CH 101 Chemistry (3108)
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: LCAOMO; 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 C_{v} and C_{p}; 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 regiochemistry 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 (UVvis, IR, NMR); Solid phase synthesis and combinatorial
chemistry; Green chemical processes.
Texts:
1. P. W. Atkins, Physical Chemistry, 5^{th} Ed., ELBS, 1994.
2. C.
N. Banwell, and E. M. McCash,
Fundamentals of Molecular Spectroscopy,
4^{th} Ed., Tata McGrawHill, 1962.
3. F.
A. Cotton, and G. Wilkinson, Advanced
Inorganic Chemistry, 3^{rd} Ed., Wiley Eastern Ltd., New Delhi,
1972, reprint in 1988.
4. D. J. Shriver, P. W. Atkins, and C. H.
Langford, Inorganic Chemistry, 2^{nd}
Ed., ELBS ,1994.
5. S. H. Pine, Organic Chemistry, McGrawHill, 5^{th} Ed., 1987
References:
1. I. A. Levine, Physical Chemistry, 4^{th} Ed., McGrawHill, 1995.
2. I. A. Levine, Quantum Chemistry, EE Ed., prentice Hall, 1994.
3. G. M. Barrow, Introduction to Molecular Spectroscopy, International Edition, McGrawHill,
1962
4. J.
E. Huheey, E. A. Keiter
and R. L. Keiter, Inorganic Chemistry: Principle, structure and reactivity, 4^{th}
Ed., Harper Collins, 1993
5. L. G. Wade (Jr.), Organic Chemistry, Prentice Hall, 1987.

CS 101
Introduction to Computing (3006)
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, insertionsort, bubblesort, selectionsort, radixsort,
countingsort; Introduction to objectoriented programming
Texts:
1. A Kelly and I Pohl, A Book on C, 4^{th} 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, 4^{th} Ed., Tata Mcgraw
Hill, 2000
2. B Kernighan and
D Ritchie, The C Programming Language,
4^{th} Ed., Prentice Hall of India, 1988.

CS 110 Computing
Laboratory (0033)
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
(3108)
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; higherorder 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 firstorder equations,
phase plane, critical points, stability.
Texts:
1.
G. B. Thomas (Jr.) and R. L. Finney, Calculus and Analytic Geometry, 9^{th}
Ed., Pearson Education India, 1996.
2.
S. L. Ross, Differential Equations, 3^{rd} Ed., Wiley India,
1984.
References:
1. T.
M. Apostol, Calculus
 Vol.2, 2^{nd} Ed., Wiley India, 2003.
2. W.
E. Boyce and R. C. DiPrima, Elementary Differential Equations and Boundary Value Problems, 9^{th}
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 (3108)
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; Workenergy; Power; Potential energy; Impulsemomentum and associated
conservation principles; Euler
equations of motion and its application.
Texts
1. I. H. Shames, Engineering Mechanics:
Statics and Dynamics, 4^{th} Ed., PHI, 2002.
2.
F. P. Beer and E. R. Johnston, Vector Mechanics for Engineers, Vol I  Statics, Vol
II – Dynamics, 3^{rd} Ed., Tata McGraw Hill, 2000.
References
1. J.
L. Meriam and L. G. Kraige,
Engineering Mechanics, Vol I –
Statics, Vol II – Dynamics, 5^{th}
Ed., John Wiley, 2002.
2. R. C. Hibbler,
Engineering Mechanics, Vols. I
and II, Pearson Press, 2002.
PH 102 Physics
 II
(2106)
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, BiotSavart 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:
 D. J.
Griffiths, Introduction to Electrodynamics,
3^{rd} Ed., PrenticeHall of India, 2005.
 A.K.Ghatak, Optics, Tata Mcgraw
Hill, 2007.
References:
 N. Ida, Engineering Electromagnetics,
Springer, 2005.
 M. N. O. Sadiku, Elements
of Electromagnetics, Oxford, 2006.
 R. P. Feynman,
R. B. Leighton and M. Sands, The Feynman
Lectures on Physics, Vol.II, Norosa Publishing House, 1998.
 I. S. Grant
and W. R. Phillips, Electromagnetism,
John Wiley, 1990.
EE 102 Basic Electronics Laboratory (0033)
Experiments using diodes
and bipolar junction transistor (BJT): design and analysis of half wave and
fullwave rectifiers, clipping circuits and Zener
regulators, BJT characteristics and BJT amplifiers; experiments using
operational amplifiers (opamps): 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 flipflops: sequential circuits such as nonoverlapping
pulse generator, ripple counter, synchronous counter, pulse counter and
numerical display.
References:
 A. P. Malvino, Electronic
Principles, Tata McGrawHill, New Delhi, 1993.
 R. A. Gayakwad, OpAmps
and Linear Integrated Circuits, PHI, New Delhi, 2002.
3.
R.J. Tocci, Digital Systems, 6^{th} Ed.,
2001.

MA 201 Mathematics
 III (3108)
Complex numbers and elementary properties.
Complex functions  limits, continuity and differentiation. CauchyRiemann
equations. Analytic and harmonic functions. Elementary functions.
Antiderivatives and path (contour) integrals. CauchyGoursat
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 secondorder 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 nonrectangular 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, 7^{th} Ed., McGraw Hill, 2004.
2.
I. N. Sneddon, Elements of Partial Differential Equations,
McGraw Hill, 1957.
3.
S. L. Ross, Differential Equations, 3^{rd}
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, 3^{rd} 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, 4^{th}
Ed., Prentice Hall, 1998.

MA 221 Discrete
Mathematics (4008)
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, 2^{nd} Ed., Tata
McGrawHill, 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, 2^{nd}
Ed., AddisonWesley, 1994.
2. K.
H. Rosen, Discrete Mathematics &
its Applications, 6^{th} Ed., Tata McGrawHill, 2007.
3. J.
L. Hein, Discrete Structures, Logic,
and Computability, 3^{rd} 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, 2^{nd}
Ed., Tata McGrawHill, 1999.
6. J. P. Tremblay and R. P. Manohar, Discrete
Mathematics with Applications to Computer Science, Tata McGrawHill,
1997.

MA 222 Modern
Algebra
(3006)
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, 6^{th} Ed., Elsevier,
2005.
2. J.
A. Gallian, Contemporary
Abstract Algebra, 4^{th} 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
(3108)
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, discretetime Markov chains, Poisson process,
continuoustime Markov chains, renewal and semiMarkov 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, 3^{rd} Ed., New
Age International, 2009.
3. S. Ross, A First Course in Probability, 6^{th} 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, 3^{rd}
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, 2^{nd} Ed., Wiley, 1996.
5. C. M. Grinstead and J. L. Snell, Introduction to Probability, 2^{nd}
Ed., Universities Press India, 2009.

MA 224 Real
Analysis
(3006)
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 –
sigmaalgebra of sets, measure space, Lebesgue
measure, measurable functions, Lebesgue integral,
dominated convergence theorem, monotone convergence theorem, Lp spaces.
Texts:
1.
J. E. Marsden and M. J. Hoffman, Elementary Classical Analysis, 2^{nd}
Ed., W. H. Freeman, 1993.
2.
M. Capinski
and E. Kopp, Measure, Integral and
Probability, 2^{nd} 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
(0124)
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 acceptancerejection
methods of transformation of uniform deviates, simulation of univariate and multivariate normally distributed random
variables: BoxMuller and Marsaglia methods,
variance reduction techniques, generation of Brownian sample paths,
quasiMonte Carlo: Low discrepancy sequences.
Texts:
1. P.
Glasserman, Monte
Carlo Methods in Financial Engineering, Springer, 2004.
2. R.
U. Seydel, Tools
for Computational Finance, 4^{th} Ed., Springer, 2009.

MA
252 Data
Structures And Algorithms
(3006)
Prerequisite:
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 (redblack 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,
AddisonWesley, 1983.
3.
S. Sahni, Data
Structures, Algorithms and Applications in C++, 2^{nd} Ed.,
Universities Press, 2005.

MA 253 Data Structures Lab with ObjectOriented
Programming (0124)
The tutorials will be based on
objectoriented 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 ObjectOriented
Programming, AddisonWesley, 2002.

MA 271 Financial Engineering  I
(3006)
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 – riskreward
analysis, mean variance portfolio optimization, Markowitz model and efficient
frontier, CAPM and APT; Discrete time market models – assumptions,
portfolios and trading strategies, replicating portfolios, Noarbitrage
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, CoxRossRubinstein
(CRR) formula, American options in binomial model, BlackScholes
formula derived as a continuoustime 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, 2^{nd} Ed., Springer,
2010.
2. J.
C. Hull, Options, Futures and Other
Derivatives, 8^{th} Ed., Pearson India/Prentice Hall, 2011.
References:
1. J.
Cvitanic and F. Zapatero,
Introduction to the Economics and
Mathematics of Financial Markets, PrenticeHall 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,
2^{nd} ed., Academic Press/Elsevier India, 2009.

MA 322 Scientific Computing
(3028)
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, RungeKutta methods, multistep methods,
predictorcorrector 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 CrankNicolson schemes, ADI methods, Lax Wendroff
method, upwind scheme).
Texts:
1. D. Kincaid and W. Cheney, Numerical Analysis: Mathematics of Scientific Computing, 3^{rd}
Ed., AMS, 2002.
2.
G. D. Smith, Numerical Solutions of Partial Differential
Equations, 3^{rd} 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, McGrawHill, 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
(3006)
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, ItôDoeblin
formula; Derivation of the BlackScholesMerton
differential equation, BlackScholesMerton
formula, the Greeks, putcall parity, multivariable stochastic calculus;
Riskneutral valuation – riskneutral 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, FeynmanKac 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 (3006)
Classification
and general theory of optimization; Linear programming (LP): formulation and
geometric ideas, simplex and revised simplex methods, duality and
sensitivity, interiorpoint methods for LP problems, transportation,
assignment, and integer programming problems; Nonlinear optimization, method
of Lagrange multipliers, KarushKuhnTucker theory,
numerical methods for nonlinear optimization, convex optimization, quadratic
optimization; Dynamic programming; Optimization models and tools in finance.
Texts:
 D. G. Luenberger
and Y. Ye, Linear
and Nonlinear Programming, 3^{rd} Ed., Springer India, 2008.
 N. S. Kambo,
Mathematical Programming
Techniques, EastWest Press, 1997.
References:
 E.
K. P. Chong and S. H. Zak, An Introduction
to Optimization, 2^{nd} Ed., Wiley India, 2001.
 M. S. Bazarra,
H. D. Sherali and C. M. Shetty,
Nonlinear Programming Theory and
Algorithms, 3^{rd} Ed., Wiley India, 2006.
 S. A. Zenios
(ed.), Financial Optimization,
Cambridge University Press, 2002.
 K. G. Murty,
Linear Programming, Wiley,
1983.
 D. Gale, The Theory of Linear Economic Models, The University of Chicago
Press, 1989.

MA 351 Formal Languages and Automata Theory
(3006)
Prerequisite: MA 221 or equivalent.
Alphabets, languages,
grammars; Finite automata, regular languages, regular expressions;
Contextfree 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, SpringerVerlag,
1997.

MA 373 Financial
Engineering  II
(3 0 0 6)
Prerequisites: MA 372 or equivalent.
Continuous time financial market models,
BlackScholesMerton model, BlackScholes PDE and formulas, riskneutral 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, termstructures of interest rates, bond pricing; Short rate models,
martingale models for short rate (Vasicek, HoLee,
CoxIngersollRoss and HullWhite models), multifactor models; Forward rate
models, HeathJarrowMorton 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:
 T.
Bjork, Arbitrage
Theory in Continuous Time, 3^{rd} Ed., Oxford University
Press, 2003.
 J.
C. Hull, Options, Futures and
Other Derivatives, 8^{th} Ed., Pearson India/Prentice Hall,
2011.
References:
 S.
Shreve, Stochastic Calculus for
Finance, Vol. 2, Springer
India, 2004.
 R. A. Dana and M. Jeanblanc, Financial
Markets in Continuous Time, Springer 2001.
 D. Brigo and F. Mercurio, Interest rate models: Theory and
Practice, Springer, 2006.
 N. H. Bingham
and R. Kiesel, RiskNeutral Valuation, 2nd Ed., Springer, 2004.
 J. Cvitanic and F. Zapatero, Introduction to the Economics and
Mathematics of Financial Markets, PrenticeHall of India, 2007.
 M. Musiela and M. Rutkwoski, Martingale Method in Financial Modelling, 2^{nd} Ed., Springer, 2005.
 P. Wilmott, Derivatives:
The Theory and Practice of Financial Engineering, Wiley, 1998.

MA 374 Financial Engineering Lab
(0033)
This course will focus on implementation of
the financial models such as CAPM, binomial models, BlackScholes
model, interest rate models and asset pricing based on above models studied
in MA 271 and MA 373. The implementation will be done using
SPLUS/MATLAB/C++.
Texts:
 Y. Lyuu,
Financial Engineering and
Computation, Cambridge University Press, 2002.
 P. Glasserman,
Monte Carlo Methods in Financial
Engineering, Springer, 2004.
References:
 D. Higham,
Introduction to Financial Option
Valuation: Mathematics, Stochastics and
Computation, Cambridge University Press, 2004.

MA 423 Matrix Computations
(3028)
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; GramSchmidt 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,
MoorePenrose inverse; Rank deficient leastsquares problems; Sensitivity
analysis of leastsquares 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; GolubKahan algorithm for computing SVD.
Texts:
1.
D. S. Watkins, Fundamentals
of Matrix Computations, 2^{nd} 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, 3^{rd}
Ed., John Hopkins University Press, 1996.
2.
J. W. Demmel, Applied Numerical
Linear Algebra, SIAM, 1997.

MA 471 Statistical Analysis of Financial
Data
(3028)
Prerequisites: MA
271 or equivalent.
Introduction to
statistical packages (R / SPlus / 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, QQ
plots, quantile estimation with CornishFisher
expansion, VaR, expected short fall,
timetodefault 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 SPlus, 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 Splus,
2^{nd} Ed., Springer, 2006.
2.
P. J. Brockwell and R. A.
Davis, Time Series: Theory and Methods,
2^{nd} Ed., Springer, 2009.
3.
V. K. Rohatgi and A. K. Md.
E. Saleh, An
Introduction to Probability and Statistics, 2^{nd} Ed., Wiley
India, 2009.
4.
T. W. Anderson, An Introduction to
Multivariate Statistical Analysis, 3^{rd} Ed., Wiley India, 2009.

MA 453 Theory of Computation
(3006)
Prerequisite: MA 351 or equivalent.
Models
of computation – Turing machine, RAM, µrecursive 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:
 J. E. Hopcroft and J. D. Ullman,
Introduction to Automata Theory, Languages and Computation, Narosa, 1979.
 S. Arora,
and B. Barak, Computational Complexity: A Modern Approach,
Cambridge University Press, 2009.
 C. H. Papadimitriou, Computational
Complexity, AddisonWesley Publishing Company, 1994.
 D. C. Kozen,
Theory of Computation, Springer, 2006.
 D. S. Garey
and G. Johnson, Computers and Intractability: A Guide to the Theory of
NPCompleteness, Freeman, New York, 1979.

MA 473 Computational Finance
(3028)
Prerequisites: MA
373 or equivalent.
Review of financial models for option pricing
and interest rate modeling, BlackScholes PDE;
Finite difference methods, CrankNicolson method, American option as free
boundary problems, computation of American options, pricing of exotic
options, upwind scheme and other methods, LaxWendroff
method; MonteCarlo simulation, generating sample paths, discretization
of SDE, MonteCarlo for option valuation and Greeks, MonteCarlo for American
and exotic options; Termstructure modeling, short rate models, bond prices,
multifactor models; Forward rate models, implementation of HeathJarrowMorton model; LIBOR market model, Volatility
structure and Calibration.
Texts:
 P. Glasserman,
Monte Carlo Methods in Financial
Engineering, Springer, 2004.
 R. U. Seydel,
Tools for Computational Finance,
4^{th} Ed., Springer, 2009.
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, Cambridge University
Press, 1997.
 Y. Lyuu, Financial
Engineering and Computation, Cambridge University Press, 2002.
