1

0

8

 

MA 252

Data Structures and Algorithms

3

0

0

6

CS 221

Digital Design

3

0

0

6

 

HS2xx

HSS Elective - II

3

0

0

6

HS2xx

HSS Elective - I

3

0

0

6

 

MA 253

Data Structures Lab with Object-Oriented Programming

0

1

2

4

SA 201

Physical Training -III

0

0

2

0

 

MA 271

Financial Engineering-I

3

0

0

6

NCC/NSO/NSS

0

0

2

0

 

SA 202

Physical Training -IV

0

0

2

0

19

2

0

42

 

 

NCC/NSO/NSS

0

0

2

0

 

 

 

 

 

 

 

15

2

4

38

Semester 5

 

Semester 6

MA 322

Scientific Computing

3

0

2

8

 

MA 321

Optimization

3

0

0

6

MA 372

Stochastic Calculus for Finance

3

0

0

6

 

MA 351

Formal Languages and Automata Theory

3

0

0

6

CS 341

Operating Systems

3

0

0

6

 

MA 373

Financial Engineering-II

3

0

0

6

CS 342

Operating Systems Lab

0

0

3

3

 

MA 374

Financial Engineering Laboratory

0

0

3

3

CS 343

Data Communication

3

0

0

6

 

CS 344

Databases

3

0

0

6

HS3xx

HSS Elective - III

3

0

0

6

 

CS 345

Databases Lab

0

0

3

3

15

0

5

35

 

CS 348

Computer Networks

3

0

0

6

 

CS 349

Networks Lab

0

0

3

3

 

 

 

15

0

9

39

Semester 7

 

Semester 8

MA 423

Matrix Computations

3

0

2

8

 

MA 473

Computational Finance

3

0

2

8

MA 471

Statistical Analysis of Financial Data

3

0

2

8

 

MA xxx

Department Elective-II

3

0

0

6

MA 453

Theory of Computation

3

0

0

6

 

MA xxx

Department Elective-III

3

0

0

6

MA xxx

Department Elective-I

3

0

0

6

 

HS4xx

HSS Elective - IV

3

0

0

6

MA 498

Project-I

0

0

6

6

 

MA 499

Project-II

0

0

10

10

12

0

10

34

 

 

 

12

0

12

36

 

 

CH 101             Chemistry                    (3-1-0-8)

Structure and Bonding; Origin of quantum theory, postulates of quantum mechanics; Schrodinger wave equation: operators and observables, superposition theorem and expectation values, solutions for particle in a box, harmonic oscillator, rigid rotator, hydrogen atom; Selection rules of microwave and vibrational spectroscopy; Spectroscopic term symbol; Molecular orbitals: LCAO-MO; Huckel theory of conjugated systems; Rotational, vibrational and electronic spectroscopy; Chemical Thermodynamics: The zeroth and first law, Work, heat, energy and enthalpies; The relation between C­­v and Cp; Second law: entropy, free energy (the Helmholtz and Gibbs) and chemical potential; Third law; Chemical equilibrium; Chemical kinetics: The rate of reaction, elementary reaction and chain reaction; Surface: The properties of liquid surface, surfactants, colloidal systems, solid surfaces, physisorption and chemisorption; The periodic table of elements; Shapes of inorganic compounds; Chemistry of materials; Coordination compounds: ligand, nomenclature, isomerism, stereochemistry, valence bond, crystal field and molecular orbital theories; Bioinorganic chemistry and organometallic chemistry; Stereo and regio-chemistry of organic compounds, conformers; Pericyclic reactions; Organic photochemistry; Bioorganic chemistry: Amino acids, peptides, proteins, enzymes, carbohydrates, nucleic acids and lipids; Macromolecules (polymers); Modern techniques in structural elucidation of compounds (UV-vis, IR, NMR); Solid phase synthesis and combinatorial chemistry; Green chemical processes.

 

Texts:

1. P. W. Atkins, Physical Chemistry, 5th Ed., ELBS, 1994.

2. C. N. Banwell, and E. M. McCash, Fundamentals of Molecular Spectroscopy, 4th Ed., Tata McGraw-Hill, 1962.

3. F. A. Cotton, and G. Wilkinson, Advanced Inorganic Chemistry, 3rd Ed., Wiley Eastern Ltd., New Delhi, 1972, reprint in 1988.

4. D. J. Shriver, P. W. Atkins, and C. H. Langford, Inorganic Chemistry, 2nd Ed., ELBS ,1994.

5. S. H. Pine, Organic Chemistry, McGraw-Hill, 5th Ed., 1987

 

References:

1. I. A. Levine, Physical Chemistry, 4th Ed., McGraw-Hill, 1995.

2. I. A. Levine, Quantum Chemistry, EE Ed., prentice Hall, 1994.

3. G. M. Barrow, Introduction to Molecular Spectroscopy, International Edition, McGraw-Hill, 1962

4. J. E. Huheey, E. A. Keiter and R. L. Keiter, Inorganic Chemistry: Principle, structure and reactivity, 4th Ed., Harper Collins, 1993

5. L. G. Wade (Jr.), Organic Chemistry, Prentice Hall, 1987.

 

 

 

CS 101             Introduction to Computing                  (3-0-0-6)

 

Introduction: The von Neumann architecture, machine language, assembly language, high level programming languages, compiler, interpreter, loader, linker, text editors, operating systems, flowchart; Basic features of programming (Using C): data types, variables, operators,  expressions, statements, control structures, functions; Advanced programming features: arrays and pointers, recursion, records (structures), memory management, files, input/output, standard library functions, programming tools, testing and debugging; Fundamental operations on data: insert, delete, search, traverse and modify; Fundamental data structures: arrays, stacks, queues, linked lists; Searching and sorting: linear search, binary search, insertion-sort, bubble-sort, selection-sort, radix-sort, counting-sort; Introduction to object-oriented programming

 

Texts:

 

1.  A Kelly and I Pohl, A Book on C, 4th Ed., Pearson Education, 1999.

2.  A M Tenenbaum, Y Langsam and M J Augenstein, Data Structures Using C, Prentice Hall India, 1996.

 

References:

 

1. H Schildt, C: The Complete Reference, 4th Ed., Tata Mcgraw Hill, 2000

2. B Kernighan and D Ritchie, The C Programming Language, 4th Ed., Prentice Hall of India, 1988.

 

CS 110                         Computing Laboratory             (0-0-3-3)

 

Programming Laboratory will be set in consonance with the material covered in CS101. This will include assignments in a programming language like C.

 

References:

 

1.     B. Gottfried and J. Chhabra,  Programming With C,  Tata Mcgraw Hill, 2005

 

MA 102       Mathematics - II           (3-1-0-8)

 

Vector functions of one variable – continuity and differentiability; 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, moments of inertia, change of variables; vector fields, line and surface integrals; Green’s, Gauss’ and Stokes’ theorems and their applications.

 

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.        G. B. Thomas (Jr.) and R. L. Finney, Calculus and Analytic Geometry, 9th Ed., Pearson Education India, 1996.

2.        S. L. Ross, Differential Equations, 3rd Ed., Wiley India, 1984. 

References:

1.      T. M. Apostol, Calculus - Vol.2, 2nd Ed., Wiley India, 2003.

2.      W. E. Boyce and R. C. DiPrima, Elementary Differential Equations and Boundary Value Problems, 9th Ed., Wiley India, 2009.

3.      E. A. Coddington, An Introduction to Ordinary Differential Equations, Prentice Hall India, 1995.

4.      E. L. Ince, Ordinary Differential Equations, Dover Publications, 1958.

 

ME 101             Engineering Mechanics                        (3-1-0-8)

 

Basic principles: Equivalent force system; Equations of equilibrium; Free body diagram; Reaction; Static indeterminacy. Structures: Difference between trusses, frames and beams, Assumptions followed in the analysis of structures; 2D truss; Method of joints; Method of section;  Frame; Simple beam;  types of loading and supports;  Shear Force and bending Moment diagram in beams; Relation among load, shear force and bending moment. Friction: Dry friction; Description and applications of friction in wedges, thrust bearing (disk friction), belt, screw, journal bearing (Axle friction); Rolling resistance. Virtual work and Energy method: Virtual Displacement; Principle of virtual work; Applications of virtual work principle to machines; Mechanical efficiency; Work of a force/couple (springs etc.); Potential energy and equilibrium; stability. Center of Gravity and Moment of Inertia: First and second moment of area; Radius of gyration;  Parallel axis theorem;  Product of inertia, Rotation of axes and principal moment of inertia;  Moment of inertia of simple and composite bodies. Mass moment of inertia. Kinematics of Particles: Rectilinear motion; Curvilinear motion; Use of Cartesian, polar and spherical coordinate system; Relative and constrained motion; Space curvilinear motion. Kinetics of Particles: Force, mass and acceleration; Work and energy; Impulse and momentum; Impact problems; System of particles. Kinematics and Kinetics of Rigid Bodies: Translation; Fixed axis rotational;  General plane motion; Coriolis acceleration;  Work-energy;  Power;  Potential energy;  Impulse-momentum and associated conservation principles;  Euler equations of motion and its application.

 

Texts

1. I. H. Shames, Engineering Mechanics: Statics and Dynamics, 4th Ed., PHI, 2002.

2. F. P. Beer and E. R. Johnston, Vector Mechanics for Engineers, Vol I - Statics, Vol II – Dynamics, 3rd Ed., Tata McGraw Hill, 2000.

 

 

References

1. J. L. Meriam and L. G. Kraige, Engineering Mechanics, Vol I – Statics, Vol II – Dynamics, 5th Ed., John  Wiley, 2002.

2. R. C. Hibbler, Engineering Mechanics, Vols. I and II, Pearson Press, 2002.

 

 

PH 102             Physics - II                   (2-1-0-6)

 

Vector Calculus: Gradient, Divergence and Curl, Line, Surface, and Volume integrals, Gauss's divergence theorem and Stokes' theorem in Cartesian, Spherical polar, and Cylindrical polar coordinates, Dirac Delta function.

 

Electrostatics: Gauss's law and its applications, Divergence and Curl of Electrostatic fields, Electrostatic Potential, Boundary conditions, Work and Energy, Conductors, Capacitors, Laplace's equation, Method of images, Boundary value problems in Cartesian Coordinate Systems, Dielectrics, Polarization, Bound Charges, Electric displacement, Boundary conditions in dielectrics, Energy in dielectrics, Forces on dielectrics.

 

Magnetostatics: Lorentz force, Biot-Savart and Ampere's laws and their applications, Divergence and Curl of Magnetostatic fields, Magnetic vector Potential, Force and torque on a magnetic dipole, Magnetic materials, Magnetization, Bound currents, Boundary conditions.

 

Electrodynamics: Ohm's law, Motional EMF, Faraday's law, Lenz's law, Self and Mutual inductance, Energy stored in magnetic field, Maxwell's equations, Continuity Equation, Poynting Theorem, Wave solution of Maxwell Equations.

 

Electromagnetic waves: Polarization, reflection & transmission at oblique incidences.

 

Texts:

  1. D. J. Griffiths, Introduction to Electrodynamics, 3rd Ed., Prentice-Hall of India, 2005.
  2. A.K.Ghatak, Optics, Tata Mcgraw Hill, 2007.

 

References:

  1. N. Ida, Engineering Electromagnetics, Springer, 2005.
  2. M. N. O. Sadiku, Elements of Electromagnetics, Oxford, 2006.
  3. R. P. Feynman, R. B. Leighton and M. Sands, The Feynman Lectures on Physics, Vol.II, Norosa Publishing House, 1998.
  4. I. S. Grant and W. R. Phillips, Electromagnetism, John Wiley, 1990.

 

 

EE 102 Basic Electronics Laboratory               (0-0-3-3)

 

Experiments using diodes and bipolar junction transistor (BJT): design and analysis of half -wave and full-wave rectifiers, clipping circuits and Zener regulators, BJT characteristics and BJT amplifiers; experiments using operational amplifiers (op-amps): summing amplifier, comparator, precision rectifier, astable and monostable multivibrators and oscillators; experiments using logic gates: combinational circuits such as staircase switch, majority detector, equality detector, multiplexer and demultiplexer; experiments using flip-flops: sequential circuits such as non-overlapping pulse generator, ripple counter, synchronous counter, pulse counter and numerical display.

References:

 

  1. A. P. Malvino, Electronic Principles, Tata McGraw-Hill, New Delhi, 1993.
  2. R. A. Gayakwad, Op-Amps and Linear Integrated Circuits, PHI, New Delhi,  2002.

3.     R.J. Tocci, Digital Systems, 6th Ed., 2001.

 

MA 201           Mathematics - III                                                          (3-1-0-8)

 

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 & 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 equation, 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.

4.     R. Haberman, Elementary Applied Partial Differential equations with Fourier Series and Boundary Value Problem, 4th Ed., Prentice Hall, 1998.

 

 

MA 221       Discrete Mathematics   (4-0-0-8)

Set theory – sets, relations, functions, countability; Logic – formulae, interpretations, methods of proof, soundness and completeness in propositional and predicate logic; Number theory – division algorithm, Euclid's algorithm, fundamental theorem of arithmetic, Chinese remainder theorem, special numbers like Catalan, Fibonacci, harmonic and Stirling; Combinatorics – permutations, combinations, partitions,  recurrences, generating functions; Graph Theory – paths, connectivity, subgraphs, isomorphism, trees, complete graphs, bipartite graphs, matchings, colourability, planarity, digraphs; Algebraic Structures –  semigroups, groups, subgroups, homomorphisms, rings, integral domains, fields, lattices and Boolean algebras.

Texts:

1.     C. L. Liu, Elements of Discrete Mathematics, 2nd Ed., Tata McGraw-Hill, 2000.

2.     R. C. Penner, Discrete Mathematics: Proof Techniques and Mathematical Structures, World Scientific, 1999.

References:

1.     R. L. Graham, D. E. Knuth, and O. Patashnik, Concrete Mathematics, 2nd Ed., Addison-Wesley, 1994.

2.     K. H. Rosen, Discrete Mathematics & its Applications, 6th Ed., Tata McGraw-Hill, 2007.

3.     J. L. Hein, Discrete Structures, Logic, and Computability, 3rd Ed., Jones and Bartlett, 2010.

4.     N. Deo, Graph Theory, Prentice Hall of India, 1974.

5.     S. Lipschutz and M. L. Lipson, Schaum's Outline of Theory and Problems of Discrete Mathematics, 2nd Ed., Tata McGraw-Hill, 1999.

6.     J.  P. Tremblay and R. P. Manohar, Discrete Mathematics with Applications to Computer Science, Tata McGraw-Hill, 1997.

 

 

MA 222             Modern Algebra            (3-0-0-6)

 

 

Formal properties of integers, equivalence relations, congruences, rings, homomorphisms, ideals, integral domains, fields; Groups, homomorphisms, subgroups, cosets, Lagrange’s theorem , normal subgroups, quotient groups, permutation groups; Groups actions, orbits, stabilizers, Cayley’s theorem, conjugacy, class equation, Sylow’s theorems and applications; Principal ideal domains, Euclidean domains, unique factorization domains, polynomial rings; Characteristic of a field, field extensions, algebraic extensions, separable extensions, finite fields, algebraically closed field, algebraic closure of a field.

 

Texts:

1.     N. H. McCoy and G. J. Janusz, Introduction to Abstract Algebra, 6th Ed., Elsevier, 2005.

2.     J. A. Gallian, Contemporary Abstract Algebra, 4th Ed., Narosa, 1998.

 

References:

 

1. I. N. Herstein, Topics in Algebra, Wiley, 2004.

2. J. B. Fraleigh, A First Course in Abstract Algebra, Addison Wesley, 2002.

 

 

MA 225       Probability Theory and Random Processes    (3-1-0-8)

Axiomatic construction of the theory of probability, independence, conditional probability, and basic formulae, random variables, probability distributions, functions of  random variables; Standard univariate discrete and continuous distributions and their properties, mathematical expectations, moments, moment generating function, 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 theorems.

 

Definition and classification of random processes, discrete-time Markov chains, Poisson process, continuous-time Markov chains, renewal and semi-Markov processes, stationary processes, Gaussian process, Brownian motion, filtrations and martingales, stopping times and optimal stopping.

 

Texts:

1.     P. G. Hoel, S. C. Port and C. J. Stone, Introduction to Probability Theory, Universal Book Stall, 2000.

2.     J. Medhi, Stochastic Processes, 3rd Ed., New Age International, 2009.

3.     S. Ross, A First Course in Probability, 6th Ed., Pearson Education India, 2002.

 

References:

1.     G. R. Grimmett and D. R. Stirzaker, Probability and Random Processes, Oxford University Press, 2001.

2.     W. Feller, An Introduction to Probability Theory and its Applications, Vol. 1, 3rd Ed., Wiley, 1968.

3.     K. S. Trivedi, Probability and Statistics with Reliability, Queuing, and Computer Science Applications, Wiley India, 2008.

4.     S.M. Ross, Stochastic Processes, 2nd Ed., Wiley, 1996.

5.     C. M. Grinstead and J. L. Snell, Introduction to Probability, 2nd Ed., Universities Press India, 2009.

 

 

MA 224                       Real Analysis          (3-0-0-6)

 

 

Metrics and norms – metric spaces, normed vector spaces, convergence in metric spaces, completeness; 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, 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.

 

 

MA 226       Monte Carlo Simulation               (0-1-2-4)

 

Prerequisites: MA 225 or equivalent

 

Principles of Monte Carlo, generation of random numbers from a uniform distribution: linear congruential generators and its variations, inverse transform and acceptance-rejection methods of transformation of uniform deviates, simulation of univariate and multivariate normally distributed random variables: Box-Muller and Marsaglia methods, variance reduction techniques, generation of Brownian sample paths, quasi-Monte Carlo: Low discrepancy sequences.

Texts:

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

2.     R. U. Seydel, Tools for Computational Finance, 4th Ed., Springer, 2009.

 

MA 252       Data Structures And Algorithms         (3-0-0-6)

Pre-requisite: MA 221 or equivalent.

Asymtotic notation; Sorting – merge sort, heap sort, priortiy queue, quick sort, sorting in linear time, order statistics; Data structures – heap, hash tables, binary search tree, balanced trees (red-black tree, AVL tree); Algorithm design techniques – divide and conquer, dynamic programming, greedy algorithm, amortized analysis; Elementary graph algorithms, minimum spanning tree, shortest path algorithms.

 

Text:

1.     T. H. Cormen, C. E. Leiserson, R. L. Rivest and C. Stein, Introduction to Algorithms, MIT Press, 2001.

 

References:

 

1. M. T. Goodrich and R. Tamassia, Data Structures and Algorithms in Java, Wiley, 2006.

2. A. V. Aho and J. E. Hopcroft, Data Structures and Algorithms, Addison-Wesley, 1983.

3. S. Sahni, Data Structures, Algorithms and Applications in C++, 2nd Ed., Universities Press, 2005.

 

MA 253       Data Structures Lab with Object-Oriented Programming (0-1-2-4)

 

 

The tutorials will be based on object-oriented programming concepts such as classes, objects, methods, interfaces, packages, inheritance, encapsulation, and polymorphism. Programming laboratory will be set in consonance with the material covered in MA 252. This will include assignments in a programming language like C++ in GNU Linux environment.

 

Reference:

1.     T. Budd, An Introduction to Object-Oriented Programming, Addison-Wesley, 2002.

 

 

MA 271       Financial Engineering - I            (3-0-0-6)

 

Prerequisites: 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 bonds pricing, yield, duration and convexity, term structure of interest rates, spot and forward rates;  Risky assets – risk-reward analysis, mean variance portfolio optimization, Markowitz model and efficient frontier, CAPM and APT; Discrete time market models – assumptions, portfolios and trading strategies, replicating portfolios, No-arbitrage principle; Derivative securities – forward and futures contracts, hedging strategies using futures, pricing of forward and futures contracts, interest rate futures, swaps; General properties of options, trading strategies involving options; Binomial model, risk neutral probabilities, martingales, valuation of European contingent claims, Cox-Ross-Rubinstein (CRR) formula, American options in binomial model, Black-Scholes formula derived as a continuous-time limit; Options on stock indices, currencies and futures, overview of exotic options.

 

Texts:

 

1.     M. Capinski and T. Zastawniak, Mathematics for Finance: An Introduction to Financial Engineering, 2nd Ed., Springer, 2010.

2.     J. C. Hull, Options, Futures and Other Derivatives, 8th Ed., Pearson India/Prentice Hall, 2011.

References:

 

1.     J. Cvitanic and F. Zapatero, Introduction to the Economics and Mathematics of Financial Markets, Prentice-Hall of India, 2007.

2.     S. Roman, Introduction to the Mathematics of Finance: From Risk Management to Options Pricing, Springer India, 2004.

3.     S. R. Pliska, Introduction to Mathematical Finance: Discrete Time Models, Blackwell, 1997.

4.     S. N. Neftci, Principles of Financial Engineering, 2nd ed., Academic Press/Elsevier India, 2009.

 

MA 322       Scientific Computing                (3-0-2-8)

 

 

Errors; Iterative methods for nonlinear equations; Polynomial interpolation, 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.

 

 

MA 372       Stochastic Calculus for Finance          (3-0-0-6)

 

Prerequisites: MA 224 plus MA 271 or equivalent.

 

General probability spaces, filtrations, conditional expectations, martingales and stopping times, Markov processes; Brownian motion and its properties; Itô’s integral and its extension to wider classes of integrands, isometry and martingale properties of Itô’s integral, Itô processes, Itô-Doeblin formula; Derivation of the Black-Scholes-Merton differential equation, Black-Scholes-Merton formula, the Greeks, put-call parity, multi-variable stochastic calculus; Risk-neutral valuation – risk-neutral measure, Girsanov's theorem for change of measure, martingale representation theorems, representation of Brownian martingales, the fundamental theorems of asset pricing; Stochastic differential equations, existence and uniqueness of solutions, Feynman-Kac formula and its applications.

 

Texts:

1.     S. Shreve, Stochastic Calculus for Finance, Vol. 2, Springer India, 2004.

2.     M. Baxter and A. Rennie, Financial Calculus, Cambridge University Press, 1996.

References:

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

2.             A. Etheridge, A Course in Financial Calculus, Cambridge University Press, 2003.

3.             J. M. Steele, Stochastic Calculus and Financial Applications, Springer, 2001

4.             T. Bjork, Arbitrage theory in Continuous Time, Oxford University Press, 1999.

5.             R. J. Elliott and P. E. Kopp, Mathematics of Financial Markets, Springer, 1999.

6.             D. Lamberton and B. Lapeyre, Introduction to Stochastic Calculus Applied to Finance, Chapmans & Hall/CRC, 2000.

 

 

MA 321   Optimization             (3-0-0-6)

 

Classification and general theory of optimization; Linear programming (LP): formulation and geometric ideas, simplex and revised simplex methods, duality and sensitivity, interior-point methods for LP problems, transportation, assignment, and integer programming problems; Nonlinear optimization, method of Lagrange multipliers, Karush-Kuhn-Tucker theory, numerical methods for nonlinear optimization, convex optimization, quadratic optimization; Dynamic programming; Optimization models and tools in finance.

 

Texts:

 

  1. D. G. Luenberger and Y. Ye, Linear and Nonlinear Programming, 3rd Ed., Springer India, 2008.
  2. N. S. Kambo, Mathematical Programming Techniques, East-West Press, 1997.

 

 

References:

 

  1. E. K. P. Chong and S. H. Zak, An Introduction to Optimization, 2nd Ed., Wiley India, 2001.
  2. M. S. Bazarra, H. D. Sherali and C. M. Shetty, Nonlinear Programming Theory and Algorithms, 3rd Ed., Wiley India, 2006.
  3. S. A. Zenios (ed.), Financial Optimization, Cambridge University Press, 2002.
  4. K. G. Murty, Linear Programming, Wiley, 1983.
  5. D. Gale, The Theory of Linear Economic Models, The University of Chicago Press, 1989.

 

 

MA 351 Formal Languages and Automata Theory        (3-0-0-6)

 

Prerequisite: MA 221 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; Chomsky hierarchy; Decision questions on languages.

 

Texts:

1. J. E. Hopcroft and J. D. Ullman, Introduction to Automata Theory, Languages and Computation, Narosa, 1979.

 

References:

1.M. Sipser, Introduction to the Theory of Computation, Thomson, 2004.  

2.H. R. Lewis and C. H. Papadimitriou, Elements of the Theory of Computation, Pearson Education Asia, 2001.

3.D. C. Kozen, Automata and Computability, Springer-Verlag, 1997.

 

 

MA 373       Financial Engineering - II                 (3 0 0 6)

Prerequisites: MA 372 or equivalent.

Continuous time financial market models, Black-Scholes-Merton model, Black-Scholes PDE and formulas, risk-neutral valuation, change of numeraire, pricing and hedging of contingent claims, Greeks, implied volatility, volatility smile; Options on futures, European, American and Exotic options; Incomplete markets, market models with stochastic volatility, pricing and hedging in incomplete markets; Bond markets, term-structures of interest rates, bond pricing; Short rate models, martingale models for short rate (Vasicek, Ho-Lee, Cox-Ingersoll-Ross and Hull-White models), multifactor models; Forward rate models, Heath-Jarrow-Morton framework, pricing and hedging under short rate and forward rate models, swaps and caps; LIBOR and swap market models, caps, swaps, swaptions, calibration and simulation.

 

Texts:

 

  1. T. Bjork, Arbitrage Theory in Continuous Time, 3rd Ed., Oxford University Press, 2003.
  2. J. C. Hull, Options, Futures and Other Derivatives, 8th Ed., Pearson India/Prentice Hall, 2011.

 

References:

 

  1. S. Shreve, Stochastic Calculus for Finance, Vol. 2, Springer India, 2004.
  2. R. A. Dana and M. Jeanblanc, Financial Markets in Continuous Time, Springer 2001.
  3. D. Brigo and F. Mercurio, Interest rate models: Theory and Practice, Springer, 2006.
  4. N. H. Bingham and R. Kiesel, Risk-Neutral Valuation, 2nd Ed., Springer, 2004.
  5. J. Cvitanic and F. Zapatero, Introduction to the Economics and Mathematics of Financial Markets, Prentice-Hall of India, 2007.
  6. M. Musiela and M. Rutkwoski, Martingale Method in Financial Modelling, 2nd Ed., Springer, 2005.
  7. P. Wilmott, Derivatives: The Theory and Practice of Financial Engineering, Wiley, 1998.

 

 

MA 374       Financial Engineering Lab             (0-0-3-3)

 

This course will focus on implementation of the financial models such as CAPM, binomial models, Black-Scholes model, interest rate models and asset pricing based on above models studied in MA 271 and MA 373. The implementation will be done using S-PLUS/MATLAB/C++.

Texts:

  1. Y. Lyuu, Financial Engineering and Computation, Cambridge University Press, 2002.
  2. P. Glasserman, Monte Carlo Methods in Financial Engineering, Springer, 2004.

References:

  1. D. Higham, Introduction to Financial Option Valuation: Mathematics, Stochastics and Computation, Cambridge University Press, 2004.

 

 

MA 423       Matrix Computations             (3-0-2-8)

 

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.             G. H. Golub and C. F. Van Loan, Matrix Computations, 3rd Ed., John Hopkins University Press, 1996.

2.             J. W. Demmel, Applied Numerical Linear Algebra, SIAM, 1997.

 

 

MA 471       Statistical Analysis of Financial Data           (3-0-2-8)

 

Prerequisites: MA 271 or equivalent.

 

Introduction to statistical packages (R / S-Plus / MATLAB / SAS) and data analysis – financial data, exploratory data analysis tools, kernel density estimation; Basic estimation and testing; Random number generator and Monte Carlo samples; Financial time series analysis – AR, MA, ARMA. ARIMA, ARCH and GARCH models, identification, inference, forecasting, stochastic volatility time series models for term structure of interest rates; Linear regression – least squares estimation, inference, model checking;  Multivariate data analysis – multivariate normal and inference, Copulae and random simulation, examples of copulae family, fitting Copulas, Monte Carlo simulation with Copulas, dimension reduction techniques, principal component analysis;  Risk management – riskmetrics, quantiles, Q-Q plots, quantile estimation with Cornish-Fisher expansion, VaR, expected short fall, time-to-default modeling, extreme value theory (generalized extreme value (GEV), generalized Pareto distribution (GPD); Block Maxima, and Hill methods).

 

Texts:

1.             R. A. Carmona, Statistical Analysis of Financial Data in S-Plus, Springer India, 2004.

2.             D. Ruppert, Statistics and Finance: An Introduction, Springer India, 2009

 

References:

1.             E. Zivot and J. Wang, Modeling Financial Time Series with S-plus, 2nd Ed., Springer, 2006.

2.             P. J. Brockwell and R. A. Davis, Time Series: Theory and Methods, 2nd Ed., Springer, 2009.

3.             V. K. Rohatgi and A. K. Md. E. Saleh, An Introduction to Probability and Statistics, 2nd Ed., Wiley India, 2009.

4.             T. W. Anderson, An Introduction to Multivariate Statistical Analysis, 3rd Ed., Wiley India, 2009.

 

 

MA 453       Theory of Computation              (3-0-0-6)

 

Prerequisite: MA 351 or equivalent.

 

Models of computation – Turing machine, RAM, µ-recursive function, grammars; Undecidability  Rice's theorem, Post correspondence problem, logical theories; Complexity classes – P, NP,  coNP, EXP, PSPACE, L, NL, ATIME, BPP, RP, ZPP, IP.

 

Texts:

1.     M. Sipser, Introduction to the Theory of Computation, Thomson, 2004.

2.     H. R. Lewis and C. H. Papadimitriou, Elements of the Theory of Computation, PHI, 1981.

 

References:

  1. J. E. Hopcroft and J. D. Ullman, Introduction to Automata Theory, Languages and Computation, Narosa, 1979.
  2. S. Arora, and B. Barak, Computational Complexity: A Modern Approach, Cambridge University Press, 2009.
  3. C. H. Papadimitriou, Computational Complexity, Addison-Wesley Publishing Company, 1994.
  4. D. C. Kozen, Theory of Computation, Springer, 2006.
  5. D. S. Garey and G. Johnson, Computers and Intractability: A Guide to the Theory of NP-Completeness, Freeman, New York, 1979.

 

MA 473       Computational Finance                  (3-0-2-8)

 

Prerequisites: MA 373 or equivalent.

 

 

Review of financial models for option pricing and interest rate modeling, Black-Scholes PDE; Finite difference methods, Crank-Nicolson method, American option as free boundary problems, computation of American options, pricing of exotic options, upwind scheme and other methods, Lax-Wendroff method; Monte-Carlo simulation, generating sample paths, discretization of SDE, Monte-Carlo for option valuation and Greeks, Monte-Carlo for American and exotic options; Term-structure modeling, short rate models, bond prices, multifactor models; Forward rate models, implementation of Heath-Jarrow-Morton model; LIBOR market model, Volatility structure and Calibration.

Texts:

  1. P. Glasserman, Monte Carlo Methods in Financial Engineering, Springer, 2004.
  2. R. U. Seydel, Tools for Computational Finance, 4th Ed., Springer, 2009.

References:

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