Download cbcs - course outline for 2005-2006

10. SCHOOL OF MATHEMATICS, STATISTICS AND COMPUTER SCIENCE
Mathematics, Statistics and Computer Science together constitute a school with wide scope for interaction aiming at
excellence in fundamental research and applications.
The University of Madras is known for its nurturing the genius in Srinivasa Ramanujan, the great mathematical luminary
whose mathematics is engaging the attention of leading mathematicians even today for its profoundness and applications. The
University department of Mathematics was created in 1927. The Ramanujan Institute of Mathematics, founded by Dr.Rm.Alagappa
Chettiar came into existence in 1957. In 1967, with the assistance from UGC it become a Centre of Advanced Study in Mathematics
merging the two units. This centre is now known as the Ramanujan Institute for Advanced Study in Mathematics (RIASM). The
RIASM offers Masters, M.Phil. and . programmes.
An independent Department of Statistics started functioning in 1941 and became a full fledged department of study and
research from 1975 under the leadership of Prof.K.N.Venkataraman. The department offers Masters, M.Phil and Ph.D.
Programmes. The department also offeres M.Sc. Actuarial Science programme under UGC Innovative programme.
Study of Computer Science in the University began in 1984. An independent department was instituted in 1995. The
Department of Computer Science concentrates research in the areas of Parallel Algorithms, Architectures and Applications, Parallel
Computing, Computational Geometry and it too has a well equipped Computer Laboratory. The department currently offers Master
of Computer Applications and programmes.
Faculty
Dr. P.Thangavel, Ph.D.
-
Chairperson
S. Parvathi, Ph.D.
K. Parthasarathy, Ph.D.
Premalatha
Kumaresan, Ph.D.
M. Loganathan, Ph.D.
V. Thangaraj, Ph.D.
R. Sahadevan, Ph.D.
G.Balasubramanian, Ph.D.
G.P.Yuvaraj, Ph.D.
N.Agarwal Sushama, Ph.D.
-
Director and Head
Professor
-
Professor
Professor
Professor
Professor
Professor
Reader
Lecturer
G.Gopal, Ph.D.
P.Dhanavanthan, Ph.D.
M.R.Srinivasan, Ph.D.
T. Anbupalam, Ph.D.
M.R. Sindhumol
K.M.Sakthivel
-
Professor and Head
Professor
Professor
Lecturer
Lecturer
Lecturer (on contract)
-
Professor and Head
Lecturer
Lecturer
Lecturer
Lecturer
RIAS in Mathematics
Statistics
Computer Science
P.Thangavel, Ph.D.
S.Gopinathan, M.Sc.
P.L. Chitra, M.C.A.
Sornam, M.Sc., M.C.A.
B.Lavanya
1
M.Sc. MATHEMATICS
M.Sc Mathematics (CBCS) 2007 – 2009.
Course Code
Times New
Roman
C001
C002
C003
C004
UOM S 001
C005
C006
C007
C008
UOM S 002
C009
C010
C011
C012
UOM S 003
UOM I 001
C013
C014
C015
UOM S 004
Credit
L
T
P
C
C
C
C
C
E
S
3
3
3
0
2
1
1
1
0
1
0
0
0
4
0
4
4
4
4
3
2
M.Loganathan
G.P.Youvaraj
R.Sahadevan
Guest Faculty
C
C
C
C
E
S
3
3
3
3
2.
1
1
1
1
1
0
0
0
0
0
4
4
4
4
3
2
S.Parvathi
G.P.Youvaraj
Guest Faculty
Faculty Concerned
C
C
C
C
E
E
S
S
3
3
3
3
2
2
1
1
1
1
1
1
0
0
0
0
0
0
4
4
4
4
3
3
2
2
Guest Faculty
Premalatha Kumaresan
V.Thangaraj
R.Sahadevan
C
C
C
E
E
S
3
3
3
2
2
1
1
1
1
1
0
0
0
0
0
4
4
4
3
3
2
K.Parthasarathy
Premalatha Kumaresan
Sushama Agrawal
Title of the Course
SEMESTER I
C/E/S
Linear Algebra
Real Analysis
Ordinary Differential Equations
Computational Mathematical Laboratory– I
Elective
Soft Skill*
SEMESTER II
Algebra
Topology
Partial Differential Equations
Seminar
Elective
Soft Skill*
SEMESTER III
Complex Analysis
Measure & Integration theory
Probability theory
Computational Mathematical Laboratory–II
Elective
Elective
Soft Skill*
Internship**
SEMESTER IV
Advanced Analysis
Differential Geometry
Functional Analysis
Elective
Elective
Soft Skill*
Note: Compulsory Components for Postgraudate Programmes
Core Courses
- 60 Credits minimum
Elective Courses
- 18 Credits minimum
Soft Skill Courses
- 08 Credits minimum
Internship
- 02 Credits
Total
- 88 Credits minimum
Elective Courses Offered by the RIASM
Course
Code
Title of the Course
C/E/
S/
SS
L
2
Faculty
Credits
T
P
C
MSI E001
MSI E002
E
E
2
2
1
1
0
0
3
3
Guest Faculty
Guest Faculty
MSI E003
Discrete Mathematics
Number Theory and
Cryptography
Programming and Soft Computations
E
1
1
1
3
Guest Faculty
MSI E004
Computer Based Numerical Methods
E
1
1
1
3
Guest Faculty
MSI E005
MSI E006
MSI E007
MSI E008
MSI E009
Lie Algebras
Stochastic Processes
Representation Theory of Finite Groups
Graph Theory
Lie Groups of Transformations and
Ordinary Differential Equations
Lie Groups of Transformations and
Partial Differential Equations
Potential Theory in Rn
Linear Lie groups
Banach Algebras and Operator theory
Algebraic Number Theory
Mathematical Theory of Electromagnetic Waves
E
E
E
E
E
2
2
2
2
2
1
1
1
1
1
0
0
0
0
0
3
3
3
3
3
Guest Faculty
V.Thangaraj
S.Parvathi
M.Loganathan
R.Sahadevan
E
2
1
0
3
R.Sahadevan
E
E
E
E
E
2
3
3
2
2
1
0
0
1
1
0
0
0
0
0
3
3
3
3
3
Premalatha Kumaresan
K.Parthasarathy
Agrawal Sushama N.
S.Parvathi
G.P.Youvaraj
SS
SS
SS
SS
SS
SS
SS
SS
SS
SS
0
0
0
0
0
0
0
0
0
0
4
4
4
4
4
4
4
4
4
4
0
0
0
0
0
0
0
0
0
0
4
4
4
4
4
4
4
4
4
4
S.Parvathi
M.Loganathan
V.Thangaraj
N.Agrawal Sushama
Premalatha Kumaresan
K.Parthasarathy
K.Parthasarathy
V.Thangaraj
V.Thangaraj
S.Parvathi
MSI E010
MSI E011
MSI E012
MSI E013
MSI E014
MSI E015
Self-Study Courses
MSI S001
Algebraic Theory of Numbers
MSI S002
Algebraic Topology
MSI S003
Financial Calculus
MSI S004
Fuzzy Analysis
MSI S005
Harmonic Function Theory
MSI S006
Introduction to Fractals
MSI S007
Lie Groups and Lie Algebras
MSI S008
Probability on Abstract Spaces
MSI S009
Quantum Computations
MSI S010
Quantum Groups
P.G.DIPLOMA IN COMPUTATIONAL MATHEMATICS AND STATISTICS.
Paper
I SEMESTER
MSI C076
MSI C077
II SEMESTER
MSI C078
MSI C079
III SEMESTER
MSI C080
MSI C081
IV SEMESTER
MSI C082
MSI C083
Title of the course
L
T
P
C
Discrete Mathematics
Mathematics of Finance and Insurance
3
4
1
1
-
4
5
Computational Mathematics
Introduction to Information Technology + Computational Laboratory –
I
3
2
1
1
1
1
5
4
Computational Statistics
Computer Programming in C and C+++ Computational Laboratory – II
3
2
1
1
1
1
5
4
Game Theory and Strategy
Internet and Java Programming + Computational Laboratory –II
4
2
1
1
1
5
4
3
M.Phil DEGREE PROGRAMME (CBCS) 2006 – 2007
Credits
Course Code
MSI C001
MSI C002
MSI C003
MSI C004
Title of the Course
Algebra
Analysis
Topology and Geometry
Dissertation and
Viva-voce
Core
C
C
C
C
Faculty
L
T
P
C
4
4
4
1
1
1
0
0
0
5
5
5
21
M.Loganathan
Agrawal Sushama
K.Parthasarathy
All Faculty Members.
Masters Courses - Abstract
MSI C001
Linear Algebra
3
1
0
4
M.Loganathan / Guest
Faculty
Pre-requisite: Undergraduate Level Mathematics.
Course Objective:
To lay the foundation for a variety of courses.
Unit I
Review of Vector spaces - Linear Transformations - Representation of Transformations by Matrices- Linear Functionals.Algebra of Polynomials- Determinants – Properties of determinants- Characteristic Polynomials- Characteristic values –
Characteristic vectors – minimal Polynomials.
Unit II
Invariant subspaces
Theorem
- Direct sum Decompositions - Diagonalization of linear operators – Primary Decomposition
Unit III
Cyclic Vectors – Cyclic subspaces – Cyclic Decomposition Theorem- Generalised Cayley- Hamilton Theorem- Rational
form – Jordan Canonical form.
Unit IV
Bilinear forms - positive - definite, symmetric and Hermitian forms – Sylvester’s theorem.
Unit V
Spectral representation of symmetric, Hermitian and normal operators - Applications.
Books for Reference:
Kenneth Hoffman and Ray Kunze, Linear Algebra. Prentice Hall of India Private Ltd. New Delhi 2005.
Michel Artin, Algebra. Prentice Hall of India Private Ltd. New Delhi 1994.
MSI C002
Real Analysis
Pre-requisite: Undergraduate Level Mathematics.
3
Course Objective:
4
1
0
4
G.P.Youvaraj
To provide a systematic development of Riemann – Sticltjes integral and the calculus on Rn
Unit I
Riemann – Stieltjes Integral: Definition and Properties of the Integral – Integration and Differentiation Integration of vector valued functions
Unit II
Sequences and Series of functions : Pointwise Convergence – Uniform Convergence – Weierstrass Approximation
Theorem.
Unit III
Special Functions: Power Series – Exponential and Logarithmic Functions – Trigonometric Functions – Fourier series –
Gamma function.
Unit IV
Functions of Several Variables: Derivatives of a function from Rn to Rm – Chain Rule – Partial Derivatives – Derivatives
of Higher order.
Unit V
Basic Theorems of Differential Calculus: Inverse function Theorem – Implicit function Theorem – Rank Theorem.
Books for Reference:
Text Book: Walter Rudin, Principles of Mathematical Analysis, Third Edition, McGraw Hill 1976.
MSI C003
Ordinary Differential Equations
Pre-requisite: Undergraduate Level Mathematics.
3
1
0
4
R.Sahadevan
Course objective:
To learn mathematical methods to solve higher ordinary and partial differential equations and apply to dynamical
problems of practical interest.
Unit I:
HIGHER ORDER LINEAR EQUATIONS
General Theory of nth order Linear Equations - Homogeneous equations with Constant Coefficients - The Method of
Undetermined Coefficients - The Method of Variation of Parameters
Unit II :
POWER SERIES SOLUTIONS AND SPECIAL FUNCTIONS
Series Solutions of First Order Equations - Second Order Linear Equations – Ordinary Points - Regular singular Points Gauss's Hyper-geometric Equation
Unit III :
SOME SPECIAL FUNCTIONS OF MATHEMATICAL PHYSICS AND EXISTENCE AND UNIQUENESS THEOREM
Legedre Differential Equation: Solutions and its Properties - Bessel's Differential equations: Solutions and its Properties
- The Method of Successive approximations - Existence Uniqueness Theorem.
Unit IV :
NONLINEAR DIFFERENTIAL EQUATIONS AND STABILITY
The Phase plane- Linear systems – Autonomous systems and stability – Almost Linear systems- Competing species –
Predator Prey equations – Liapunov method
5
MSI C004
Computational Mathematical Laboratory – I
0
0
2
2
Guest Faculty
Pre – requisite:
Calculus, Linear Algebra, basic knowledge of Differential Equations and some knowledge of Programming
Language.
Course Objective:
This is the first of two-semester Computational Mathematical Laboratory sequence (MSI 1008 to MSI 2008). In this
sequence, we will emphasize the fundamentals of numerical computation and analysis: to explain how, why, and
when numerical methods can be expected to work along with soft computational techniques using
MAPLE/MATHEMATICA.
Section I : Mathematical Software : MAPLE/MATHEMATICA
Plotting Curves-Composition of functions, inverses-Sequences and series (finite and infinite sum)-Slope of a line, a secant, a tangentEquations of tangents-Limit and continuity-2-D and 3-D graphs-Symbolic - Differentiation and Symbolic Integration- Conversion of
coordinates, Areas in Polar coordinates- Symbolic manipulation on matrices - Solution to equations - Solution to Differential equations.
Section II : Programming Exercises using C++
1. Non-Linear Equations
1.1 Bisection Method
1.2 Regula-falsi Method
1.3 Newton-Raphson Method
1.4 Secant Method
1.5 Fixed Point Iteration
2.
System of linear Equations
2.1 Gauss Elimination
2.2 Gauss-Seidel Method
3.
Interpolation
3.1 Lagrange’s Interpolation Formula
3.2 Newton Interpolation Formula
4.
Numerical Differentiation
4.1 Differentiation using limits
4.2 Differentiation using Extrapolation
5.
Numerical Integration
5.1 Composite Tapezoidal Rule
5.2 Composite Simpson’s 1/3 Rule
6.
Numerical Solution to Differential Equations
6.1 Euler’s Method
6.2 Taylor’s Method of order 4
6.3 Runge-Kutta Method of order 4
6.4 Milne-Simpson Method
MSI C005
Algebra
Pre-requisite: Undergraduate Level Mathematics.
Course Objective:
3
1
0
4
S.Parvathi
To lead the aspirant to modern aspects of Algebra.
Unit I
Review of Basic Group theory: Groups - homomorphisms, isomorphisms, - cosets, quotient groups .
Symmetry: Group of motions of the plane - finite groups of motions - Solvable groups- nilpotent groups.
6
Unit II
Group actions- Counting formula - symmetric groups - Sylow theorems.
Unit III
Field theory – Algebraic and transcendental elements – degree of a field extension – adjunction of roots – algebraically
closed fields - splitting fields.
Unit -IV
Normal extension – Galois Correspondence.
Unit V
Galois theory- Galois Fields - Applications of Galois theory – Classical groups.
MSI C006
Topology
3
1
0
4
Pre-requisite: Undergraduate Level Mathematics and MSI C002.
G.P.Youvaraj
Course objective:
Topology is a basic discipline of pure Mathematics. Its ideas and methods have transformed large parts of geometry
and analysis. It has also greatly stimulated the growth of abstract algebra. Much of modern pure mathematics must
remain a closed book to person who dose not acquire a working knowledge of at least the elements of Topology.
Unit I
Topological spaces - subspaces – product spaces – continuous functions - homeomorphisms .
Unit II
Connectedness - compactness
Unit III
Separation properties - Urysohn's lemma - Tietze's extension theorem .
Unit IV
Separable and second countable spaces – metrization theorems.
Unit V
Homotopy - fundamental group – induced homomorphisms - covering spaces - fundamental group of the circle.
MSI C007
Partial Differential Equations
3
1
0
4
Guest Faculty
Course objective:
To give an introduction to mathematical techniques in and analysis of partial differential equations.
FIRST ORDER EQUATIONS : Cauchy problem – Linear equations - Integral surfaces-Surfaces orthogonal to a given
system – Compatible system – Charpits mathod – Special types of first order equations – Solutions satisfying given
conditions – Jacobi’s method.
SECOND ORDER EQUATIONS – Linear equations with constant and variable coefficients – characteristic curves – The
solution of hyperbolic equations – Separation of variables – The method of integral transforms.
The Laplace equation –
Elementary solutions – Families of equi-potential surfaces-Boundary value problemsSeparation of Variables- wave equation – elementary solutions- Riemann,Volteera solution – Diffusion equation and its
Solutions.
NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS WITH APPLICATIONS:
7
Introduction- One dimensional nonlinear wave equation- Method of Characteristics-Linear and nonlinear dispersive
wave- The Kortewerg de Vries equation and solitons.
MSI C008
Seminar
2
0
0
2
All Faculty Members
Objectives :


To develop written, oral and visual presentation skills
To prepare students for Paper/Thesis/Dissertation writing practice in Mathematics
Course Outline :

Each student is assigned a topic for term paper and seminar. It is an individual work. During the term, the
student will meet periodically the faculty to discuss different stages of the term paper preparation and
seminar.

Preparation of Term Paper : Choosing a Topic in consultation with the Student Advisor – Finding sources of
materials – Gathering the relevant findings – Outlining the Paper – Writing the first draft (manuscript) –
Converting into Compuscript (using Latex) and Editing the paper as advised by the Advisor.

Exposure to collect research papers and to prepare documentation of results in a scientific manner with proper
citation principles will form integral part of the course.

Every student is expected to give at least 3 seminar talks during the course of study. Topics for seminars will
be approved by the faculty. Preparation of seminar talks in the form of compuscripts (using mathematical
software Latex) is compulsory and talks based on the Term paper be delivered using blackboard/ OHP/ LCD.

Evaluation is based on the (i) Preparation of the compuscript (30%) (ii) Presentation style (30%) (iii) Oral
presentation (50%). Passing minimum 50% of (i), (ii) and (iii) put together.
Books for Reference :
1. English Expression :
1. Carey, G.V. Punctuation, Cambridge University Press.
2. Partridge, E. Usage and Abusuge : A guide to good English, Middlesex, Penguin.
2. Research Writing :
1. Berry, R. : How to write a Research paper. Pergamon Press, London.
2. Cooper, B.C. : Writing Technical Reports, Middlesex , Penguin.
3. Turabian, Kate L. : A manual for writers of term paper, Thesis and Dissertations,
University of Chicago Press.
3. Mathematical Typesetting Software:
1. Leslie Lamport . LaTeX : A Documentation Preparation System User's Guide and
Reference Manual , Addison Wesley, Mass, 1994.
2. Goossens, Rahtz, and Mittelbach .The LaTeX Graphics Companion , Addison Wesley ,
Mass, 1997.
3. George Gratzer . First Steps in LaTeX Birhauser, 1999
4. George Gratzer . Math Into LaTeX ,Birhauser, 2000.
5. F. Mittelbach and M Goossens with Braams, Carlisle, and Rowley , The LaTeX
Companion, second edition , Addison Wesley. Mass, 2004
4. Mathematical Writing :
1. N.E.Steenrod, P.R.halmos, M.M.Schiffer and J.E.Dieudonne. How to write
Mathematics, AMS Publication, 1973.
2. Steven G.Krantz. A Primer of Mathematical Writing, AMS Publication, 1997
3. Ellen Swanson, Mathematics into Type, (updated Edition) AMS Publication, 1999.
4. Steven G. Krantz. Mathematical Publishing, AMS Publication, 2005
MSI C009
Complex Analysis
3
8
1
0
4
Guest Faculty
Pre-requisite: Undergraduate Level Complex Analysis .
Course Objective:
This course provides
(i) A modern treatment of classical Complex Analysis
Unit I
Unit I
A quick review of basic Cauchy Theory: Cauchy’s Theorem and Cauchy’s integral formula for convex regions,
Morera’s Theorem, power series representation of analytic functions, zeros of analytic functions, open mapping
theorem, argument principle, Rouche’s theorem, maximum modulus theorem, Schwarz lemma, Weierstrass theorem on
limits of analytic functions.
Unit II
Isolated singularities, Laurent series, Casorati-Weierstrass theorem, meromorphic functions, Mittag-Leffler’s theorem,
Weierstrass product theorem, gamma function.
Unit III
Homology and homotopy versions of Cauchy’s theorem, simply connected regions, normal families, Riemann mapping
theorem.
Unit IV
Harmonic functions, mean value property, Poisson integral, Dirichlet problem for the disc, Harnack’s inequality.
Harnack’s principle.
Unit V
Riemann
zeta
function,
functional
equation,
Euler
product,
MSI C010
Measure and Integration Theory
Pre-requisite: Undergraduate level Mathematics
3
elliptic
1
0
functions,
4
Weierstrass
-function.
Premalatha Kumaresan
Course Objective:
To develop the theory of integration via: measure, the knowledge of which is essential for working in most branches of
modern Analysis.
Lebesgue outer measure, Measurable sets, Regularity, Measurable functions, Borel and Lebesgue Measurability.
Unit II
Integration of non- negative functions, the general integral. Integration of series, Riemann and Lebesgue integrals.
Unit III
Functions of bounded variation, Differentiation and Integration, Abstract measure spaces, Completion of a measure
Unit IV
Signed measures, Hahn, Jordan Decompositions, Radon Nikodym derivatives, Lebesgue Decomposition.
Unit V
Measurability in a product space, the product measure and Fubini’s theorem, Lebesgue measure in Euclidean space.
9
MSI C011
Probability Theory
Pre-requisite: Under Graduate level Calculus
3
1
0
4
V.Thangaraj
Course objective:
This course provides
- An axiomatic treatment of probability theory and an interplay between measure and probability
- Different tools to solve mathematical problems.
Unit I
Probability space
Axiomatic definitions for probability space(finite, countably infinite and uncountably infinite outcome spaces)- Events –
Fields of events-  - fields of events – conditional probability and Bayes’ theorem
Unit II
Random Variables and their distributions
Random Variables – distributions function – decomposition of distribution function – probability mass function and
Probability density function – Classification of Random Variables – Moments and inequalities – Functions of Random
Variables – Discrete and continuous distributions
Unit III
Independence, conditioning and Convergence
Independence of events – of  - fields –of Random Variables- conditional expectation – Radon – Nikodym derivatives –
convergence of Random Variables(in Prob., a.s., in dist., r-th mean)
Unit IV
Characteristic functions
Definitions and Simple properties – Inversion theorem – Moments and Characteristic functions – Weak convergence
Unit V
Limit Theorems
Zero –one Laws – WLLN and SLLN for iid and id random variables. CLT for iid and id random variables
MSI C012
Computational Mathematical Laboratory-II
0
0
2
2
R.Sahadevan
Description :
Introduction to computer graphics and mathematical computer programming in MAPLE, as tools for the solution of
mathematical problems and for mathematical experimentation. Programming topics will include data types,
expressions, statements, control structures, procedures and recursion. Examples and practical work will include
computing with integers, polynomials, matrices, data files and numerical approximations. Practical work will form
an integral part of the course and assessment.
Course Objective:
Students will learn to apply Maple to more advanced computation than that introduced in Computational
Mathematics I. The main themes of the course are these:

Mathematical problem solving. Visualising mathematical objectives via computer graphics and animation.
Approximate numerical solution.

Computer programming. Data structures: numbers; sequences, sets and lists; tables and arrays; algebraic
structures. Program structures: conditional execution, loops and iteration; operators, procedures and functions;
mapping over a structure; recursion. Date types: type testing; implementing polymorphism.
Mathematics-> Algorithms-> Programs. Selected applications, such as implementing vector and matrix algebra;
elementary data processing.
Topics to be covered from following the Course:
Linear Algebra, Real and Complex Analysis, Differential Geometry and Differential Equations
10
MSI C013
Advanced Analysis
3
1
0 4
K.Parthasarathy
Pre-requisite: Undergraduate level Mathematics, MSI C002, C005 and MSI C008.
Course objective:
Treatment of some advanced topics in Real, Complex and Fourier analysis.
Unit I
Differential forms, integration of forms, Stokes’ theorem classical vector analysis.
Unit II
Ahlfors’ Schwarz lemma, Pick’s lemma, hyperbolic geometry in the unit disc, Schottky’s theorem, the Big Picard
theorem.
Unit III
Analytic continuation, the monodromy theorem, Riemann surfaces, uniformization theorem and covering surfaces.
Unit IV
Fourier series: Dirichlet’s theorem, norm convergence, Fejer’s theorem, Riemann-Lebesgue lemma uniqueness theorem,
completeness of exponentials in L2, Parseval formula, isoperimetric inequality, heat equation.
Unit V
Fourier transforms: Convolution, differentiation and Fourier transform, Schwartz space of rapidly decreasing functions,
inversion and plancherel theorems.
MSI C014
Differential Geometry
Pre-requisite: MSI C001 and MSI C005
3
1
0
4
Premalatha Kumaresan
Course Objective:
To give a modern introduction to differential geometry of curves and surfaces.
Unit I
Plane curves, space curves, arc length, curvature, Frenet Serret Formula.
Unit II
Smooth surfaces: Examples of Smooth surfaces tangent, normal and orientability, first fundamental form,curves and
surfaces, isometries.
Unit III
Curvature of smooth surfaces : Weingarten map and the second fundamental form, normal, principal, Gaussian and mean
curvatures.
Unit IV
Surfaces of constant mean curvature, Gauss map, Geodesics.
Unit V
Gauss’s theorema of Egregium, Gauss equation – Codazzi-Mainardi Equations, isometries of surfaces,
MSI C015
Functional Analysis
Pre-requisite: Knowledge of MSI C002 and C005.
3
Course objective:
11
1
0
4
Agrawal Sushama N.
Functional Analysis embodies the abstract approach to analysis. It highlights the interplay between algebraic structure and distance
structures. It also provides a major link between Mathematics and its applications.
Fundamentals of normed spaces, Completeness, continuity of linear maps, Hahn Banach theorems and their applications.
Dual spaces, dual of lP, Lp , Uniform boundedness principle, closed graph and open mapping theorems
Unit V
II
III
IV
Unit I
Inner product spaces, orthonormal sets - ,Riesz - Fischer theorems, Riesz Representation theorem.
Bounded operators and adjoints, Projections, Projection theorem , Normal, Unitary and self-adjoint operators, spectrum
of a bounded operator
Compact Operators, Spectral Theorem for Compact Selfadjoint Operators.
Syllabi for various Elective Courses
MSI E001
Discrete Mathematics
Pre-requisite: High school Level Mathematics:
2
1
0
3
Guest faculty
Course Objective:
To introduce some basic mathematical concepts that are used in many computer science courses. To develop skills to
use these concepts in certain practical applications.
Unit I
Mathematical Logic: Connection – Normal Forms – Theory of Inferences –Predicate Calculus.
Unit II
Set Theory: Operations on Sets – Basic Set Identities – Relations and Orderings.
Unit III
Recursion: Functions – Recursive Functions – Partial Recursive Functions.
Unit IV
Graph Theory: Basic Concepts of Graph Theory- Paths – Connectedness – Matrix Representation of Graphs – Trees –
List structures and Graphs
Unit V
Grammers and Languages: Free Semigroups – Grammers and Languages.
MSI E002
Number Theory & Cryptography
Pre-requisite: Undergraduate Level Mathematics:
2
1
0
3
Guest Faculty
Course Objective:
To provide an introductory course in Number theory.
To Introduce the fast growing and relevant topic of cryptography as an application of Number theory
Unit I
12
Elementary Number theory
Divisibility and the Euclidean Algorithm, Congruences, Finite fields and Quadratic residues, Cryposystems,
Enciphering matrices, Public key Cryptography, RSA, Discrete Log, Knapsack, Primality and Factoring.
Unit II
Introduction to classical cryptosystems
Some simple crypto systems , en ciphering matrices, DES
Unit II
III
IIV
Unit III
Finate fields and quadratic residues
Finate fields, quadratic residues and reciprocity.
Unit IV
Public Key Cryptography
The idea of a public key Cryptography, RSA, Discrete Log, Algorithms to find discrete logs in finite Fields: Shank’s
giant – step - baby -step algorithm, Silver-Pohlig – Hellman’s algorithm, Diffie – Hellman key - exchange system,
ElGamal, zero – knowledge protocols.
Unit V
Primality-Factoring and Elliptic curves.
Pseudoprimes and strong Pseudoprimes, some methods to factor a composite integer:Pollard’s rho method, fermat
factorization and factor bases, the quadratic Sieve method, elliptic curves-basic facts, elliptic curve cryptosystems
MSI E003
Programming and Soft Computations
2
1
0
3
Guest Faculty
Tokens, Expressions and Control Structures – Functions in C++
Classes and Objects – Constructors and Destructors
Operator Overloading and Type conversions - Inheritance
Pointers – Virtual Functions and Polymorphism – Templates and Exception handling
Unit V
Maple / Mathematica Commands (without programming)
MSI E004
Computer Based Numerical Methods
2
1
0
3
Guest Faculty
The solution of Nonlinear Equations f(x)=0
Iteration for solving x=g(x) – Bracketing methods for locating a root – Initial approximations and convergence criteria – NewtonRaphson and secant methods- Aitken’s and Steffensen’s and Muller’s methods
The solution of Linear systems AX= B
Upper triangular linear systems-Gaussian elimination and pivoting-Matrix inversion- Triangular factorization- InterpolationLagrange approximation – Newton polynomials
13
Unit III
Numerical Differentiation, Integration and optimization
Approximating a derivative – Numerical differentiation formulae – quadrature – Composite trapezoidal and Simpson’s rule –
recursive rules – Romberg Integration – Minimisation of a function.
Unit IV
Solution of Differential Equations
Differential Equations – Euler’s method – Heun method- Taylor series method – Runga-Kutta methods – Predictor-Corrector
methods
Unit V
Solution to Partial differential methods
Hyperbolic quations – Parabolic equations – Elliptic equations.
Contents and Treatment as in :
John H.Mathews, Numerical Methods for Mathematics, Science and Engineering (2 nd Edn.), Prentice Hall, New Delhi,
2000
MSI E005
Lie Algebras
Pre-requisite: Knowledge of MSI C001 and C004
2
1
0
3
Guest Faculty
0
3
V.Thangaraj
Course objective:
To initiate the study of Lie Algebras
Unit I
Basic Concepts of Lie Algebras
Unit II
Ideals and homomorphisms
Unit III
Solvable and nilpotent Lie algebras
Unit IV
Semisimple Lie algebras : Theorems of Lie and Cartan, Killing form
Unit V
Complete reducibility of representations and representation of sl(2,F).
MSI E006
Stochastic Processes
Pre-requisite: MSI C010
2
1
Course objective:
This course aims

To introduce standard concepts and methods of stochastic modeling

To analyze the variability that are inherent in natural, engineering and medical sciences

To provide new prespective, methodology, models and intuition and aid in other mathematical and statistical
studies
Unit I
14
Markov chains, an introduction- Definitions, Transition probability matrix of a Markov chain, some Markov chain
models, First Step Analysis, some special Markov chains, Functionals of Random Walks and Success runs
Unit II
Long run behaviour of Markov chains - Regular Markov chains - Transition probability matrices – Examples,
Classification of states, Basic limit theorem of Markov chains, Reducible Markov chains
Unit V
I
II
IV
Unit III
Unit III
Poisson Processes - Poisson distribution and Poisson Processes, Law of rare events, distributions associated with
Poisson Processes, Uniform Distribution and Poisson Processes, Spatial Poisson Processes, Compound and Marked
Poisson Processes
Unit IV
Continuous time Markov chains - Pure birth processes – Pure Death processes, Limiting behaviour of birth and death
Processes, birth and death Processes with absorbing states , Finite state Continuous time Markov chains, A Poisson
Process with a Markov intensity
Unit V
Renewal phenomena – Definitions, examples, the Poisson Process viewed as a renewal process
MSI E007
Representation Theory of Finite Groups
Pre-requisite: MSI C001 and C004
2
1
0
3
S.Parvathi
Course Objective:
To highlight the importance of combination of techniques used from group theory,ring theory and linear algebra
To motivate the students for further study
Classical groups: General linear group , Orthogonal group, Symplectic group, Unitary group.
Group representation, conjugate representation, G-invariant spaces - irreducible representations - Schur’s lemma
The Group Algebra - Maschke’s theorem - characters. Orthogonality relations for characters – Number of irreducible
representations
Permutation representations - Regular representation. Representations of Symmetric groups
Representation of Finite abelian groups - Dihedral groups.
MSI E008
Graph Theory
Pre-requisite: Undergraduate Level Mathematics.
2
1
0
3
M.Loganathan
Unit I
Graphs – Vertex degrees - Sub-graphs - Paths and cycles - Connected graphs - Connected components
Unit II
A cyclic graphs – Trees - Cut edges - Cut vertices – Spanning Tree .
Unit III
Euler tours - Euler graphs - Hamiltonian paths - Hamiltonian graphs - Closure of a graph.
15
Unit IV
Planar graphs - Euler’s formula- Vertex colouring - Chromatic number - Chromatic polynomial – R - Critical graphs.
Unit V
Edge colouring - Edge Chromatic number - Dual of a plane graph -Map colouring - Four and five colour theorems.
Unit II
I
MSI E009
Lie Groups of Transformations and
Ordinary Differential Equations
Pre-requisite: MSI C002 and C005
2 1 0 3
R.Sahadevan
Course Objective:
To introduce for advanced research in mathematics and applications of Lie group.
Unit I
Introduction - Lie groups of transformations - infinitesimal transformations.
Unit II
Extended group transformations and infinitesimal transformations (one independent and one dependent variables).
Unit III
Lie Algebras and applications.
Unit IV
Invariance of first and second order ordinary differential equations.
MSI E010
Lie Groups of Transformations and
Partial Differential Equations
Pre-requisite: MSI E009
2
1
0
3
R.Sahadevan
Unit I
Introduction - Lie groups of transformations - infinitesimal transformations.
Unit II
Extended group transformations and infinitesimal transformations.
Unit III
Invariance of a partial differential equations of first and second order - elementary examples.
Unit IV
Noether's theorem and Lie Backlund symmetries.
MSI E011
Potential Theory in Rn
Pre-requisite: MSI C009
2
1
Harmonic functions - Dirichlet problem.
Functions harmonic on a ball - Directed families of harmonic functions.
16
0
3
Premalatha Kumaresan
Super harmonics functions – Equivalent definitions - Minimum principle.
Properties of Super harmonic functions
Directed families of super harmonic functions – Properties of surface and volume mean values.
Unit V
III
IV
MSI E012
Linear Lie Groups
3
0
0
3
K.Parthasarathy
Unit I
Linear Lie Groups: Definition and examples, the exponential map and the Lie algebra of a linear Lie groups.
Unit II
The Lie Correspondents, Homomorphisms.
Unit III
Basic Representation Theory, irreducible representations of SU(2) and SO(3).
Unit IV
Characters, Orthogonality and Peter-Weyl Theorem.
Unit V
Roots, Weights and Weyl’s Formulas.
MSI E013
Banach Algebras and Operator Theory
3 0
0
3
Agrawal Sushama N.
Unit I
Banach Algebras definition, examples, ideals and quotients, invertibility and the Spectrum, Banach – Mazur theorem.
Unit II
Spectral radius formula, Gelfand theory of commutative Banach Algebras.
Unit III
C* - Algebras, Selfadjoint, normal, unitary operators on a Hilbert space, Projectors.
Unit IV
Gelfand – Naimark Theorem for commutative C* - algebras, continuous functional Calculus for normal operators,
Positive Operators and Square root.
Unit V
Borel functional Calculus for normal operators, Spectral measures, Spectral Theorem for bounded normal operators.
MSI E014
Algebraic Number Theory
Pre-requisite: MSI C001 and C005
2
Course Objective:
To provide basic understanding of Algebraic Number Theory
17
1
0
3
S.Parvathi
Unit I
Algebraic Background – Symmetric Polynomials – Modules – Free Abelian Groups
Unit II
Algebraic Numbers – Conjugates and Discriminants – Algebraic integers – Integral Bases – Norms and Traces – Rings of
Integers – Noetherian rings and Noetherian Modules.
Unit III
Quadratic fields and Cyclotomic fields – and integers in Quadratic fields and Cyclotomic fields
Unit IV
The group of units – The factorization into irreducible elements – examples of non-unique factorization into irreducibles –
Euclidean Quadratic fields.
Unit V
Prime factorization of ideals - Dedekind rings- the norm of an ideal – class groups
MSI E015
Mathematical Theory of Electromagnetic Waves
2
1
0
3
G.P.Youvaraj
Pre – requisite:
Vector Calculus, Real Analysis, Differential Equations.
Course Objective:
This is aimed at introducing the mathematical theory behind electromagnetic wave propagation. While learning
this theory we shall also understand acoustic wave propagation in bounded and unbounded regions. We shall also
discuss the scattering aspect of both electromagnetic, and acoustic waves.
Course Contents:
1. Review of Vector Calculus
1.1 Space Curves and Surfaces
1.2 Gradient, Divergence, Curl
1.3 Green’s Theorem,
1.4 Gauss Divergence Theorem
2.
Electromagnetic Fields
2.1 Maxwell’s Equations
2.2 Electromagnetic Waves
2.3 Reduced Wave Equation
3.
Solutions in Bounded Domain
3.1 Fundamental Solutions of Reduced Wave equation
3.2 Green’s Function
3.3 Structure of Wave functions
3.4 Representation of Wave functions
4.
Solutions in the Exterior Domain
4.1 Structure of Wave functions
4.2 Sommerfeld’s Radiation Conditions
4.3 Green’s Representation Theorem
4.4 Far Field Patterns
5.
Boundary Value Problems
5.1 Boundary Value Problems in the bounded domain
5.2 Boundary Value Problems in the Exterior domain
18
5.3 Scattering and Inverse Scattering
Self-Study Courses for the Ramanujan Institute only
The detailed syllabi will be provided at the time of registration by the faculty concerned.
MSI S001
MSI S002
MSI S003
MSI S004
MSI S005
MSI S007
MSI S008
MSI S009
MSI S010
MSI S011
Algebraic Theory of Numbers
Algebraic Topology
Financial Calculus
Fuzzy Analysis
Harmonic Function Theory
Introduction to Fractals
Lie Groups and Lie Algebras
Probability on Abstract Spaces
Quantum Computations
Quantum Groups
SS
SS
SS
SS
SS
SS
SS
SS
SS
SS
0
0
0
0
0
0
0
0
0
0
4
4
4
4
4
4
4
4
4
4
0
0
0
0
0
0
0
0
0
0
4
4
4
4
4
4
4
4
4
4
S.Parvathi
M.Loganathan
V.Thangaraj
N.Agrawal Sushama
Premalatha Kumaresan
K.Parthasarathy
K.Parthasarathy
V.Thangaraj
V.Thangaraj
S.Parvathi
P.G.DIPLOMA IN COMPUTATIONAL MATHEMATICS AND STATISTICS
SYLLABUS ABSTRACTS
MSI C076
Discrete Mathematics
3
1
-
4
Objectives :

To develop mathematical maturity and ability to deal with abstraction.

To develop problem-solving skills in different aspects of application mathematics
Course Content:
Unit-I :
Logic and the Language of Mathematics
Propositions – Conditional propositions and Logical Equivalence – Quantifiers – Proofs – Mathematical Induction – Sets
sequences and Strings – Number Systems – Relations – Equivalence Relations – Matrics of Relations – Functions.
Unit-II :
Counting Methods and the Recurrence Relations: Basic Principles Permutations and Combinations – Generalized
Permutations and Combinations – Binomial Coefficients and Combinatorial Identities – The Pigeonhole Principle –
Solving recurrence relations –Simple problems and applications
Unit-III :
Graph Theory: Paths and Cycles – Hamiltonian Cycles and the Traveling Salesman Problem – Representations of
Graphs – Trees – Spanning trees – Minimal spanning trees – Binary trees – Tree Traversals.
Unit-IV :
Network models, Boolean algebras and Combinatorial circuits:
Algorithms – A Maximal Flow Algorithms – The Max flow, Min cut Theorem – Matching – Combinatorial Circuits and
heir properties – Boolean algebras – Boolean functions – Synthesis of circuits – Applications
Unit - V:
Automata, Grammars and Language
Sequential Circuits and Finite State Machines- Finite State Automata – Language and Grammars – Non-deterministic
Finite State Automata – Relationships between Language and Automat
MSI C077
Mathematics of Finance and Insurance
4
Objectives :
19
1
-
5
To provide fundamentals in financial transactions, discounting, repayments, term structure, derivatives and stochastic
interest rate models.
To gain practice to apply in Actuarial planning
Course Contents.
Unit-I :
Theory of Interest – The basic compound interest functions – Nominal
Discounted cash flow
rates of interest annuities payable p-thly –
Unit-II :
Capital redemption policies- The valuation of securities- Capital gains tax – cumulative sinking funds.
Unit-III :
Yield curves, discounted mean terms, matching and immunization
Consumer credit and Stochastic interest rates models
Unit-IV :
Morality table – Annuities, Assurances, Premiums – Functions other than yearly.
Unit-V :
Policy values – surrender and paid-up values: Bonus: Special policies – Applications of calculus : Population Theory
MSI C078
Computational Mathematics
3
1
1
5
Objectives :
To develop computational problem-solving skills, ideas – To apply mathematical
concepts other science and social science subjects.
Course Content:
Unit-I :
Graphs and Functions: Cartesian Coordinate Systems and Straight Lines – Linear and Quadratic Functions –Aids to
Graphing Functions – Exponential and Logarithmic Functions – Analytical Geometry and the Conic Sections – Polar
Coordinates – Area Computational in Polar Coordinates – Parametric Curves – Applications
Unit-II :
Systems of Linear Equations:
Systems of Linear Equations in Two Variables – Systems of Linear Equations and
Augmented Matrices – Gauss – Jordan Elimination – Matrices – Addition and Multiplication by a number – Matrix
Multiplication – Inverse of a Square Matrix – Matrix Equations and Systems of Linear Equations – Leontief Input –
Output Analysis.
Unit-III :
Differential Calculus: Limits and Continuity – A Geometric Introduction – Computation of Limits – The Derivative of
constants, Power Forms and Sums – Derivatives of Products and Quotients – Chain Rule: Power Form – Marginal
Analysis in Business and Economics.
Unit – IV
Integral Calculus: Antiderivatives and Indefinite Integrals – Integration by Substitution – Differential Equations –
Growth and Decay – Area under a curve – Definite Integrals – The Fundamental Theorem of Calculus – Applications in
Business and Economics
20
Unit – V :
MAPLE Programming: Introduction to mathematical computer programming in MAPLE, as tools for the solution of
mathematical problems and for the mathematical experimentation. Programming topics will include data types ,
expressions, statements, control structures, procedures and recursion. Example and practical work will include
computing will integers, polynomials, matrices, data files and numerical approximations.
Computational Laboratory Exercises: MAPLE Exercises: Plotting Curves Compositions of functions, inverse Sequences
and Series (finite and infinite sum) Slope of a line, a secant, a tangent Equations of tangent Limit and continuity 2-D and
3-D graphs Symbolic Differentiation and Symbolic Integration Conversion of coordinates. Areas in Polar coordinate
Symbolic manipulation on matrices Solution to equation Solution to Differential equations.
MSI C079
Introduction to Information Technology + Computational Lab. – I
2
1 1
4
Objectives:
To provide basic understanding of information technology.
Course Content:
Unit – I :
Introduction to Computer – Classification of Digital Computer System – Computer Architecture – Number SystemMemory unit – Input – Output Device.
Unit – II :
Logic Gates – Truth Table Introduction to Computer Software – Programming Languages.
Unit – III:
Introduction to MS-WORD – Creating documents, Tables, Importing charts, Mails merge – Preparing bio-data –
Copying Text and Pictures from Excel.
Unit – IV :
MS-ACCESS Creating Recruitment Databases and Create Application Table which has Applicant Name, Name
Address, Phone Number, E-mail, etc – MS-ACCESS – Planning and Creating Tables and Using the features of Chart.
Bar Chart, Pie.
Unit – V :
MS-EXCEL – Creating Tables Using EXCEL – Using Tables and Creating Graphs Usage of formulae and Built –in
Functions – File Manipulations,.
POWER POINT – Inserting Clip Art and Pictures – Insertion of new slides – Presentation using Wizards – Usage of
design Templates.
Computer Laboratory Exercises:
MS-WORD – To create Bio-Data – To create Bar Chart – To create Mail Merge – MS EXCEL
1. Student Mark List
Bar Chart creation with Employee details – Pie-Chart – Company’s Growth from 1990- 2000-MS-POWER POIN-Birth
day Greeting – Marriage Invitation –Demo in your specializations – MS-ACCESS-Employee Database Creation-Library
Information System- Hospital Management System
MSI C080
Computational Statistics
3
1
1
5
Objective:
To provide a through grounding in classical-methods of statistical inference with an introduction to more new
developments in statistical methodology. To provide students with the necessary technical skills and practical
21
experience to enable them critically to evaluate research results and to carry out high quality empirical work for
themselves. Emphasis throughout the course is on the application of statistical techniques rather than the development
of theory.
UNIT- I :
Data and Statistics : Data – Data Sources - Descriptive Statistics: Tabular and Graphical Methods:- Summarizing the
Qualitative Data and Quantitative Data – Exploratory Data Analysis (Stem and Leaf Display) – Cross tabulations and
scatter diagrams
Descriptive Statistics: Numerical methods :- Measures of location – measures of variability – Measures of relative
location and detecting outliers – Exploratory Data Analysis – Measures of association between two variables – the
weighted mean and working with grouped Data
UNIT-II :
Introduction to Probability – discrete probability distributions and Continuous distribution functions:
Experiments – events – assigning probabilities – basic relationships of probability – conditional probability – Bayes
theorem – Moments- binomial, Poisson and hyper-geometric distributions – uniform(continuous), normal. Exponential
distributions.
UNIT-III :
Sampling and Sampling Distributions:- Sampling methods – Sampling distributions of sample mean and sample
proportion – Point estimation and properties. - Tests of Goodness of Fit and Independence – Multinomial population,
Poisson and Normal distributions – Test of independence.
UNIT-IV :
Analysis of Variance and Experimental Design:- Testing of the equality of k population means- – Completely
randomized Design – Randomized Block design – Multiple comparison procedures -Factorial Experiments (22)
UNIT-V :
Simple linear and multiple Regressions :- The regression model – Least squares model – coefficient determination –
Model assumptions – Testing of significance – using the estimated regression equation and prediction – Residual
analysis - qualitative Independent variables in the case of multiple regression(binary response).
Computational Laboratory Exercises :
EXCEL Exercises :
Tabular and Graphical Methods- Descriptive Statistics (mean, median, mode, variance and Standard deviation)-Discrete
Probability Distributions (computing binomial and Poisson probabilities)-Continuous Probability distributions (Normal
distribution)-Random Sampling -Interval Estimation of a Population mean (Large-Sample and Small-Sample cases)Hypothesis Testing for mean (Large-Sample and Small-Sample cases)-Hypothesis Testing about the difference between
two population means(Large-Sample, Small-Sample and Matched Sample)-Population variances (One population and
two populations) -Tests of Goodness of fit and Independence -Analysis of Variance and Experimental Design ( SingleFactor Observational Studies and Completely randomized designs – Factorial Experiments(22))-Simple Linear
Regression Analysis-Correlation Analysis
MSI C081
Computer Programming in C and C+++ Computational Laboratory –
II
2
Objectives:
To develop skill in writing codes in C and C++ programming languages
Course Content:
UNIT-I :
Identifiers – Keywords – Data Types – Access Modifiers – Data Type Conversions – Operators
UNIT-II :
Conditional Controls – Loop Control – Input/Output Operations – Function Prototypes –
Function Arguments – Arrays – Structures – Unions – Pointers.
22
1
1
4
UNIT-III :
Introduction to OOPS – Overview of C++ - Classes – Structures
UNIT-IV :
Friend Functions – Constructors – Destructors – Arrays
UNIT-V :
Function Overloading, Operator Overloading – Inheritance – Polymorphism.
Computer Laboratory Exercises:
Programming Problems in C:
Factorial of a number-Farenheit to Celicius-To count the no. of vowels and consonants in given string-Matrix
manipulation-Palindrome checking-Fibonacci series
Programming Problems in C++:
To calculate simple interest and compound interest using class and objects-Initialising and destructing the character
array using constructor and destructor functions-Adding 2 complex numbers using operator overloading-To calculate
volume of sphere , cube and rectangle using function overloading-Calculate the area of triangle and rectangle using
single inheritance-To maintain student’s details using multiple inheritance
MSI C082
Game Theory and Strategy
4
1
-
5
Objectives:
To provide mathematical game theory in an interdisciplinary context
Course Content:
UNIT-I :
Two-person zero-sum games : The nature of game – matrix games: dominance and saddle points – matrix games: mixed
strategies- Application to Anthropology: Jamaican Fishing- Application to Warfare: Guerrillas, Police, and Missiles Application to Philosophy : Newcomb’s Problem and Free Will – Game trees- Application to Business: Competitive
Decision making – Utility theory – Games against nature.
UNIT-II :
Two-person non-zero-sum games : Nash Equilibria and non-co-operative solutions – The Prisoner’s Dilemma –
Applications to Social Psychology: Trust, Suspicion, and the F-Scale – Strategic Moves – Application to Biology :
Evolutionarily Stable Strategies – The Nash Arbitration Scheme and Co-operative solutions- Application to Business:
Management Labour Arbitration – Application to Economics: The duopoly Problem.
UNIT-III :
N-Person Games : An introduction to N-person games – Application to Politics: Strategic Voting – N-person Prisoner’s
Dilemma – Application to Athletics: Prisoner’s dilemma and the Football Draft – Imputations, Domination and Stable
sets – Application to Anthropology: Pathan Organization.
UNIT-IV :
N-Person Games : The Core – The Shapley Value – Application to Politics: The Shapley-Shubik Power Index –
Application to Politics: The Banshaf Index and the Canadian Constitution
UNIT-V :
N-Person Game : Bargaining sets – Application to Politics: Parliamentary Coalitions – The Nucleolus and the Gately
Point – Application to Economics: Cost Allocation in India.
MSI C083
Internet and Java Programming + Computational Lab. –II
Objectives:
23
2
1
1
4
To have hands-on experience on internet and to develop skills in writing codes for internet.
Course Content :
UNIT-I :
Internet Concepts – Internet Services – Types of Accounts – Media for Internet – ISP – TCP/IP and connection software
– Dial-Up Networking - Setting up and Internet Connections.
UNIT-II :
Introduction to Web – Using the Web – URLs, Schemes, Host Names and Port Numbers – Using the Browser –
Hypertext and HTML
UNIT-III :
Introduction to Java – Features of Java – Object Oriented Concepts – Lexical Issues – Data Types – Variables – Arrays
– Operators
UNIT-IV :
Control Statements, Packages – Access Protection – Importing Packages – Interfaces
UNIT-V :
Exception Handling – Throw and Throws – Threads – Applets – Java Utilities – Code Documentation.
Computer Laboratory Exercises:
Learn to use Internet Explorer and Netscape Navigator-Creation of E-Mail and sending messages-Chat-Greetings with
Pictures-Downloading images-Voice mail service-Search Engines (Search a given topic and produce the details about
that topic)-Design a web page of your favourite teacher, explaining his academic and personal facts and give suitable
headings and horizontal rules. Design it in appropriate color-Design a web page advertising a product for marketing
with charts of sales-Develop discussion forum for the purpose of communication between groups -Develop a page to
send a mail to more than one person-Post a simple job site for the facility of the career.
24
Department of Computer Science
Eligibility for Admission to Master of Computer Applications (M.C.A)
Candidate who have passed the under-mentioned degree examinations of this University or an examination of
other institution recognized by this University as equivalent thereto provided they have undergone the course under
10+2+3 or 11+1+3 or 11+2+2 pattern or under the Open University System, shall be eligible for admission to the M.C.A.
Degree Course under CBCS.
(a) B.C.A/B.E.S/B.Sc. in Computer Science/Mathematics/Physics/ Statistics / Applied Sciences OR (b) B.Com /
Bachelor of Bank Management/B.B.A/B.L.M/B.A Corporate Secretaryship / B.A. Economics/ any other Bachelor’s Degree
in any discipline with Business Mathematics and Statistics or Mathematics/Statistics in Main/Allied level OR (c) B.Sc.,
Chemistry with Mathematics and Physics as allied subjects OR (d) B.E/B.Tech/M.B.A OR (e) A Bachelor’s Degree in any
discipline with Mathematics as one of the subjects at the Higher Secondary level (i.e. in +2 level of the 10+2 pattern)
Core and Elective Courses offered by the Department of Computer Science for M.C.A. Degree programme
Course Code
MSI C324
MSI C325
MSI C303
MSI C332
MSI C333
Core/E
lective
C
C
C
C
C
E
S
C
C
C
C
C
Title of the Courses
Credits
L-T-P-C
3-0-0-3
3-0-0-3
3-0-0-3
3-1-0-4
0-0-3-3
2-1-0-3
2-0-0-2
3-1-0-4
3-0-0-3
3-0-1-4
3-0-0-3
0-0-3-3
Course Faculty
UOMS001
MSI C306
MSI C307
MSI C308
MSI C309
MSI C334
Digital Principles
Programming in C
Object Oriented Data Structures
Object Oriented Programming with C++
C, C++ and Data Structures Lab.
Elective
Soft Skill*
Computer Oriented Statistical Methods
Programming in Java
Microprocessors and Applications
Visual Basic and Web Technology
Java, Visual Basic and Web Design Lab.
UOMS002
MSI C311
MSI C312
MSI C313
MSI C314
Elective
Soft Skill*
Operating Systems
Design and Analysis of Algorithms
Database Management Systems
Computer Graphics
E
S
C
C
C
C
2-1-0-3
2-0-0-2
3-0-0-3
3-0-0-3
3-0-0-3
3-0-0-3
S.Gopinathan
PL. Chithra
B.Lavanya (B.L)
M.Sornam
PL. Chithra/ G.F.
Faculty Concerned
Faculty Concerned
Guest Faculty
PL.Chithra/G. F.
S.Gopinathan
M.Sornam/B.L
PL. Chithra &
M.Sornam / B.L.
Faculty Concerned
Faculty Concerned
PL. Chithra/G.F.
P.Thanagvel
B.Lavanya
S.Gopinathan
MSI C335
Graphics and RDBMS Lab.
C
0-0-3-3
S.Gopinathan/ B.L
Elective
E
2-1-0-3
Faculty Concerned
Elective
E
2-1-0-3
Faculty Concerned
UOMS003
Soft Skill*
S
UOMI 001
Internship-I
S
0-0-2-2
Faculty Concerned
MSI C316
Computer Networks
C
3-1-0-4
P.Thangavel
MSI C336
Unix and Shell Programming
C
2-1-0-3
PL.Chithra
MSI C337
Software Engineering
C
3-1-0-4
S.Gopinathan
MSI C328
MSI C329
Network Programming and .NET
Unix, Network Programming and .NET lab
C
C
3-0-0-3
0-0-2-2
UOMS004
MSI C338
MSI C322
Elective
Elective
Soft Skill*
Mini Project and Group Discussion
Multimedia Systems
E
E
S
C
C
3-0-0-3
3-0-0-3
2-0-0-2
0-0-2-2
3-0-1-4
M.Sornam & B.L
PL.Chitra,
M.Sornam & B.L
Faculty Concerned
Faculty Concerned
Faculty Concerned
All Faculty
B.Lavanya
25
2-0-0-2
Faculty Concerned
E
E
E
S
S
C
E
E
3-0-0-3
3-0-0-3
3-0-0-3
2-0-0-2
2-0-0-2
0-0-20-20
3-0-0-3
3-0-0-3
Faculty Concerned
Faculty Concerned
Faculty Concerned
Faculty Concerned
Faculty Concerned
All Faculty
Guest Faculty
P.Thangavel
Courses offered for other Departments/Schools
MSI E303
Advanced Java Programming
MSI E304
Programming in COBOL
MSI E306
Artificial Neural Networks
MSI E307
Artificial Intelligence &Expert Systems
MSI E308
Distributed Computing
MSI E309
Data Mining and Warehousing
MSI E311
Software Project Management & Testing
MSI E312
Software Quality And Assurance
MSI E313
Digital Image Processing
E
E
E
E
E
E
E
E
E
2-0-1-3
2-0-1-3
3-0-0-3
3-0-0-3
3-0-0-3
3-0-0-3
3-0-0-3
3-0-0-3
3-0-0-3
MSI E314
MSI E315
Computer Simulation & Modeling
Computer Aided Design
E
E
3-0-0-3
3-0-0-3
MSI E316
MSI E321
MSI E317
MSI E318
Pattern Recognition
Mobile Computing
Web-Commerce
Object Oriented Analysis and Design
E
E
SS
SS
3-0-0-3
3-0-0-3
2-2-0-4
2-2-0-4
Guest Faculty
Guest Faculty
M.Sornam
Guest Faculty
Guest Faculty
Guest Faculty
Guest Faculty
Guest Faculty
P.Thangavel/
PL.Chithra
P.Thangavel/G.F.
S.Gopinathan/
M.Sornam
Guest Faculty
Guest Faculty
Guest Faculty
Guest Faculty
MSI E319
Introduction to Information Technology and
Programming in C
Internet and Java Programming
E
2-0-1-3
Guest Faculty
E
2-0-1-3
Guest Faculty
UOMS005
UOMS006
MSI C339
MSI E301
MSI E302
MSI E320
MSI C324
Elective
Elective
Elective
Soft Skill*
Soft Skill*
Project Work
Computer Architecture
Principles of Compiler Design
Digital Principles
3
0 0 3 S.Gopinathan
Number systems - compliments -logic gates-truth tables.
Boolean algebra-truth table simplification of boolean
function-Map method tabulation method - sequential logic-Flipflops-Registers-shiftreg-counters-processor design design of an Accumulator Combinational Logic -adders, subtractors, decoders, encoders, multiplexer, demultiplexer.
Processor design-arithmetic logic unit - status register - design of accumulator. Computer design - system configuration
- computer instructions.
MSIC325
Programming in C
3 0
0 3
PL.Chithra
Identifiers, Keywords, Data Types, Access Modifiers, Data Type Conversions, Operators, Conditional Controls - Loop Control –
Input/Output Operations, Function Prototypes, Function Arguments - Pointers. Arrays, Accessing Array Elements, Dynamic
Memory Allocation, Storage Classes, Structures, Unions, character I/O, String I/O, Formatting Input/Output file, Command Line
Arguments.
MSIC303
Object Oriented Data Structures
3
0 0
3 B.Lavanya
ADT- asymptotic notations- algorithmic analysis - classes and objects - concepts OOP - Arrays, representation of arrays
- linked lists - circular linked lists - Stacks and queues - Binary trees - binary search tree - binary tree traversals-threaded binary tree - binary tree representation of trees - Graphs - spanning trees - shortest paths - sorting and
searching - hashing- balanced trees - B-trees – Tries – AVL Tree, SPLAY tree.
MSI C332
Object Oriented Programming in C++
3 1 0 4 M.Sornam
Introduction to OOPS – Overview of C++, Classes, Structures – Union - Friend Functions, Friend Classes – Inline Functions,
Constructors – destructors – Static Members – Scope resolution Operator – Passing Objects to Functions, Array, Pointers – Function
26
Overloading, Overloading Constructors. Operator Overloading – Inheritance - Protected Members - Polymorphism – virtual
Functions - Exception Handling - I/O Streams – Formations I/O with IOS Class Functions and Manipulators.
MSIC333
C, C++ and Data Structures Lab.
0
0 3
3 PL.Chithra/B.Lavanya
Primality test, string manipulation, matrix manipulation, generating permutations and combinations, creating database
for telephone numbers and related operations, file processing., etc.- C++ - Implementation of arrays (single and
multidimensional), polynomial object and overload operators – circular linked lists – doubly linked lists –
implementation of stacks and queues – circular queues – evaluation of expressions – sorting – AVL trees – insertion etc.
MSIC306
Computer Oriented Statistical Methods
3
1 0
4
Guest Faculty
Sample spaces - events - Axiomatic approach to probability - conditional probability - Independent events - Baye's
formula - Random Variables - Continuous and Discrete - distribution function - Expectation, variance, coefficient of
variation, moment generation function - Chebyshev's inequality Bivariate distribution - conditional and marginal
distributions - Binomial, Poison and geometric Distributions - Uniform, Normal, Exponential and Gamma distributions.
Correlation - Rank correlation - Linear Regression - Method of Least squares - Fitting of the curve of the form ax + b, ax 2
+ bx + c, abx and axb - multiple and partial correlation( 3 -variables only). sampling - simple random sampling Systematic sampling and stratified random sampling - concepts of sampling distributions and standard error - point
estimation - Interval Estimation of mean and proportion. Tests of Hypotheses - Critical Region - Errors - Level of
significance - power of the test - Large sample tests for mean and proportion - Exact tests based on Normal, t, F and
Chi-square distributions. Basic principles of experimentation - Analysis of variance - one way and two way
classifications - computing randomized design - Randomized Block design - Time series Analysis - Measurement of
Trend and Seasonal variations.
MSIC307
Programming in Java
3
0 0 3 PL.Chithra/G.F.
Differences with C++ - interfaces - packages - applications - Applet - threading - synchronization - errors and exception
- graphics - input/output files - streams - applet life cycle - thread life cycle.
MSI C308
Microprocessors and Applications
3 0
1 4
S.Gopinathan
Prerequisite : MSI C324
Introduction to 8085/8086 Microprocessor Architecture and Pin Function. Introduction to 8086 Instruction Set – Data Transfer –
Arithmetic – Logic – Shift – Compare – Jump – Loop – Flag – Stack – Subroutine Instructions – 8086 Instruction formats –
Assembly Language - Programs with Examples. Interfacing Data Converter – Digital–to-Analog , Analog–to- Digital - Memory
Interface - Address Space - Programmable Peripheral Interface (8255A) – 8279 Programmable Keyboard Interface – 8086 Interrupts
– Direct Memory Access – Burst Mode and Cycle Stealing. Temperature Control Monitoring Systems – Traffic Light Control
Interface – Stepper Motor Interface – Interfacing 7 Segment LED Display – Introduction to Operational Amplifier.
MSI C309
Visual Basic and Web Technology
3
0
0
3
M.Sornam/B.Lavanya
Visual Basic: Features - VB Application - Control/properties/methods - Dialog boxes - VB Language - procedures and
functions - in built function - object variables- API function. Internet concepts, Type of Accounts, ISP-TCP/IP and
Connection software, Designing Interactive Webpages, HTML, DHTML, Basic Scripting-Java script, VB script,
XML,ASP, ASP.NET,VB.NET.
MSIC334
Java, Visual Basic and Web Design Lab.
0 0
3 3
PL.Chithra/M.Sornam/B.L
avanya
Sub-string removal from a string using string buffer class – determining the order of numbers generated randomly
using random class – usage of data classes – string manipulation using char array – usage of vector class – thread based
applications – Applets- working with frames and various controls – working with dialogs and menus – panels and
layouts – incorporating graphics – working with colors and fonts, etc. Visual programming – building simple
applications – working with intrinsic controls and ActiveX controls – applications with multiple forms, dialogs, menus
– application using data controls, common dialogs – drag and drop events – database managements – creating ActiveX
controls, etc. Web Technology – greeting with pictures – downloading text and images – design a web page of your
27
teacher, about your personal details, for a latest product, for any educational institution, for railway reservation, for
social awareness, for environmental awareness and design web page for a hospital, etc.
MSI C311
Operating Systems
3
0
0
3
PL.Chithra/G. F.
Multiprogramming - Time sharing - Distributed system - Real - Time systems - I/O structure - storage hierarchy Hardware protection - General system architecture - Operating system services - System calls - System programs System design and implementation. Processes - CPU scheduling - process synchronization - Deadlocks - Storage
management - memory management - virtual memory - Secondary storage management - file system interface,
implementation - secondary storage structure - protection - security - UNIX system.
MSI C312
Design and Analysis of Algorithms
3
0 0
3
P. Thangavel
Introduction - asymptotic time analysis. Divide and conquer Method: binary search, finding maximum and minimum,
merge sort and quick sort. Greedy method: optimal storage on tapes, knapsack problem, minimum spanning trees and
single source shortest path problem. Dynamic programming: multistage graphs, 0/1 knapsack and traveling salesman
problem. Basic search and traversal techniques: And/Or graph, bi-connected components, depth first search.
Backtracking: 8 queens problem, sum of subsets, graph coloring, Hamiltonian cycle and knapsack problem. Branch and
bound: 0/1 knapsack problem, traveling salesman problem.
MSIC313
Database Management Systems
3
0 0 3 B.Lavanya
Prerequisite: (MSI C303 )
Purpose of Database Systems - relational, hierarchical and network models - SQL - PL/SQL - Client Server Concepts relational calculus - relational algebra - QBE - normalization - virtual records - DBTG model - query processing and
interpretation - query optimizer - database recovery - security and integrity.
MSI C314
Computer Graphics
3
0 0 3 S.Gopinathan /G.F.
Line Generation : Circle Generation - Graphics Primitives - Display devices - Display file co-ordinates - Polygons :
Polygon Filling - Scaling, Rotation & Translation Transformations - Display procedures - Segments - Segment
manipulation - Raster Techniques - Windowing and Clipping - Device handling algorithms - Simulating devices Echoing - Interactive Techniques - 3D Fundamentals - Projections - Clipping in 3D- 3D viewing transformation Hidden surfaces and lines. Dimension - Binary space partition- Light, color and shading - Transparency - Shadows Ray tracing - Halftones - Color - Gamma correction - Fractals - Splines.
MSIC335
Graphics and RDBMS Lab.
0 0
3 3
S.Gopinathan/ B.Lavanya
Generate line, circle and box etc., using graphics primitives – generate line, zigzag line using DDA algorithm – generate
line, circle, ellipse using Bressenham’s algorithm - generate character using bit-map method and DDA line drawing
method – 2D transformation for scaling, translation, rotation, reflection, shearing – 3D transformation for scaling,
translation, rotation – line clipping, character clipping and polygon clipping – generate any type of 3D object etc.
RBDMS – creation of database and performing the operation given below using menu driven programming - insert,
delete, modification, and report preparation – payroll – mark sheet processing – savings bank account for banking –
inventory – invoice – library information system – railway reservation – income tax processing system – election ballot
system – telephone directory maintenance – etc.
MSIC316
Computer Networks
3
1 0 4 P.Thangavel
Prerequisite : MSI C311
Goals and Applications of networks - Network Architectures - OSI reference model and services - Network topology Physical layer - Transmission media - switching methods- Data link layer Design issues - error detection and correction
- elementary data link protocols - sliding window protocols-Protocol specification & verification. Network layer-design
issues-Routing, congestion, inter networking, - Routing algorithms - Shortest path, Multipath, Centralized, Isolated,
Flooding, Distributed, Optimal, flow Based, Hierarchical & Broadcasting - Congestion control algorithms - pre
28
allocation of buffer, packet discarding, flow control, choke packets, deadlocks. Transport layer - design issues Connection management - Addressing, Establishing & Releasing a connection, Timer based Connection Management,
Multiplexing, Crash Recovery, Email, - Cryptography - case studies: Arcnet, Ethernet, Arpanet.
MSIC336
Unix and Shell Programming
2
1 0 3 PL.Chithra
File and Common Commands - Shell – Directories – Devices – Permission – The Grep Family Filters – Streams – Concepts of
Shell – Trapping Exit Codes- Shell Programming – Standard Input/Output – file Access – System Calls-Interprocess
Communication-DeadLock
Detection-Scheduling
algorithmsInodes
–
Processes
–
SignalsInterrupts – Preprocessors – Manual Page.
MSIC337
Software Engineering
3
1
0 4 S.Gopinathan
Prerequisite : MSI C325
Software and Software Engineering - Software Metrics - Estimation - Planning. Software Requirement Analysis:
Computer systems Engineering - Fundamentals of Requirement Concepts of Structured Analysis - SADT; Object
Oriented Analysis and Data Modeling - Alternate analysis techniques - Specification techniques. Software Design and
Implementation :
Programming Languages and Coding. Software Testing Techniques and Strategies. Software
Quality Assurance. Software Maintenance - Software Configuration
Management. Computer Aided Software
Engineering Integrated CASE Environments (I-CASE ).
MSI C328
Network Programming and .NET
3
0 0
3 M.Sornam and B.Lavanya
Prerequisite : MSI C309
OOPs Fundamentals – Programming Concepts – Application Frame Work, Project Utility – MFC Library – Bar Chart
with Resources. Graph Applications – Word Processor Applications – OLE Features and Specifications Continual
Application, ActiveX Controls, Com – DHTML – ATL Vs ACTIVEX-Overview of ActiveX Scripting-Java Scripting –
Standalone scripts-ActiveX Controls- Creating ActiveX Controls- ActiveX Documents- ActiveX Document ArchitectureURL Monikers- Hyper linking interface- Working with URL Monikers- Overview of ISAPI- ISAPI Extension-ISAPI
Filter-Designing IIS Application-Building IIS Application-Building Data Driven DHTML Application- ActiveX
documents-Technology Migration Wizard-Modified Code-Launching and Testing document-Testing the DLL.
“Beginning ASP.NET 1.1 with VB.NET 2003” -- Chris Ullman,John Kauffman, Chris Hart, David Sussmann.--- Wiley
Publishing Inc. , WROX.
Introduction – Server Controls and variables – Control structures – Procedural Programming – Subroutines and Functions – Event
driven programming – Objects – Database Management – ADO.NET – ASP.NET Server Controls – Web Controls - .NET Assemblies –
Error Handling – Web Services – ASP.NET Security.
MSIC329
Unix,Network Programming and .NET Lab.
0 0
2 2
PL.Chithra , M.Sornam and
B.L
Shell script to solve quadratic equation – menu driven – user friendly changing modes – simple script for all control
structures – process scheduling – authorized access – using pipes to calculate NCR – inter process communication
using message queues – IPU using pipes – implementation of wait and signal using counting semaphores automatic counter update problem – signaling process – deadlock detection - producer, consumer problems.
creating menus – implementing keyboard accelerators – checking / un-checking and enabling / disabling menus –
inserting and removing menus at runtime – floating popup menus – MDI with cascaded and tiled window –
creating model and modeless dialog box - creating status bar – using list box with Clist Box class - using edit box
with Cedit Box class – working of spin button controls – creating graphics editor etc. Network programming –
working with java scripts – creating ActiveX controls – OLE server – OLE container – working with URL monikers
– creating an ISAPI extension - creating an ISAPI editor – building IIS application – data driven DHTML
application – ActiveX documents. Create a web form for an On-line Library.-Password Checking-Display records
from a Database-Web server controls implementation-On-line shopping site-Quiz application-Usage of range
validator control-Palindrome Checking-Sensex Application-Implementation of Cookies
MSIC338
MiniProject and Group Discussion
0
29
0 2 2 All Faculty
Each student will take a specific problem for the Mini Project and solve it using any one of latest tool and submit the
report.
MSI C322
Multimedia Systems
3
0 1
4 B.Lavanya
Prerequisite : MSI C314
Evaluation of Multimedia - Components of Multimedia system - Hardware - Multimedia PC-Memory and Storage
devices for multimedia - ODD and CD Technology and standards - Input devices - Output devices - Communication
devices and peripheral connections. Software components of multimedia - text, audio, image and video processing Elementary and Authoring tools - Interactive video and 3D Graphics in Multimedia. Multimedia Information Systems Extending RDBMS to Image Management Systems, and voice Information Systems - MPEG, JPEG, DVI and UVC
standards applied to multimedia and Distributed Information Systems. Organizing, Deign, production and Testing of
Multimedia projects. Case studies in Education - Industrial Design - Presentation of software and concepts of virtual
reality – video compression, audio compression, video conferencing and mobile multimedia.
MSIC339
Project Work
0
0 20
20
All Faculty
Each student will do a project work and submit report of their work carried.
MSIE301
Computer Architecture
3
0 0 3 Guest Faculty
Data representation - micro operations - Register transfer - micro programmed control - Central processing unit - Pipe
lining - Vector processing and Array processors. Computer Arithmetic. Input-output organization - Memory
organization - multi processors
MSIE302
Principles of Compiler Design
3
0 0 3 P. Thangavel
Introduction - Finite Automata and lexical Analysis. Syntax Analysis - Context free grammars - Derivations and parse
trees - Basic parsing techniques - LR parsing - Syntax - directed translation - symbol tables. Code optimization,
generation - Error detection and recovery.
MSIE303
Advanced Java Programming
2
0
1
3
Guest Faculty
Servelet Overview, Java Webserver, Servelet Chaining, Session Management, Using JDBC in Servelets, Applet to
Servelet Communication, Java Beans EJB Architecture, Design and Implementation, EJB Session Beans, EJB Entity
Beans, Implementation and Entity Direction of EJB, JSP,J2EE
MSIE304
Programming in COBOL
2
0
1
3
Guest Faculty
Introduction to COBOL-IDENTIFICATION Division-PROCEDURE Division-Debugging and program testingKeyboard Input and screen Display-Output formatting –Arithmetic Operations-Report design and coding-Conditional
Operations-Designing and writing Control Break programs-Data Validation design and coding-processing
Arrays/Tables-Processing multidimensional Tables-Sorting-Master-Transaction File Processing-Indexed File
Processing-Program Management.
MSIE306
Artificial Neural Networks
3
0 0 3 M.Sornam
Prerequisite : MSI C316
Basics of ANN - Characterization of biological neural networks - Artificial intelligence Vs Neural networks - Principles
and Promises - Learning rules. Functional Units - Activation functions - Feed forward ANN - single layer network
Limitation - Need for Multi-layer network - Capabilities - Back propagation algorithm - applications - limitations.
Feedback ANN - Hopfield network - Architecture - Dynamics - energy function - Applications - optimization Traveling Salesman Problem - A/D converter. Feedback and feed forward networks - Competitive learning algorithm weight initialization issues solving convex combination method - Noise addition and Neighborhood method - feature
mapping - self organizing map - Applications. Neural architectures for complex pattern recognition tasks - counter
propagation network - applications - image compression - function approximation look up table - Bi-directional
Associative Memory - Variations on BAM - Applications.
30
MSIE307
3 0 0 3 Guest Faculty
Artificial Intelligence &Expert Systems
Prerequisite : MSI C303
Evolution of Artificial Intelligence production systems - search strategies - Hill climbing, backtracking graph search algorithm A and A *, monotone restriction specialized production systems - AO* algorithm. Searching game trees:
Minimax Procedure alpha beta
pruning - predicate calculus - Answer extraction - knowledge based systems knowledge processing, inference techniques. Expert system Definition - stages in development - knowledge
representation and acquisition techniques - building expert systems - Forward and Backward Chaining - Tools Explanation facilities - Meta Knowledge - fuzzy reasoning - case study: Mycin. Applications of A.I - Natural language
processing and understanding - perception - Learning using Neural nets.
MSIE308
Distributed Computing
3
0 0 3 Guest Faculty
Prerequisite : MSIC313
Models for Distributed Computing - Remote procedure calls - Switched multiprocessor - Bus based multi-computer Switched
multi-computers - Network operating systems and NFS - Time distributed systems - Transparency Flexibility - Reliability - performance - scalability - The client - server model - Blocking and un-buffered primitives Implementation of client-server model. Synchronization in distributed systems - Clock synchronization - Mutual
exclusion - Election algorithms - Atomic transactions - Dead locks in distributed system - Threads - Thread usage and
implementation of thread packages - processor allocation - Distributed File System - Implementation of new trends in
distributed file systems - Distributed databases.
MSIE309
Data Mining and Warehousing
3
0 0 3 Guest Faculty
Main operations: Clustering, Classification, Regression, Neural Networks, Feature Selection, Deviation, Detection –
Context of Data mining – Four approaches to Data mining – Data mining Methodology – Three pillars of Data mining –
Data for Data mining – Dirty Data – Settling Data mining Environment – Data Warehouse Database – Analyzing
context of Data Warehouse, Basic Data Warehouse Architecture, Online Analytical Processing Systems (OLAP). Success
and failure stories of Data mining - Survey of existing mining & OLAP Products. Applications in Web mining.
MSIE311
Software Project Management & Testing
3
0 0 3 Guest Faculty
Introduction to Software Project Management- Software project versus other types of project- problems- management
control- Stakeholders- Requirement Specification – Information and control in organizations Introduction to step wise
project planning- Select-identify scope and objectives- waterfall model- v-process model-spiral model- software
prototyping- ways of categorizing prototypes- tools- incremental delivery- selecting process model -Software effort
estimation- introduction- where-problems with over and under estimates- basis for software estimating- software effort
estimation technique- expert judgment-COCOMO -Activity Planning- Objectives- Project schedules- projects and
activities- sequencing and scheduling activities- sequencing and scheduling problem-job sequencing-n jobs through two
machines, two jobs through m-machines and n-jobs through m-machines, PERT and CPM techniques-critical pathNormal path and crash time-Resource allocation-Resource leveling and smoothing.
MSIE312
Software Quality And Assurance
3
0 0 3 Guest Faculty
Introduction - Quality and the quality system - standards and procedures technical activities. Software tasks management responsibility - quality system - contract review - design control - document control - purchasing product identification and traceability. Process control - checking - identification of testing tools - control of
nonconforming product - Corrective action. Handling, storage, packing and delivery - Quality records - Internal quality
audits - Training - Servicing - statistical techniques. QA and new technologies - QA and Human - Computer interface process modeling - standards and procedures. ISO-9001 - Elements of ISO 9001 - Improving quality system - Case
study.
MSIE313
Digital Image Processing
3
Prerequisite : MSI C314
31
0 0 3 P.Thangavel/PL.Chithra
Introduction - Problems and Applications - Two dimensional systems and Mathematical preliminaries - Linear Systems
and Shift invariance - Fourier Transform - Properties - Fourier Series - Matrix theory results - Block Matrices and
kronecker products. Image perception - light, luminance, Brightness and Contrast - MTF of Visual systems Monochrome vision models - image fidelity criteria - color representation. Digital image sampling and quantization 2D sampling theory - image reconstruction from samples, Bandlimited images, sampling theorem, Nyquist rate,
Aliasing and foldover frequencies - image quantization - Optimum mean square Quantizer. Image Enhancement point operations - contrast structuring, clipping & thresholding etc - Histogram modeling - spiral operations - special
averaging & low pass filtering,
Directional Smoothing, median filtering, Replication, Linear interpolation,
Magnification & interpolation (Zooming) - false color and pseudo color. Image restoration - Image observation models
- Inverse and Wiener filtering - Least square filters - Image Analysis - Edge Detection - Boundary extraction Boundary representation - Region representation - Image
Segmentation - Classification Techniques - Image
understandings. Image Data Compression - Pixel coding - PCM, Entropy coding, Runlength, Bitplane extraction Predictive techniques - Delta Modulation line by line DCPM etc - Interface - Coding of two tone images.
MSIE314
Computer Simulation & Modeling
3
0 0
3 P.Thangavel
Prerequisite : MSI C306
Introduction to Simulation: types of system - Discrete and Continuous Systems Model of a System - Types of
Models - Discrete-Event System Simulation - Steps in a Simulation Study; Simulation Examples. Discrete and
continuous simulation Languages -study and use of one language in detail. Simulation of Manufacturing and
Material Handling Systems - Simulation of Queuing Systems - Random-Number Generation- Tests for Random
Numbers. Random Variate Generation: Inverse Transformation Technique:Uniform Distribution - Exponential
Distribution - Weibull Distribution - Triangular Distribution - Empirical Continuous Distribution - Discrete
Distribution - Direct Transformation for the Normal Distribution - Convolution Method for Erlang Distribution Acceptance - Rejection Technique: Poisson Distribution - Gamma Distribution. Input Data Analysis: Data Collection
- Identifying the Distribution with Data - Parameter Estimation - Goodness-of- Fit Tests:- Chi-Square Test Kolmogorov-Smirnov Test; Selecting Input Models without Data - Multivariate and Time-Series Input Models.
Verification and Validation of Simulation Models - Calibration and Validation of Models - Output Data Analysis Alternative System Designs
MSIE315
Computer Aided Design
3
0 0 3 S.Gopinathan/M.Sornam
Prerequisite : MSI C314
Introduction to CAD; Role of Computers in the design process. Hardware - Input devices, Display devices, Output
devices, Computation devices. Computer Graphics Software and Data Base - Software configuration of a Graphics
System - Data Base Structure and content - Wire Frame Modeling, Surface Modeling, Solid Modeling. Numerical
Control, The beginning of CAM : Conventional Numerical Control - Components of an NC system - NC procedure Coordinate systems - Applications.
NC Part Programming - Manual Part Programming. NC Programming with
Interactive Graphics. Computer Controls in NC - Computer and Direct Numerical Control - Adaptive Control
Machining system. Applications: CAD for LSI/VLSI applications: Device circuit and process modeling for IC
technology: optimization techniques in IC design: Design automation, Design for testability: Specific examples.
Mechanical Drafting: Basic CAD Two-dimensional drafting, mechanical CAD software, developing a mechanical
database, solid modeling. Electrical applications: Advantages of computer graphics systems for electrical design and
drafting, CAD as an aid to electrical designers and drafters, production of an electrical schematic or wiring diagram,
production of a printed-circuited board design, designing integrated circuits. Piping and Instrumentation diagrams:
Setting up the system, applying P and ID, creating the drawing, drawing revisions, text drawing annotation, text
revisions, drawing formats, report generation, documentation: Plotters. Solid Modeling: Converging technologies of
CAD, CAM and CAE, interacting with SM systems, display requirements. Cartography: Mapping applications - uses
and users, map production, automated cartography. Case Studies: LPKF, Unigraphics CAD/CAM Software, NISA
Finite Element Analysis Software, GOS CAD Package.
MSIE316
Pattern Recognition
3
0 0 3 Guest Faculty
Prerequisite : MSI C306
Basic concepts, Fundamental Problems, Design concepts and examples. Decision Function: Role of decision functions in
Pattern recognition, Linear and Generalised decision functions, concepts of pattern space and weight space.
Geometrical properties. Implementation of decision functions, Multivariable functions. Pattern Classification : Pattern
32
Classification by distance functions, Likelihood function - Minimum distance classification. Clusters and cluster seeking
algorithms. Introduction to the problem of feature selection and extraction. Binary feature selection, Statistical and
Structural Feature Extraction. Introduction to Tree languages and Syntactic Pattern Recognition. Syntactic Pattern
Recognition on the Basis of Functional approximation Syntactic pattern description, recognition grammars. Acquisition
and Utilisation of Access Patterns in Relational Data Base Implementation, Knowledge Acquisition Algorithms.
MSIE321
Mobile Computing
3
0 0 3 Guest Faculty
Introducing the mobile internet-Key Services for the mobile internet-making internet “Mobile” – challenges and pitfalls
– Overview of the wireless application protocol – Implementing WAP services – WML – Wireless binary extensible
markup language – enhances WML – User interface design - Advanced WAP – Tailoring content to the Client – Push
Messaging.
MSIE317
Web – Commerce
2
2 0 4 Guest Faculty
Pre-Requisite: MSI C313
Environment - Opportunities - Modes - Security - E-Cash - E-Payment - E-Transaction - E-Mail Technologies for ECommerce - Web Site Establishment - Internet Resources - Advertising - Publishing issues - Approaches - Legalities Technologies.
MSIE318
Object Oriented Analysis & Design
2
2 0 4 Guest Faculty
Prerequisite : MSI C326/ MSI C307
Systems Development - Object Basics - Development Life Cycle - Methodologies - UML - Use-Case Models - Object
Analysis - Object Relations - Design Processes - Design Axioms - Class Design - Object Storage - Object Interoperability View Layer - Software Quality Assurance - System Usability - Measuring User Satisfaction - Case Studies.
Elective Courses offered for other Departments/Schools
MSI E319
Introduction to Information Technology and
Programming in C
2
0
1
3
Guest Faculty
Introduction to Computer – Classification of Digital Computer System – Computer Architecture – Number System – Memory Unit
– Input–Output Device – Logic Gates – Truth Table. Introduction to Computer Software - Programming Language C– Identifiers
– Keywords – Data Types – Access Modifiers – Data Type Conversions – Operators – Conditional Controls – Loop Control –
Input/Output Operations – Function Prototypes – Function Arguments – Arrays – Structures-Implementing some Problems Using
‘C’ Language. Introduction to MS-WORD, MS-ACCESS, MS-EXCEL – Creating Recruitment Database and Create Application
Table - Creating Tables Using EXCEL - Creating Graphs – MS-ACCESS – Planning and Creating Tables and Using the feature of
Chart, Bar Chart, Pie Chart etc. Introduction to Internet – Creating an E-Mail Account using E-mail Service.
MSI E320
Internet and Java Programming
2
0
1
3
Guest Faculty
Internet Concepts – Internet Services – Types of Accounts – Media for Internet – ISP – TCP/IP and connection software – Dial-Up
Networking - Setting up and Internet Connections. Introduction to Java – Features of Java – Object Oriented Concepts – Lexical
Issues – Data Types – Variables – Arrays – Operators – Control Statements, Packages – Access Protection – Importing Packages –
Interfaces – Exception Handling – Throw and Throws – Threads – Applets – Java Utilities – Code Documentation.
Department of Computer Science
Eligibility for Admission to Master of Science in Computer Science
Bachelor's degree in Computer Science or Computer Science & Technology or B.C.A. degree of University of
Madras or any other degree accepted as equivalent thereto by the Syndicate.
M.Sc. Degree Programme in Computer Science – List of Core Courses
Core/E
Course Code
Title of the Courses
lective
33
Credits
L-T-P-C
Course Faculty
MSIC401
MSIC402
MSIC414
MSIC404
Mathematics for Computer Science
Design and Analysis of Algorithms
Information Theory
Java and Operating Systems Lab.
Elective
Elective
Soft Skill*
Theory of Computation
Computer Networks
Advanced Database Systems
Advanced Database Systems Lab.
Elective
Elective
Soft Skill*
Artificial Intelligence
Digital Image Processing
C
C
C
C
E
E
S
C
C
C
C
E
E
S
C
C
3-1-0-4
3-0-1-4
3-1-0-4
0-0-2-2
3-0-0-3
3-0-0-3
2-0-0-2
3-1-0-4
3-1-0-4
3-0-0-3
0-0-2-2
3-0-0-3
3-0-0-3
2-0-0-2
3-0-0-3
3-1-0-4
Multimedia Systems
Mini Project
Elective
C
C
E
3-0-1-4
0-0-2-2
3-0-0-3
Guest Faculty(G.F.)
P.Thangavel
P.Thangavel
GuestFaculty
Faculty Concerned
Faculty Concerned
Faculty Concerned
M.Sornam/G.F.
P.Thangavel
B.Lavanya/G.F.
B.Lavanya/G.F.
Faculty Concerned
Faculty Concerned
Faculty Concerned
M.Sornam/G.F.
P.Thangavel/
PL.Chithra
B.Lavanya
All Faculty
Faculty Concerned
Elective
E
3-0-0-3
Faculty Concerned
UOMS003
Soft Skill*
S
2-0-0-2
Faculty Concerned
UOMS004
Soft Skill*
S
2-0-0-2
Faculty Concerned
UOMI001
Internship-I
S
2-0-0-2
Faculty Concerned
MSIC416
Project Work
C
0-0-20-20
UOMS001
MSIC405
MSIC406
MSIC407
MSIC408
UOMS002
MSIC409
MSIC410
MSIC415
MSIC412
All Faculty
Additional list of Elective courses:
Course
Code
MSIE401
MSIE402
MSIE403
MSIE404
MSIC401
Electiv
e
E
E
E
E
Title of the Courses
Computer Graphics
Cryptography
Unix and Shell Programming
Network Programming and .NET
Mathematics for Computer Science
3 1
Credits
L-T-P-C
3-0-0-3
3-0-0-3
3-0-0-3
3-0-0-3
0
4
Course Faculty
S.Gopinathan
P.Thangavel/G.F.
Guest Faculty
Guest Faculty
Guest Faculty
Set theory: Operations on sets – Basic set identities – Relations and orderings – Functions. Linear vector spaces: Linear
operators – vectors in n-dimensions – matrix representation of vectors and operators in a basis – linear independence,
dimension – inner product – Schwarz inequality – Orthonormal basis – Gram-Schmidth process – Eigen values and
eigen functions of operators/matrices – Hermitian and Unitary operators/matrices – Cayley Hamilton theorem –
Diagonalizing matrix. Linear differential equations: Second order linear differential equations – Strum-Liouville theory
– Orthogonality of eigen functions – Illustration with Legendre, Laguerre, Hermite, Chebyshev differential equations expansion of polynomials – location of zeros polynomials – Wronskian, ordinary and singular points – Dirac delta
function. Laplace and Fourier transforms: Laplace Transforms – Solution of linear differential equations with constant
coefficients – Fourier integral – Fourier transform – Fourier sine and cosine transforms – convolution theorems.
MSIC402
Design and Analysis of Algorithms
3 0
1
4
P. Thangavel
Introduction - asymptotic time analysis. Divide and conquer Method: binary search, finding maximum and minimum,
merge sort and quick sort. Greedy method: optimal storage on tapes, knapsack problem, minimum spanning trees and
single source shortest path problem. Dynamic programming: multistage graphs, 0/1 knapsack and traveling salesman
34
problem. Basic search and traversal techniques - Bi-connected components, depth first search. Backtracking: 8 queens
problem, sum of subsets, graph coloring, Hamiltonian cycle and knapsack problem. Branch and bound: 0/1 knapsack
problem, traveling salesman problem.
MSIC414
Information Theory
3
1 0 4 P.Thangavel
Basics of Probability – conditional and joint probability – Baye’s theorem. Models for Information channel: Discrete
Memoryless Channel, Binary Symmetric Channel (BSC), Burst Channel, Bit-error rates. Entropy and Shannon’s measure
of Information. Channel capacity theorem. Rate and Optimality of Information transmission. Variable Length Codes:
Prefix Codes, Huffmann Codes, Lempel-Zev (LZ) Codes. Optimality of these codes, Information Content of these
Codes. Error Correcting and Detecting Codes: Finite fields, Hamming distance, Bounds of Codes, Linear (Parity Check)
codes, Parity Check Matrix, Generator matrix, Decoding of Linear codes, Hamming Codes.
MSIC404
Java and Operating systems lab.
0
0 2 2 Guest Faculty
Java Programming: HTML to Servlet Applications - Applet to Servlet Communication - Designing online applications
with JSP - Creating JSP program using JavaBeans - Working with Enterprise JavaBeans - Performing Java Database
Connectivity - Creating Web services with RMI - Creating and Sending Email with Java - Building web applications.
Operating systems: Inter Process Communication (IPC) using Message Queues - IPC using pipes - Implementation of
wait and signal using counting semaphores -Implementation of wait and signal using binary semaphores - Atomic
Counter update problem -Counting Semaphores at the user level using binary semaphores- Signaling processes Deadlock detection (for processes passing messages) - Process Scheduling: FCFS , Least Frequently Used, Round Robin
- Producer-Consumer problem with limited buffers - Dining-Philosopher Problem - Reader-Writer problem - Two
Process Mutual Exclusion.
MSIC405
Theory of Computation
3
1 0 4 M.Sornam/G.F.
Introduction to finite Automata – Regular expression and languages – Algebraic Laws for regular expressions –
Properties of regular languages – Pumping Lemma for regular expressions – Closure properties of regular languages –
Decision properties of regular languages – Equivalence and minimization of Automata – Parse trees – Applications of
context free grammars – Parsers – ambiguity in grammars and languages – Pushdown Automata – Properties of
Context free languages – Introduction to Turing Machines – programming techniques for Turing Machines –
Undecidability – Post’s correspondence problem – other undecidable problems.
MSI C406
Computer Networks
3
1 0 4 P.Thangavel
Goals and Applications of networks - Network Architectures - OSI reference model and services - Network topology Physical layer - Transmission media - switching methods- Data link layer Design issues - error detection and correction
- elementary data link protocols - sliding window protocols. MAC sublayer – general protocols. Network layer-design
issues- Routing algorithms - Shortest path, Multipath, Centralized, Isolated, Flooding, Distance vector, link state,
Hierarchical & Broadcasting - Congestion control algorithms - pre allocation of buffer, packet discarding, flow control,
choke packets. Transport layer - design issues - Connection management - Addressing, Establishing & Releasing a
connection, Timer based Connection Management, Multiplexing, Crash Recovery.
MSIC407
Advanced Database Systems
3
0 0 3 B.Lavanya/Guest Faculty
Purpose of Database Systems-Data models-Relational-hierarchical-network –relational calculus-relation algebra-DBATransaction Mgmt-Entity Relationship Diagrams-Normalization-SQL-QBE-QUEL-Query processing & interpretationQuery optimization-database recovery-security and integrity-object-based databases and XML-database system
architecture-distributed databases-parallel databases-Application development and administration – advanced
querying and information retrieval – advanced transaction processing-Case studies-Oracle , Microsoft SQL Server.
MSIC408
Advanced Database Systems Lab.
0
0 2 2 B.Lavanya/Guest Faculty
Library management system - bank transactions – inventory transaction system - question database and conducting
quiz – creation of character animation – designing web pages – creation of image animation –applications to show the
masking effect etc.
MSIC409
3 0 0 3 M.Sornam / G.F.
Artificial Intelligence
35
Evolution of A.I- Production system-Search strategies-Hill climbing-Backtracking graph search-Algorithm A & A*- AO*
algorithm. Adversarial search-Searching game trees-Minimax Procedure, alpha beta pruning-Reactive machinesStimulus-Response Agents-Knowledge Representation & reasoning – Predicate Calculus-Knowledge based systemsReasoning using Horn clauses- Maintenance in Dynamic Knowledge bases- Rule learning- Knowledge representation
by networks-Semantic Networks- non-monotonic reasoning, frames, scripts-Natural Languages processing –
RTN,ATN,Parsing of CFGs-Probabilistic Theory- Bayes Networks-Communication & Integration –Multiple agents.
MSIC410
Digital Image Processing
3
1 0 4 P.Thangavel/PL.Chithra
Introduction – steps in image processing, Image acquisition, representation, sampling and quantization, relationship
between pixels. – color models – basics of color image processing.
Image enhancement in spatial domain – some basic gray level transformations – histogram processing – enhancement
using arithmetic , logic operations – basics of spatial filtering and smoothing. Image enhancement in Frequency domain
– Introduction to Fourier transform: 1- D, 2 –D DFT and its inverse transform, smoothing and sharpening filters. Image
restoration: Model of degradation and restoration process – noise models – restoration in the presence of noise- periodic
noise reduction.. Image segmentation: Thresholding and region based segmentation. Image compression: Fundamentals
– models – information theory – error free compression –Lossy compression: predictive and transform coding. JPEG
standard.
MSI C415
Multimedia Systems
3
0 1
4 B.Lavanya
Evaluation of Multimedia - Components of Multimedia system - Hardware - Multimedia PC-Memory and Storage
devices for multimedia - ODD and CD Technology and standards - Input devices - Output devices - Communication
devices and peripheral connections. Software components of multimedia - text, audio, image and video processing Elementary and Authoring tools - Interactive video and 3D Graphics in Multimedia. Multimedia Information Systems Extending RDBMS to Image Management Systems, and voice Information Systems - MPEG, JPEG, DVI and UVC
standards applied to multimedia and Distributed Information Systems. Organizing, Deign, production and Testing of
Multimedia projects. Case studies in Education - Industrial Design - Presentation of software and concepts of virtual
reality – video compression, audio compression, video conferencing and mobile multimedia.
MSIC412
Mini Project
0
0 2
2
Each student will carry out a project on a selected problem and submit a report.
All Faculty
MSIC416
Project Work
0
0 20
Each student will do a project work and submit report of work carried out.
All Faculty
MSI E401
Computer Graphics
3
20
0 0 3 S.Gopinathan
Line Generation : Circle Generation - Graphics Primitives - Display devices - Display file co-ordinates - Polygons :
Polygon Filling - Scaling, Rotation & Translation Transformations - Display procedures - Segments - Segment
manipulation - Raster Techniques - Windowing and Clipping - Device handling algorithms - Simulating devices Echoing - Interactive Techniques - 3D Fundamentals - Projections - Clipping in 3D- 3D viewing transformation Hidden surfaces and lines. Dimension - Binary space partition- Light, color and shading - Transparency - Shadows Ray tracing - Halftones - Color - Gamma correction - Fractals - Splines.
MSI E402
Cryptography
3
0 0 3 P.Thangavel/G.F.
Conventional Encryption: Conventional encryption model – DES –RC 5 – Introduction to AES - Random number
generation. Number Theory: Modular arithmetic – Euler’s theorem – Euclid’s algorithm – Chinese remainder theorem –
Primarily and factorization –Discrete logarithms – RSA algorithm - Public key Cryptography: Principles – RSA
algorithm – key management- Diff – Hellman key exchange - Message Authorization and Hash functions: Hash
functions-Authentication requirements –Authentication function- Message authentication codes –Secure Hash
algorithms - Digital Signature and Authentication Protocols : Digital Signature-Authentication Protocols –Digital
signature standard.
MSIE403
Unix and Shell Programming
2
36
1 0 3 PL.Chithra
File and Common Commands - Shell – Directories – Devices – Permission – The Grep Family Filters – Streams – Concepts of
Shell – Trapping Exit Codes- Shell Programming – Standard Input/Output – file Access – System Calls-Interprocess
Communication-DeadLock
Detection-Scheduling
algorithmsInodes
–
Processes
–
SignalsInterrupts – Preprocessors – Manual Page.
MSI E404
Network Programming and .NET
3
0 0
3 M.Sornam and B.Lavanya
OOPs Fundamentals – Programming Concepts – Application Frame Work, Project Utility – MFC Library – Bar Chart
with Resources. Graph Applications – Word Processor Applications – OLE Features and Specifications Continual
Application, ActiveX Controls, Com – DHTML – ATL Vs ACTIVEX-Overview of ActiveX Scripting-Java Scripting –
Standalone scripts-ActiveX Controls- Creating ActiveX Controls- ActiveX Documents- ActiveX Document ArchitectureURL Monikers- Hyper linking interface- Working with URL Monikers- Overview of ISAPI- ISAPI Extension-ISAPI
Filter-Designing IIS Application-Building IIS Application-Building Data Driven DHTML Application- ActiveX
documents-Technology Migration Wizard-Modified Code-Launching and Testing document-Testing the DLL.
“Beginning ASP.NET 1.1 with VB.NET 2003” -- Chris Ullman,John Kauffman, Chris Hart, David Sussmann.--- Wiley
Publishing Inc. , WROX.
Introduction – Server Controls and variables – Control structures – Procedural Programming – Subroutines and Functions – Event
driven programming – Objects – Database Management – ADO.NET – ASP.NET Server Controls – Web Controls - .NET Assemblies –
Error Handling – Web Services – ASP.NET Security.
MASTER OF PHILOSOPHY PROGRAMME
M.Phil in Computer Science (Full Time )
Duration of the course : One Year (Two Semester )
Eligibility for Admission :
A Masters Degree in Computer Science or Information Technology or M.C.A. Degree of the University of Madras
or any other University recognized by the Syndicate as equivalent thereto, provided that those who have qualified for
the Master’s Degree prior to 1st January 1991 must have secured a minimum of 50 percent of marks and those who have
qualified for the master’s degree on or after 1st January 1991 must have secured a minimum of 55 percent of marks. For
SC/ST candidates who have qualified on or after 1st January 1991 a concession of 5 percent of marks shall be given in
the minimum eligibility marks
Course Code
Title of the Courses
First Semester
MSI C101
MSI C102
MSI E101
MSI E102
MSI E103
MSI E104
Second Semester
MSI C103
Core/
Electi
ve
L-T-P-C
Faculty
Research Methodology
Advance course on Computing
Selected Topics in Algorithms
C
C
E
3-2-0-5
3-2-0-5
3-2-0-5
Artificial Neural Networks
Digital Image Processing
Wireless Networks
E
E
E
3-2-0-5
3-2-0-5
3-2-0-5
Guest Faculty
P.Thangavel
P.Thangavel/G.F
.
P.Thangavel/G.F
P.Thangavel/G.F
P.Thangavel/G.F
Dissertation and Viva-voce
C
6+15=21
37
P.Thangavel/G.F
.
M.Sc. Computer Science (Self Supportive)
Eligibility for Admission to Master of Science in Computer Science
Bachelor's degree in Computer Science or Computer Science & Technology or B.C.A. degree of University of
Madras or any other degree accepted as equivalent thereto by the Syndicate.
M.Sc. Degree Programme in Computer Science – List of Core Courses
Core/E
Course Code
Title of the Courses
lective
MSIC401
Mathematics for Computer Science
C
MSIC402
Design and Analysis of Algorithms
C
38
Credits
L-T-P-C
3-1-0-4
3-0-1-4
Course Faculty
Guest Faculty(G.F.)
P.Thangavel
MSIC414
MSIC404
Information Theory
Java and Operating Systems Lab.
Elective
Elective
Soft Skill*
Theory of Computation
Computer Networks
Advanced Database Systems
Advanced Database Systems Lab.
Elective
Elective
Soft Skill*
Artificial Intelligence
Digital Image Processing
C
C
E
E
S
C
C
C
C
E
E
S
C
C
3-1-0-4
0-0-2-2
3-0-0-3
3-0-0-3
2-0-0-2
3-1-0-4
3-1-0-4
3-0-0-3
0-0-2-2
3-0-0-3
3-0-0-3
2-0-0-2
3-0-0-3
3-1-0-4
Multimedia Systems
Mini Project
Elective
C
C
E
3-0-1-4
0-0-2-2
3-0-0-3
P.Thangavel
GuestFaculty
Faculty Concerned
Faculty Concerned
Faculty Concerned
M.Sornam/G.F.
P.Thangavel
B.Lavanya/G.F.
B.Lavanya/G.F.
Faculty Concerned
Faculty Concerned
Faculty Concerned
M.Sornam/G.F.
P.Thangavel/
PL.Chithra
B.Lavanya
All Faculty
Faculty Concerned
Elective
E
3-0-0-3
Faculty Concerned
UOMS003
Soft Skill*
S
2-0-0-2
Faculty Concerned
UOMI001
Internship-I
S
2-0-0-2
Faculty Concerned
MSIC416
Project Work#
C
0-0-22-22
UOMS004
Soft Skill**
S
2-0-0-2
UOMS001
MSIC405
MSIC406
MSIC407
MSIC408
UOMS002
MSIC409
MSIC410
MSIC415
MSIC412
All Faculty
Faculty Concerned
** Instead of UOMS004: Soft Skill , any other additional elective course may be opted by M.Sc. Computer Science
students, so as to earn 88 credits.
Additional list of Elective courses:
Course
Title of the Courses
Code
MSIE401
Computer Graphics
MSIE402
Cryptography
MSIE403
Unix and Shell Programming
MSIE404
Network Programming and .NET
MSIC414
Information Theory
Electiv
e
E
E
E
E
3
Credits
L-T-P-C
3-0-0-3
3-0-0-3
3-0-0-3
3-0-0-3
Course Faculty
S.Gopinathan
P.Thangavel/G.F.
Guest Faculty
Guest Faculty
1 0 4 Guest Faculty
Basics of Probability – conditional and joint probability – Baye’s theorem. Models for Information channel: Discrete
Memoryless Channel, Binary Symmetric Channel (BSC), Burst Channel, Bit-error rates. Entropy and Shannon’s measure
of Information. Channel capacity theorem. Rate and Optimality of Information transmission. Variable Length Codes:
Prefix Codes, Huffmann Codes, Lempel-Zev (LZ) Codes. Optimality of these codes, Information Content of these
Codes. Error Correcting and Detecting Codes: Finite fields, Hamming distance, Bounds of Codes, Linear (Parity Check)
codes, Parity Check Matrix, Generator matrix, Decoding of Linear codes, Hamming Codes.
MSI C415
Multimedia Systems
3
0 1
4 B.Lavanya
Evaluation of Multimedia - Components of Multimedia system - Hardware - Multimedia PC-Memory and Storage
devices for multimedia - ODD and CD Technology and standards - Input devices - Output devices - Communication
devices and peripheral connections. Software components of multimedia - text, audio, image and video processing Elementary and Authoring tools - Interactive video and 3D Graphics in Multimedia. Multimedia Information Systems Extending RDBMS to Image Management Systems, and voice Information Systems - MPEG, JPEG, DVI and UVC
standards applied to multimedia and Distributed Information Systems. Organizing, Deign, production and Testing of
Multimedia projects. Case studies in Education - Industrial Design - Presentation of software and concepts of virtual
reality – video compression, audio compression, video conferencing and mobile multimedia.
MSIC416
Project Work
0
39
0 22
22
All Faculty
Each student will do a project work and submit report of work carried out.
MSIE403
Unix and Shell Programming
2
1 0 3 PL.Chithra
File and Common Commands - Shell – Directories – Devices – Permission – The Grep Family Filters – Streams – Concepts of
Shell – Trapping Exit Codes- Shell Programming – Standard Input/Output – file Access – System Calls-Interprocess
Communication-DeadLock
Detection-Scheduling
algorithmsInodes
–
Processes
–
SignalsInterrupts – Preprocessors – Manual Page.
MSI E404
Network Programming and .NET
3
0 0
3 M.Sornam and B.Lavanya
OOPs Fundamentals – Programming Concepts – Application Frame Work, Project Utility – MFC Library – Bar Chart
with Resources. Graph Applications – Word Processor Applications – OLE Features and Specifications Continual
Application, ActiveX Controls, Com – DHTML – ATL Vs ACTIVEX-Overview of ActiveX Scripting-Java Scripting –
Standalone scripts-ActiveX Controls- Creating ActiveX Controls- ActiveX Documents- ActiveX Document ArchitectureURL Monikers- Hyper linking interface- Working with URL Monikers- Overview of ISAPI- ISAPI Extension-ISAPI
Filter-Designing IIS Application-Building IIS Application-Building Data Driven DHTML Application- ActiveX
documents-Technology Migration Wizard-Modified Code-Launching and Testing document-Testing the DLL.
“Beginning ASP.NET 1.1 with VB.NET 2003” -- Chris Ullman,John Kauffman, Chris Hart, David Sussmann.--- Wiley
Publishing Inc. , WROX.
Introduction – Server Controls and variables – Control structures – Procedural Programming – Subroutines and Functions – Event
driven programming – Objects – Database Management – ADO.NET – ASP.NET Server Controls – Web Controls - .NET Assemblies –
Error Handling – Web Services – ASP.NET Security.
MASTER OF PHILOSOPHY PROGRAMME
M.Phil in Computer Science (Full Time )
Duration of the course : One Year (Two Semester )
Eligibility for Admission :
A Masters Degree in Computer Science or Information Technology or M.C.A. Degree of the University of Madras
or any other University recognized by the Syndicate as equivalent thereto, provided that those who have qualified for
the Master’s Degree prior to 1st January 1991 must have secured a minimum of 50 percent of marks and those who have
qualified for the master’s degree on or after 1st January 1991 must have secured a minimum of 55 percent of marks. For
SC/ST candidates who have qualified on or after 1st January 1991 a concession of 5 percent of marks shall be given in
the minimum eligibility marks
Course Code
Title of the Courses
First Semester
MSI C101
MSI C102
MSI E101
MSI E102
MSI E103
MSI E104
Second Semester
MSI C103
Core/
Electi
ve
L-T-P-C
Faculty
Research Methodology
Advance course on Computing
Selected Topics in Algorithms
C
C
E
3-2-0-5
3-2-0-5
3-2-0-5
Artificial Neural Networks
Digital Image Processing
Wireless Networks
E
E
E
3-2-0-5
3-2-0-5
3-2-0-5
Guest Faculty
P.Thangavel
P.Thangavel/G.F
.
P.Thangavel/G.F
P.Thangavel/G.F
P.Thangavel/G.F
Dissertation and Viva-voce
C
6+15=21
40
P.Thangavel/G.F
.
Department of Statistics
M.Sc Actuarial Science (Proposed Syllabus for the academic year 2007 - 08)
A – CORE COURSES
Title of the Course
Course Code
C/E/S
L
T
P
C
I SEMESTER
MSI C 201
Probability Theory
C
3
1
0
4
MSI C 202
Financial Mathematics – I
C
3
1
0
4
MSI C 203
Probability Distributions
C
3
1
0
4
MSI C 215
Principles and Practice of Insurance
Elective 1
C
E
2
2
0
1
0
0
2
3
Elective 2
E
2
1
0
3
Soft Skill
S
MSI C 204
Survival Models
C
3
1
0
4
MSI C 205
Statistical Inference
C
3
1
0
4
MSI C 206
Financial Mathematics – II
C
3
1
0
4
MSI C 216
MSI C 207
Life Contingencies – I
Computational Laboratory - I
Elective 3
C
C
E
3
0
2
1
0
1
0
2
0
4
2
3
Elective 4
E
2
1
0
3
Soft Skill
S
MSI C 209
Stochastic Modeling
C
3
1
0
4
MSI C 210
Risk Models
C
3
1
0
4
MSI C 217
MSI C 218
Life Contingencies – II
Financial Economics
C
C
3
2
1
1
0
0
4
3
Elective 5
Soft Skill
Internship
E
S
S
2
1
0
UOM S003
UOM I001
3
2
2
MSI C 219
Joint Life and Pension Benefits
C
3
1
0
4
MSI C 212
Corporate Financial Management
C
2
1
0
3
MSI C 213
MSI C 214
Computational Laboratory - II
Project & Viva voce
C
C
0
3
0
1
2
0
2
4
Elective 6
E
2
1
0
3
Soft Skill
S
UOM S001
2
II SEMESTER
UOM S002
2
III SEMESTER
IV Semester
UOM S004
41
2
B – ELECTIVE COURSES :
Course
Code
MSI E 201
Title of the Course
L
T
P
C
Object oriented programming with C++
3
0
0
3
MSI E 202
Principles of Economics
3
0
0
3
MSI E 204
Numerical Methods
3
0
0
3
MSI E 205
Finance and Financial Reporting
3
0
0
3
MSI E 207Resource optimization principles
3
0
0
3
MSI E 208
1
0
2
3
Data Analysis using R & SAS
42
Syllabi for various Courses of M.Sc. (Br. II(B)) Actuarial Science
MSI C201 PROBABILITY THEORY
UNIT 1 : Sample space – events. Random variables – distribution functions and its properties – moments – expectation – variance –
conditional probability – Baye’s theorem – computational probabilities – simple problems from Industrial and Actuary.
UNIT 2 : Moment generating function – pgf – cumulant generating functions – evaluation of moment using these
functions – functions of random variables – simple applications.
UNIT 3 : Characteristic functions – properties – inversion formulae – uniqueness theorem – moments problem – Levy
Cramer theorems – simple problems.
UNIT 4 : Independence – pairwise and complete independence - convolution - conditional expectation - smoothing
properties – Martingales – simple problems.
UNIT 5 : Laws of large numbers weak and strong law of large numbers – simple applications – central limit theorems
(iid and id) – normal approximation – simple applications.
Books for Study and Reference :
Bhat, B.R. (1999) : Modern Probability Theory, 3rd ed. New Age International Pvt.
Ltd., New Delhi.
Ash, R.B. (1972) : Real Analysis and Probability, Academic press, New York.
Ross,Sheldon,M.(1984): A First Course in Probability, 2nd ed. McMillan, New York.
Freund, JE (1998) : Mathematical Statistics, Prentice Hall International.
MSI C202 FINANCIAL MATHEMATICS - I
UNIT 1 : Rates of interest – Simple and Compound interest rates –Effective rate of interest - Accumulation and Present
value of a single payment – Nominal rate of interest – Constant force of interest  - Relationships between these rates of
interest - Accumulation and Present value of single payment using these rates of interest – accumulation and present value
of a single payment using these symbols - when the force of interest is a function of t, (t). Definition of A(t1, t2), A(t), (t1, t2)
and (t). Expressing accumulation and present value of a single payment using these symbols - when the force of interest is a
function of t, (t).
UNIT 2 : Series of Payments(even and uneven) - Definition of Annuity(Examples in real life situation) – Accumulations and
Present values of Annuities with level payments and where the payments and interest rates have same frequencies Definition and Derivation of
an
,
sn
,
an
,
sn
, Definition of Perpetuity and derivation for
a
and
a
-Examples
- Accumulations and Present values of Annuities where payments and interest rates have different frequencies. Definition
and derivation of
a n( p ) , an( p ) , s n( p ) , sn( p )
UNIT 3 : Increasing and Decreasing annuities – Definition and derivation for
an
sn
,
( I s) n
increasing continuously and payable continuously – definition and derivation of
( I a) n
payable continuously - Definition and derivation of
,
( I a) n
( Ia) n
,
,
( Is) n
and
( Da) n
- Annuities
- Annuities where payments are
,
( I s) n
.
UNIT 4 : Loan schedules – Purchase price of annuities net of tax – Consumer credit transactions
UNIT 5 : Fixed interest securities – Evaluating the securities – Calculating yields – the effect of the term to redemption
on the yield – optional redemption dates – Index linked Bonds – evaluation of annuities subject to Income Tax and
capital gains tax.
Books for Study and Reference :
Institute of Actuaries ActEd. Study Materials.
McCutcheon, J.J., Scott William, F. (1986) : An introduction to Mathematics of Finance,
London Heinemann
43
Butcher,M.V.,Nesbitt, Cecil,J. (1971) : Mathematics of compound interest, Ulrich’s
Books.
Bowers, Newton L.et al (1997):Actuarial Mathematics, Society of Actuaries, 2nd ed.
MSI C203
PROBABILITY DISTRIBUTIONS
UNIT 1 : Discrete distributions – Binomial – Poisson – Multinomial – Hyper geometric – Geometric – discrete uniform –
their characteristics and simple applications.
UNIT 2 : Continuous distributions – Uniform - Normal – exponential – Gamma – Weibull – Pareto – lognormal –
Laplace – logistic distributions – their characteristics and applications.
UNIT 3 : Bivariate and Multivariate Normal – Compound and truncated distributions – convolutions of distributions.
UNIT 4 : Sampling distributions t, 2 and F distributions and their interrelations and characteristics – order statistics and
their distribution – distribution of sample and mid range.
UNIT 5 : Applications of multivariate – normal distributions – principal components analysis – discriminant analysis –
factor analysis – cluster analysis – Canonical correlations.
Books for Study and Reference :
Fruend, John, E. (1992) : Mathematical Statistics, 5th ed., Prentice Hall International.
Forguson, T.S. (1967) : Mathematical Statistics, Academic Press, New York.
Gibbons, J.D. (1985) : Non parametric Statistical Inference, Marcel Dekker, New York.
Hogg,R.V. & Craig (1972): Introduction to Mathematical Statistics, 3rd ed., McGraw Hill
Johnson, R.A. and Wichern, D.W. (1982) : Applied Multivariate Statistical Analysis, 2nd ed., Prentice Hall, Englewood
Cliffs, New Jersey.
Mood, A.M., Graybill, F.A., and Boes, D.C. (1974) : An introduction to the theory of
Statistics, 3rd ed. McGraw Hill Book company
Rohatgi, V.K. and Ebsanes Saleh, A.K. Md. (2002) : An introduction to Probability and
Statistics, 2nd Ed., John Wiley & Sons, Inc., New York.
MSI C215
PRINCIPLES AND PRACTICE OF INSURANCE
UNIT 1 : Concept of Risk- The concept of Insurance.Classification of Insurance- Types of Life Insurance, Pure and
Terms- Types of General Insurance, Insurance Act, Fire, Marine, Motor, Engineering, Aviation and Agricultural Alternative classification- Insurance of Property, Pecuniary interest, liability and person. Distribution between Life and
General Insurance.History of Insurance in general in India. Economic Principles of Insurance – Insurance regulatory
and development Act.
UNIT 2 : Legal Principles of Insurance- The Indian Contract Act, 1872- insurable interest - Utmost Good faithindemnity- subrogation – Contribution- Proximate Cause - Representations- Warranties- Conditions. Theory of ratingActuarial principles- Mortality Tables- Physical and Moral Hazard. Risk appraisal- Risk Selection- Underwriting.
Reinsurance- Concept and Methods.
UNIT 3 : Life insurance organisation : The Indian context. The distribution system, function of appointment and continuance of
agency, remuneration to aents, trends in Life insurance distribution channels.Plans of Life Insurance – need levels, term life
insurance increasing / decreasing term policy, whole life insurance, endowment insurance, money back endowment plan, marriage
endowment plan, education annuity plan, children deferred assurance plans, annuities. Group insurance – nature of group insurance,
types of group insurance, gratuity liability, group superannuating scheme, other group schemes, social security schemes. Other
special need plan – industrial life insurance, salary saving scheme, disability plans – critical illness plans.
UNIT 4 : Application and acceptance – prospectus – proposal forms and other related documents, age proof, special reports. Policy
document – need and format – preamble, operative clauses, proviso, schedule, attestation, conditions and privileges, alteration,
duplicate policy.
UNIT 5 : Premium, premium calculation, Days of grace, Non-Forfeiture options, lapse and revival schemes. Assignment
nominations loans – surrenders, foreclosures, Married Women’s property Act Policy, calculations. Policy claims,
maturity claims, survival benefit payments, death claims, waiver of evidence of title, early claims, claim concession,
presumption of death, Accident Benefit and Disability Benefit , settlement options, Valuations and Bonus, distribution of
surplus. Types of re-insurance, exchange control regulations, payment of premia, payment of claims etc.
Books for study and Reference :
44
Neill, Alistair, Heinemann, (1977) : Life contingencies.
Gerber, Hans, U. (1997) : Life insurance mathematics, Springer, Swiss Association of
Actuaries.
Booth,Philip,M.et al(1999):Modern Actuarial theory and practice, Chapman & Hall.
Daykin,Chris,D. et al(1994): Practical risk theory for Actuaries, Chapman and Hall.
Panjer, Harry,H. (1998) : Financial economics with applications to investments,
Insurance and pensions. The Actuarial foundation.
MSI C204 SURVIVAL MODELS
UNIT 1 : Concept of Survival Models
UNIT 2 : Estimation procedures of Life time Distributions – Cox Regression model – Nelson and Aalen Estimates
UNIT 3 : Two state Markov Model
UNIT 4 : Multi state Markov Models - Statistical Models of transfers between multiple states, Derivation of
relationships between probabilities of transfer and transition intensities. Maximum Likelihood Estimators(MLE) for the
transition intensities in models of transfers between states with piecewise constant transition intensities.
UNIT 5 : Binomial and Poisson models of mortality – MLE for probability of death – Comparison with Multi state models.
Books for Study and Reference:
Institute of Actuaries Acted. Study Materials.
Neill, Allistair (1977) : Life contingencies, Heinemann.
Elandt-Johnson, Regina C; Johnson, Norman L., 2nd ed. (1999) : Survival Models and
data analysis, John Wiley.
Marubini, Ettore, Valsecchi, Marai Grazia, Emmerson, M. (1995) : Analysis of Survival
data from Clinical Trials and observation of studies, John Wiley.
MSI C205
STATISTICAL INFERENCE
UNIT 1 : Estimation Methods : Properties of a good estimator – unbiasedness – efficiency – Cramer Rao bound –
sufficiency – Methods of estimation – Methods of moments – Maximum likelihood method – minimum chisquare –
method of least squares and their properties.
UNIT 2 : Neyman Pearson theory of testing of hypothesis UMP and UMPU tests – chisquare tests – locally most
powerful tests – large sample tests – testing linear hypothesis.
UNIT 3 : Non parametric inference :
The Wilcoxon signed rank test – The Mann-Whitney – Wilcoxon Rank sum test – the runs test – chi-squire test of
goodness of fit test – Kolmogorov-Smirnov goodness of fit test – Kruskal Wallies test – Friedman test .
UNIT 4 : Confidence sets and intervals – exact and large sample confidence intervals – shortest confidence intervals.
UNIT 5 : Elements of Bayesian inference – Bayes theorem – prior and posterior distribution – conjugate and Jeffreys
priors – Baysian point estimation – minimax estimation – loss function – conflux loss functions – Bayesian interval
estimation and testing of hypothesis.
Books for Study and Reference :
Rohatgi, V.K. and Ebsanes Saleh, A.K. Md. (2002) : An introduction to Probability and
Statistics, 2nd Ed., John Wiley & Sons, Inc.
Mood, A.M. Graybill, F.A. and Boes, D.C. (1974) : An introduction to the theory of
Statistics, 3rd Ed., McGraw Hill Book Company.
MSI C206
FINANCIAL MATHEMATICS – II
UNIT 1 : Investment Project Appraisal – Discounted Cash flow techniques.
UNIT 2 : Investment and Risk characteristics of different types of Assets for Investment for investment purposes
45
UNIT 3 : Delivery price and the value of a Forward contract using arbitrage free pricing methods
UNIT 4 : Term structures of interest rates
UNIT 5 : Simple Stochastic interest rate Models
Books for Study and Reference :
Rohatgi, V.K. and Ebsanes Saleh, A.K. Md. (2002) : An introduction to Probability and
Statistics, 2nd Ed., John Wiley & Sons, Inc.
C++ Programming Exercises
Mood, A.M. Graybill, F.A. and Boes, D.C. (1974) : An introduction to the theory of
Statistics, 3rd Ed., McGraw Hill Book Company.
MSI C216
LIFE CONTINGENCIES – I
UNIT 1 : Exposed to risk
UNIT 2 : Assurance functions - Annuity functions
UNIT 3 : Life Tables
UNIT 4 : (i) Estimations of EPV’s of Assurance and Annuity functions
(ii) Net premiums & provisions
UNIT 5 : Variable benefits & with profit policies
Books for Study and Reference:
Institute of Actuaries Acted. Study Materials.
Neill, Allistair (1977) : Life contingencies, Heinemann.
Gerber, Hans U. (1997) : Life insurance Mathematics, Springer, Swiss Association of
Actuaries, 3rd edition.
MSI C207
COMPUTATIONAL LABORATORY – I
Objectives : The implementation of standard numerical algorithms are mastered and results are calculated with
precision. The strengths and limits of each algorithm are understood as well as which technique is most suitable for a
given problem. Lab time is used to master code writing in C++ .
Mathematical Exercises :
1.
Algebraic equations
1.1. Bisections method
1.2. Secant method
1.3. Newton-Raphson method
2.
System of linear equations
2.1 Gaussian Elimination
2.2 Gauss-Seidal Iteration
2.3 Gauss- Jordan Iteration
2.4 Matrix operations
3.
Interpolation and curve Fitting
1.1 Lagrange Interpolation
1.2 Newton polynomials
1.3 Straight line fitting
1.4 Curve fitting
4.
Numerical differentiation and integration
4.1 Differentiation
4.2 Trapezoidal and Simpson’s 1/3 rule
5.
Solution to differential equations
5.1 Euler method
46
5.2
5.3
5.4
Runge – Kutta method of order 2
Runge – Kutta method of order 3
Predictor – corrector method
6.
Statistical Methods
6.1 Formation of frequency distribution
6.2 Calculation of moments – mean and variance
6.3 Computation of correlations and regression coefficients
6.4 Fitting and probability distributions
6.5 ANOVA (one-way, two-way)
Statistical Exercises
6.6 Tests of significance based on t, 2 and F.
7.
Inference
7.1 Method of moments
7.2 Method of maximum likelihood
7.3 Confidence intervals based on t, 2 and F.
7.4 MP test.
MSI C209
STOCHASTIC MODELING
UNIT 1 : Stochastic process : Definitions and classification (based on state space and time) of Stochastic Processes – various types
of stochastic processes.
Markov chains : n-step TPM – classification states canonical representation of TPM – finite MC with transient states –
No Claim Discount policy – Accident Proneness.
UNIT 2 : Irreducible Markov Chain with ergodic states : Transient and limiting behaviour – first passage and related
results – applied Markov chains – industrial mobility of labor – Educational advancement – Human resource
management – term structure – income determination under uncertainty – A Markov decision process.
UNIT 3 : Simple Markov processes : Markov processes – general properties – Poisson processes – Birth problem –
death problem – birth and death problem – limiting distribution. Flexible manufacturing systems – stochastic model for
social networks – recovery, relapse and death due to disease – Health, sickness and Death model – Martial status.
UNIT 4 : Stationary processes and time series – Stochastic models for time series – the auto regressive process –
moving average process – mixed auto regressive moving average processes – time series analysis in the time domain
– Box-Jenkins model for forcasting.
UNIT 5 : Brownian motion and other Markov processes – Hitting times – maximum variable – arc sine laws – variations
of Brownian motion – stochastic integral – Ito and Levy processes – applications to Actuarial Science.
Books for Study and Reference :
Bhat, U.N. and Miller, G.K. (2002) : Elements of applied stochastic processes 3rd ed.
Wiley Inter, New York.
Brzezniak, Z and Zastawniak, T. (1998) : Basic Stochastic Processes : A course through
Exercises, Springer, New York.
Grimmett, G., Stirzaker, D. (1992) : Probability and Random Processes, Oxford
University Press.
Kulkarni, V.G. (1995) : Modelling and Analysis of Stochastic Systems, Thomson Science
and Professional.
Ross, S.M.(1996): Stochastic processes, John Wiley & Sons, Inc., New York
Institute of Actuaries : ActEd Study materials
47
MSI C210
RISK MODELS
UNIT 1 : Concept of Decision theory and its applications – Concepts of Bayesian statistics – Calculation of Bayesian
Estimators.
UNIT 2 : Calculate probabilities and moments of loss distributions both with and without simple reinsurance arrangements
– Construct risk models appropriate to short term insurance contracts and calculate MGFs and moments for the risk
models both with and without simple reinsurance arrangements. - Calculate and approximate the aggregate claim
distribution for short term insurance contracts.
UNIT 3 : Explain the concept of ruin for a risk model – Calculate the adjustment coefficients and state Lundberg’s
inequality – Describe the effect on the probability of ruin of changing parameter values and of simple reinsurance
arrangements.
UNIT 4 : Describe and apply the fundamental concepts of credibility theory – Describe and apply the fundamental concepts
of simple experience rating systems – Describe and apply techniques for analyzing a delay(or run-off) triangle and
projecting the ultimate position
UNIT 5 : Explain the fundamental concepts of a generalized linear model(GLM), and describe how a GLM may be applied.
Books for Study and Reference :
Institute of Actuaries Acted. Study Materials.
Hossack, Ian B; Pollard, John H; Zenhwirth, Benjamin (1999) : Introductory Statistics
with applications in General Insurance, Cambridge University Press. 2nd ed.
Klugman, Stuart A. et al. (1998) : Loss Models: from data to decisions, John Wiley
Daykin Chris, D; Pentikainen, Teivo; Pesonen, Martti (1994) : Practical Risk theory for
Actuaries, Chapman & Hall.
MSI C217
LIFE CONTINGENCIES – II
UNIT 1 : Gross premiums and provisions
UNIT 2 : Profit Testing
UNIT 3 : Determining provisions using profit testing
UNIT 4 : Factor affecting mortality & selections
UNIT 5 : Single figure indices
Books for Study and Reference:
Institute of Actuaries ActEd. Study Materials.
Benjamin, B. Pollard, J.H. (1993) : The analysis of mortality and other actuarial
statistics, Faculty and Institute of Actuaries, 3rd ed.
Gerber, Hans U. (1997) : Life insurance Mathematics, Springer, Swiss Association of
Actuaries, 3rd ed.
Booth, Philip M et al., (1999) : Modern Actuarial Theory and Practice, Chapman &
Hall.
Bowers, Newton L.et al (1997):Actuarial Mathematics, Society of Actuaries, 2nd ed.
MSI C218
FINANCIAL ECONOMICS
UNIT 1: Introduction to Financial Economics: - Recap of Utility Theory. The Efficient Markets Hypothesis: The three forms of
EMH - The Evidence for or against each form of EMH.
UNIT 2: Measures of Investment Risk: - Measures of Risk - Relationship between Risk measures and Utility Functions.
UNIT 3: Portfolio Theory: - Portfolio Theory - Benefits of Diversification.
48
UNIT 4: Models of Asset Returns: - Multifactor Models - The Single Index Model.
UNIT 5: Asset Pricing Models: - The Capital Asset Pricing Models (CAPM) – Limitations of CAPM – Arbitrage Pricing Theory
(APT).
Books for Study and Reference :
Institute of Actuaries ActEd , CT8 Study material.
Panjer, Harry, H. (1998) : Financial economics : with applications to investments,
insurance and pensions. The Actuarial foundations.
MSI C219 JOINT LIFE AND PENSION BENEFITS
UNIT 1 : Simple annuities and assurances involving two lives.
UNIT 2 : Contingent and reversionary benefits
UNIT 3 : Competing risks
UNIT 4 : Multiple decrement tables
UNIT 5 : Pension benefits
Books for Study and Reference:
Institute of Actuaries ActEd. Study Materials.
Benjamin, B. Pollard, J.H. (1993) : The analysis of mortality and other actuarial
statistics, Faculty and Institute of Actuaries, 3rd ed.
Booth, Philip M et al., (1999) : Modern Actuarial Theory and Practice, Chapman &
Hall.
Gerber, Hans U. (1997) : Life insurance Mathematics, Springer, Swiss Association of
Actuaries, 3rd edition
MSI C212
CORPORATE FINANCIAL MANAGEMENT
UNIT 1 : Foundations of Finance : Time value of Money – NPV, IRR, and other Measures – Valuation of Common
Stocks and Bonds.
UNIT 2 : Investment Analysis : Modern theory of Finance – Capital Budgeting Decision Rule – Capital Budgeting and
Cash Flow Analysis – Capital Budgeting and Risk.
UNIT 3 : Variance Analysis – Importance of variance analysis – Material variance, labour variance, overhead variance.
Working capital management – Factors determining working capital – Calculation of working capital.
UNIT 4 : Financial Planning : Financial Statements and Ratio Analysis – Short-term Financial Decisions – Long-term
Financial Decisions.
UNIT 5 : Special Topics : Mergers and Acquisitions and Corporate Governance – Options and Corporate Finance.
Books for Study and Reference :
Brealey, Myers and Marcus : Fundamentals of Corporate Finance, McGraw Hill.
Ross, Westerfield and Jordan : Fundamentals of Corporate Finance, Tata McGraw Hill.
Van Home and Wachowicz : Fundamentals of Financial Management, Prentice Hall
India.
MSI C213 COMPUTATIONAL LABORATORY – II
Objectives :

To provide exposure to Mathematical / Statistical software focusing more on writing source codes.

To analyse the given data by identifying appropriate tools.
49
Mathematical and Statistical Packages Exercises. S Plus/ SAS/ MAPLE/
MATHEMATICA/ MATLAB
1.
2.
3.
Data Analysis : Identifying the statistical tool and analysing the data using the appropriate tools.(S PLUS/ SAS)
Symbolic manipulation using MAPLE/ MATHEMATICA
Exercises based on the subjects taught in III & IV semesters.
(ie. Survival Analysis – Stochastic Models etc.)
Simulation study depending upon the requirement of the problem. (MATLAB)
MSI C214
PROJECT & VIVA VOCE
Objectives :

To provide written, oral and visual presentation skills

To develop team work.
Course Outline : Based on the interest of the students, they can choose their team and seminar topic. It can also an
individual work. During the term, students will meet periodically the faculty to discuss different stages of the seminar.
They are required to give three seminar presentations.
Project Work/ Internship :
Objectives : To develop student’s abilities to solve applied industrial and actuarial problems in a longer time frame
than in usual in other courses. Students will learn how to search for known results and techniques related the project
work. The students will present their project results as a written document and verbally.
Prerequisite : Completion of the course duration of first two semesters.
Course Outline :
The faculty will propose an array of problems in industrial / actuarial studies. Students may choose a problem
from this list or propose of their own provided a faculty member / Guide approves it. This work may also be carried
out as an internship programme.
On completion of the project work, each student is expected to



Submit a written document describing the results, mathematical developments, background material,
bibliographical search etc.
Present orally in a seminar setting of the work done in the thesis
Submit the software (if relevant) with appropriate documentation.
The students will meet regularly with the project guide / adviser to work out problems that appear and adjust the
goals and time frame accordingly.
MSI E201 OBJECT ORIENTED PROGRAMMING WITH C++
UNIT 1 : Principles of object oriented programming – beginning with C++ - Token, Expressions and Control structures.
UNIT 2 : Functions in C++ - Classes and objects.
UNIT 3 : Constructors and Destructors – operator overloading and type conversions
UNIT 4 : Inheritance : Extending classes – Pointers, Virtual Functions and Polymorphism.
UNIT 5 : Console I/O operations – working with files – object oriented systems development – Templates and
Exception handling.
Books for Study and Reference :
50
Balagurusamy (1999) : Object oriented programming with C++, Tata McGraw Hill
Company Ltd., New Delhi, 16th reprinting.
Hubbard, J.R. (2000) : Programming with C++ 2nd ed., McGraw Hill, New York.
MSI E202
PRINCIPLES OF ECONOMICS
UNIT 1 : Market Mechanism – Supply and Demand interaction – Determination of equilibrium Elasticity of demand and
Supply – Rational utility and consumption choice – Insurance system and its impact on Welfare.
UNIT 2 : Costs Revenue and output – Market structure – short and long run equilibrium in different markets – perfect
competition, Monopoly, Monopolistic competition.
UNIT 3 : Macro Economics – Concepts of GDP, GNP, NNP – methods of calculating National Income – problems –
difficulties and uses of National Income Analysis. Propensity to consume – multiplier – determinants of consumption.
UNIT 4 : Monetary and Fiscal policy – Government intervention – financial markets – exchange rates – International
trade – Balance of payments.
UNIT 5 : Inflation types – interest rate and exchange rate – types of unemployment – public sector finances in an
industrial economy.
Books for study and Reference :
Stonier and Hague : Economic Theory
Kovtsoyiannis : Modern micro economics ELBS publications.
Samuelson Paul & Norhaus William (1998) : Economics, McGraw Hill.
Allen, R.G.D. : Mathematical analysis for Economics, Macmillan.
Panjer, Harry, H.(ed)(1998) : Financial Economics with applications to investments,
Insurance and pension. The Actuarial foundation
MSI E204
NUMERICAL METHODS
UNIT 1 : Numerical coumputing and computers – Solving non-linear equations.
UNIT 2 : Solving set of equations.
UNIT 3 : Interpolation and curve fitting.
UNIT 4 : Numerical differentiation and Numerical integration.
UNIT 5 : Numerical solution of ordinary differential equations.
Books for Study and Reference :
Gerald, C.F. and Wheatley, P.O. (1994) : Applied Numerical Analysis, Addison Wesley,
New York, 5th Ed.
Press, W.B., Flannery, S. Teuddsky and Vetterling, W. (1989) : Numerical Recipes in C :
The art of Scientific computing. Rev. 1st ed., Cambridge University Press.
Rice, John, R. (1983) : Numerical Methods, Software and Analysis, McGraw Hill,
New York.
Atkinson, K.E. (1978) : An introduction to Numerical Analysis, Wiley & Sons,
New York.
Sastry, S.S. (1987) : Introductory methods of numerical analysis, Prentice Hall of India,
New Delhi, (10th printing).
MSI E205
FINANCE AND FINANCIAL REPORTING
UNIT 1 : Introduction to Finance – Functions of Financial Management – Scope – Organisation – Sources of funds – Long term –
Medium term and Short term – Financial risks.
UNIT 2 : Company Management – Types of business entity – pros and cons of limited company – legal documentation –
corporate and personal taxation.
51
UNIT 3 : Capital structure – Net Income approach Net operating Income approach – M M approach Traditional
approach – average and personal tax of the investors – concept of cost of capital – factors affecting cost of capital –
specific and overall cost of capital.
UNIT 4 : Dividend decision and valuation of the firm – Determinants and constraints of a dividend policy – Financial
Institution – IDBI, ICICI, IFCI, UTI, Commercial Banks, Insurance companies etc.
UNIT 5 : Financial reporting – Accounting principles – types – basic financial statement – kinds of reports – Nature of
reports – guiding principles of reporting – necessary steps for good reporting.
Books for Study and Reference :
Samuels, J.M., Wilkes, F.M., Brayshaw, R.E. (1995) : Management of company finance,
International Thomson, 6th ed.
Brealey, Richard, A. (1999) : Principles of Corporate finance, McGraw Hill, 6th ed.
Holmes, Geoffrey, Sugden, Alan (1999) : Interpreting company reports and accounts,
Prentice Hall, 7th ed.
Pandey, I.M. : Financial Management.
Prasannachandra : Financial Management
Kuchhal : Financial Management
Moshal : Management Accounting
Institute of Actuaries ActEd , Study Material :
MSI E207 RESOURCE OPTIMIZATION PRINCIPLES
UNIT 1 : Linear programming problems - model formulation and graphical solution – various types of solutions – simplex
method of solving linear programming –duality principles – dual simplex method.
UNIT 2 : Artificial variable techniques Big M method – two phase method – assignment problem – transportation
problem – MODI method of finding optimal solutions.
UNIT 3 : Sequencing problem – replacement problems – game theory – zero sum games – graphical method – solution
of games by LPP.
UNIT 4 : Decision analysis – components of decision making – decision making without probabilities – maximum –
minimax regret – Hurwicz and equal likelihood criterion – decision making with probabilities – expected value –
expected opportunity loss criterion.
UNIT 5 : Network flow models – shortest route problem – project management – the CPM and PERT Networks.
Books for Study and Reference :
Sharma, J.K. (1997) : Operations Research, Theory and applications, Macmillan.
Taha, H.A. (1996) : Operations Research, 5th edition, Prentice Hall of India, New York.
MSI E208 DATA ANALYSIS USING R & SAS
Prerequisite: compulsory knowledge in Advanced Statistical Inference and Survival Analysis
UNIT 1 : Graphs, Diagrams , Descriptive Statistics and Data Exploration Techniques
UNIT 2 : Bivariate Data Analysis, Multivariate Data Analysis
UNIT 3 : Non parametric Tests
UNIT 4 : Statistical Models ,Time series Analysis
UNIT 5 : Simulation Techniques
*****
52
53
Department of Statistics
M.Sc Actuarial Science (Proposed Syllabus for the academic year 2007 - 08)
A – CORE COURSES
Title of the Course
Course Code
C/E/S
L
T
P
C
I SEMESTER
MSI C 201
Probability Theory
C
3
1
0
4
MSI C 202
Financial Mathematics – I
C
3
1
0
4
MSI C 203
Probability Distributions
C
3
1
0
4
MSI C 215
Principles and Practice of Insurance
Elective 1
C
E
2
2
0
1
0
0
2
3
Elective 2
E
2
1
0
3
Soft Skill
S
MSI C 204
Survival Models
C
3
1
0
4
MSI C 205
Statistical Inference
C
3
1
0
4
MSI C 206
Financial Mathematics – II
C
3
1
0
4
MSI C 216
MSI C 207
Life Contingencies – I
Computational Laboratory - I
Elective 3
C
C
E
3
0
2
1
0
1
0
2
0
4
2
3
Elective 4
E
2
1
0
3
Soft Skill
S
MSI C 209
Stochastic Modeling
C
3
1
0
4
MSI C 210
Risk Models
C
3
1
0
4
MSI C 217
MSI C 218
Life Contingencies – II
Financial Economics
C
C
3
2
1
1
0
0
4
3
Elective 5
Soft Skill
Internship
E
S
S
2
1
0
UOM S003
UOM I001
3
2
2
UOM S001
2
II SEMESTER
UOM S002
2
III SEMESTER
54
IV Semester
MSI C 219
Joint Life and Pension Benefits
C
3
1
0
4
MSI C 212
Corporate Financial Management
C
2
1
0
3
MSI C 213
MSI C 214
Computational Laboratory - II
Project & Viva voce
C
C
0
3
0
1
2
0
2
4
Elective 6
E
2
1
0
3
Soft Skill
S
UOM S004
2
B – ELECTIVE COURSES :
Course
Code
MSI E 201
Title of the Course
L
T
P
C
Object oriented programming with C++
3
0
0
3
MSI E 202
Principles of Economics
3
0
0
3
MSI E 204
Numerical Methods
3
0
0
3
MSI E 205
Finance and Financial Reporting
3
0
0
3
MSI E 207Resource optimization principles
3
0
0
3
MSI E 208
1
0
2
3
Data Analysis using R & SAS
55
Syllabi for various Courses of M.Sc. (Br. II(B)) Actuarial Science
MSI C201 PROBABILITY THEORY
UNIT 1 : Sample space – events. Random variables – distribution functions and its properties – moments – expectation – variance –
conditional probability – Baye’s theorem – computational probabilities – simple problems from Industrial and Actuary.
UNIT 2 : Moment generating function – pgf – cumulant generating functions – evaluation of moment using these
functions – functions of random variables – simple applications.
UNIT 3 : Characteristic functions – properties – inversion formulae – uniqueness theorem – moments problem – Levy
Cramer theorems – simple problems.
UNIT 4 : Independence – pairwise and complete independence - convolution - conditional expectation - smoothing
properties – Martingales – simple problems.
UNIT 5 : Laws of large numbers weak and strong law of large numbers – simple applications – central limit theorems
(iid and id) – normal approximation – simple applications.
Books for Study and Reference :
Bhat, B.R. (1999) : Modern Probability Theory, 3rd ed. New Age International Pvt.
Ltd., New Delhi.
Ash, R.B. (1972) : Real Analysis and Probability, Academic press, New York.
Ross,Sheldon,M.(1984): A First Course in Probability, 2nd ed. McMillan, New York.
Freund, JE (1998) : Mathematical Statistics, Prentice Hall International.
MSI C202 FINANCIAL MATHEMATICS - I
UNIT 1 : Rates of interest – Simple and Compound interest rates –Effective rate of interest - Accumulation and Present
value of a single payment – Nominal rate of interest – Constant force of interest  - Relationships between these rates of
interest - Accumulation and Present value of single payment using these rates of interest – accumulation and present value
of a single payment using these symbols - when the force of interest is a function of t, (t). Definition of A(t1, t2), A(t), (t1, t2)
and (t). Expressing accumulation and present value of a single payment using these symbols - when the force of interest is a
function of t, (t).
UNIT 2 : Series of Payments(even and uneven) - Definition of Annuity(Examples in real life situation) – Accumulations and
Present values of Annuities with level payments and where the payments and interest rates have same frequencies Definition and Derivation of
an
,
sn
,
an
,
sn
, Definition of Perpetuity and derivation for
a
and
a
-Examples
- Accumulations and Present values of Annuities where payments and interest rates have different frequencies. Definition
and derivation of
a n( p ) , an( p ) , s n( p ) , sn( p )
UNIT 3 : Increasing and Decreasing annuities – Definition and derivation for
an
sn
,
( I s) n
increasing continuously and payable continuously – definition and derivation of
( I a) n
payable continuously - Definition and derivation of
,
( I a) n
( Ia) n
,
,
( Is) n
and
( Da) n
- Annuities
- Annuities where payments are
,
( I s) n
.
UNIT 4 : Loan schedules – Purchase price of annuities net of tax – Consumer credit transactions
UNIT 5 : Fixed interest securities – Evaluating the securities – Calculating yields – the effect of the term to redemption
on the yield – optional redemption dates – Index linked Bonds – evaluation of annuities subject to Income Tax and
capital gains tax.
Books for Study and Reference :
Institute of Actuaries ActEd. Study Materials.
McCutcheon, J.J., Scott William, F. (1986) : An introduction to Mathematics of Finance,
London Heinemann
56
Butcher,M.V.,Nesbitt, Cecil,J. (1971) : Mathematics of compound interest, Ulrich’s
Books.
Bowers, Newton L.et al (1997):Actuarial Mathematics, Society of Actuaries, 2nd ed.
MSI C203
PROBABILITY DISTRIBUTIONS
UNIT 1 : Discrete distributions – Binomial – Poisson – Multinomial – Hyper geometric – Geometric – discrete uniform –
their characteristics and simple applications.
UNIT 2 : Continuous distributions – Uniform - Normal – exponential – Gamma – Weibull – Pareto – lognormal –
Laplace – logistic distributions – their characteristics and applications.
UNIT 3 : Bivariate and Multivariate Normal – Compound and truncated distributions – convolutions of distributions.
UNIT 4 : Sampling distributions t, 2 and F distributions and their interrelations and characteristics – order statistics and
their distribution – distribution of sample and mid range.
UNIT 5 : Applications of multivariate – normal distributions – principal components analysis – discriminant analysis –
factor analysis – cluster analysis – Canonical correlations.
Books for Study and Reference :
Fruend, John, E. (1992) : Mathematical Statistics, 5th ed., Prentice Hall International.
Forguson, T.S. (1967) : Mathematical Statistics, Academic Press, New York.
Gibbons, J.D. (1985) : Non parametric Statistical Inference, Marcel Dekker, New York.
Hogg,R.V. & Craig (1972): Introduction to Mathematical Statistics, 3rd ed., McGraw Hill
Johnson, R.A. and Wichern, D.W. (1982) : Applied Multivariate Statistical Analysis, 2nd ed., Prentice Hall, Englewood
Cliffs, New Jersey.
Mood, A.M., Graybill, F.A., and Boes, D.C. (1974) : An introduction to the theory of
Statistics, 3rd ed. McGraw Hill Book company
Rohatgi, V.K. and Ebsanes Saleh, A.K. Md. (2002) : An introduction to Probability and
Statistics, 2nd Ed., John Wiley & Sons, Inc., New York.
MSI C215
PRINCIPLES AND PRACTICE OF INSURANCE
UNIT 1 : Concept of Risk- The concept of Insurance.Classification of Insurance- Types of Life Insurance, Pure and
Terms- Types of General Insurance, Insurance Act, Fire, Marine, Motor, Engineering, Aviation and Agricultural Alternative classification- Insurance of Property, Pecuniary interest, liability and person. Distribution between Life and
General Insurance.History of Insurance in general in India. Economic Principles of Insurance – Insurance regulatory
and development Act.
UNIT 2 : Legal Principles of Insurance- The Indian Contract Act, 1872- insurable interest - Utmost Good faithindemnity- subrogation – Contribution- Proximate Cause - Representations- Warranties- Conditions. Theory of ratingActuarial principles- Mortality Tables- Physical and Moral Hazard. Risk appraisal- Risk Selection- Underwriting.
Reinsurance- Concept and Methods.
UNIT 3 : Life insurance organisation : The Indian context. The distribution system, function of appointment and continuance of
agency, remuneration to aents, trends in Life insurance distribution channels.Plans of Life Insurance – need levels, term life
insurance increasing / decreasing term policy, whole life insurance, endowment insurance, money back endowment plan, marriage
endowment plan, education annuity plan, children deferred assurance plans, annuities. Group insurance – nature of group insurance,
types of group insurance, gratuity liability, group superannuating scheme, other group schemes, social security schemes. Other
special need plan – industrial life insurance, salary saving scheme, disability plans – critical illness plans.
UNIT 4 : Application and acceptance – prospectus – proposal forms and other related documents, age proof, special reports. Policy
document – need and format – preamble, operative clauses, proviso, schedule, attestation, conditions and privileges, alteration,
duplicate policy.
UNIT 5 : Premium, premium calculation, Days of grace, Non-Forfeiture options, lapse and revival schemes. Assignment
nominations loans – surrenders, foreclosures, Married Women’s property Act Policy, calculations. Policy claims,
maturity claims, survival benefit payments, death claims, waiver of evidence of title, early claims, claim concession,
presumption of death, Accident Benefit and Disability Benefit , settlement options, Valuations and Bonus, distribution of
surplus. Types of re-insurance, exchange control regulations, payment of premia, payment of claims etc.
Books for study and Reference :
57
Neill, Alistair, Heinemann, (1977) : Life contingencies.
Gerber, Hans, U. (1997) : Life insurance mathematics, Springer, Swiss Association of
Actuaries.
Booth,Philip,M.et al(1999):Modern Actuarial theory and practice, Chapman & Hall.
Daykin,Chris,D. et al(1994): Practical risk theory for Actuaries, Chapman and Hall.
Panjer, Harry,H. (1998) : Financial economics with applications to investments,
Insurance and pensions. The Actuarial foundation.
MSI C204 SURVIVAL MODELS
UNIT 1 : Concept of Survival Models
UNIT 2 : Estimation procedures of Life time Distributions – Cox Regression model – Nelson and Aalen Estimates
UNIT 3 : Two state Markov Model
UNIT 4 : Multi state Markov Models - Statistical Models of transfers between multiple states, Derivation of
relationships between probabilities of transfer and transition intensities. Maximum Likelihood Estimators(MLE) for the
transition intensities in models of transfers between states with piecewise constant transition intensities.
UNIT 5 : Binomial and Poisson models of mortality – MLE for probability of death – Comparison with Multi state models.
Books for Study and Reference:
Institute of Actuaries Acted. Study Materials.
Neill, Allistair (1977) : Life contingencies, Heinemann.
Elandt-Johnson, Regina C; Johnson, Norman L., 2nd ed. (1999) : Survival Models and
data analysis, John Wiley.
Marubini, Ettore, Valsecchi, Marai Grazia, Emmerson, M. (1995) : Analysis of Survival
data from Clinical Trials and observation of studies, John Wiley.
MSI C205
STATISTICAL INFERENCE
UNIT 1 : Estimation Methods : Properties of a good estimator – unbiasedness – efficiency – Cramer Rao bound –
sufficiency – Methods of estimation – Methods of moments – Maximum likelihood method – minimum chisquare –
method of least squares and their properties.
UNIT 2 : Neyman Pearson theory of testing of hypothesis UMP and UMPU tests – chisquare tests – locally most
powerful tests – large sample tests – testing linear hypothesis.
UNIT 3 : Non parametric inference :
The Wilcoxon signed rank test – The Mann-Whitney – Wilcoxon Rank sum test – the runs test – chi-squire test of
goodness of fit test – Kolmogorov-Smirnov goodness of fit test – Kruskal Wallies test – Friedman test .
UNIT 4 : Confidence sets and intervals – exact and large sample confidence intervals – shortest confidence intervals.
UNIT 5 : Elements of Bayesian inference – Bayes theorem – prior and posterior distribution – conjugate and Jeffreys
priors – Baysian point estimation – minimax estimation – loss function – conflux loss functions – Bayesian interval
estimation and testing of hypothesis.
Books for Study and Reference :
Rohatgi, V.K. and Ebsanes Saleh, A.K. Md. (2002) : An introduction to Probability and
Statistics, 2nd Ed., John Wiley & Sons, Inc.
Mood, A.M. Graybill, F.A. and Boes, D.C. (1974) : An introduction to the theory of
Statistics, 3rd Ed., McGraw Hill Book Company.
MSI C206
FINANCIAL MATHEMATICS – II
UNIT 1 : Investment Project Appraisal – Discounted Cash flow techniques.
UNIT 2 : Investment and Risk characteristics of different types of Assets for Investment for investment purposes
58
UNIT 3 : Delivery price and the value of a Forward contract using arbitrage free pricing methods
UNIT 4 : Term structures of interest rates
UNIT 5 : Simple Stochastic interest rate Models
Books for Study and Reference :
Rohatgi, V.K. and Ebsanes Saleh, A.K. Md. (2002) : An introduction to Probability and
Statistics, 2nd Ed., John Wiley & Sons, Inc.
C++ Programming Exercises
Mood, A.M. Graybill, F.A. and Boes, D.C. (1974) : An introduction to the theory of
Statistics, 3rd Ed., McGraw Hill Book Company.
MSI C216
LIFE CONTINGENCIES – I
UNIT 1 : Exposed to risk
UNIT 2 : Assurance functions - Annuity functions
UNIT 3 : Life Tables
UNIT 4 : (i) Estimations of EPV’s of Assurance and Annuity functions
(ii) Net premiums & provisions
UNIT 5 : Variable benefits & with profit policies
Books for Study and Reference:
Institute of Actuaries Acted. Study Materials.
Neill, Allistair (1977) : Life contingencies, Heinemann.
Gerber, Hans U. (1997) : Life insurance Mathematics, Springer, Swiss Association of
Actuaries, 3rd edition.
MSI C207
COMPUTATIONAL LABORATORY – I
Objectives : The implementation of standard numerical algorithms are mastered and results are calculated with
precision. The strengths and limits of each algorithm are understood as well as which technique is most suitable for a
given problem. Lab time is used to master code writing in C++ .
Mathematical Exercises :
8.
Algebraic equations
8.1. Bisections method
8.2. Secant method
8.3. Newton-Raphson method
9.
System of linear equations
2.1 Gaussian Elimination
2.2 Gauss-Seidal Iteration
2.5 Gauss- Jordan Iteration
2.6 Matrix operations
10. Interpolation and curve Fitting
3.1 Lagrange Interpolation
3.2 Newton polynomials
3.3 Straight line fitting
3.4 Curve fitting
11. Numerical differentiation and integration
4.3 Differentiation
4.4 Trapezoidal and Simpson’s 1/3 rule
12. Solution to differential equations
5.5 Euler method
59
5.6
5.7
5.8
Runge – Kutta method of order 2
Runge – Kutta method of order 3
Predictor – corrector method
13. Statistical Methods
6.7 Formation of frequency distribution
6.8 Calculation of moments – mean and variance
6.9 Computation of correlations and regression coefficients
6.10 Fitting and probability distributions
6.11 ANOVA (one-way, two-way)
Statistical Exercises
6.12 Tests of significance based on t, 2 and F.
14. Inference
7.5 Method of moments
7.6 Method of maximum likelihood
7.7 Confidence intervals based on t, 2 and F.
7.8 MP test.
MSI C209
STOCHASTIC MODELING
UNIT 1 : Stochastic process : Definitions and classification (based on state space and time) of Stochastic Processes – various types
of stochastic processes.
Markov chains : n-step TPM – classification states canonical representation of TPM – finite MC with transient states –
No Claim Discount policy – Accident Proneness.
UNIT 2 : Irreducible Markov Chain with ergodic states : Transient and limiting behaviour – first passage and related
results – applied Markov chains – industrial mobility of labor – Educational advancement – Human resource
management – term structure – income determination under uncertainty – A Markov decision process.
UNIT 3 : Simple Markov processes : Markov processes – general properties – Poisson processes – Birth problem –
death problem – birth and death problem – limiting distribution. Flexible manufacturing systems – stochastic model for
social networks – recovery, relapse and death due to disease – Health, sickness and Death model – Martial status.
UNIT 4 : Stationary processes and time series – Stochastic models for time series – the auto regressive process –
moving average process – mixed auto regressive moving average processes – time series analysis in the time domain
– Box-Jenkins model for forcasting.
UNIT 5 : Brownian motion and other Markov processes – Hitting times – maximum variable – arc sine laws – variations
of Brownian motion – stochastic integral – Ito and Levy processes – applications to Actuarial Science.
Books for Study and Reference :
Bhat, U.N. and Miller, G.K. (2002) : Elements of applied stochastic processes 3rd ed.
Wiley Inter, New York.
Brzezniak, Z and Zastawniak, T. (1998) : Basic Stochastic Processes : A course through
Exercises, Springer, New York.
Grimmett, G., Stirzaker, D. (1992) : Probability and Random Processes, Oxford
University Press.
Kulkarni, V.G. (1995) : Modelling and Analysis of Stochastic Systems, Thomson Science
and Professional.
Ross, S.M.(1996): Stochastic processes, John Wiley & Sons, Inc., New York
Institute of Actuaries : ActEd Study materials
MSI C210
RISK MODELS
UNIT 1 : Concept of Decision theory and its applications – Concepts of Bayesian statistics – Calculation of Bayesian
Estimators.
60
UNIT 2 : Calculate probabilities and moments of loss distributions both with and without simple reinsurance arrangements
– Construct risk models appropriate to short term insurance contracts and calculate MGFs and moments for the risk
models both with and without simple reinsurance arrangements. - Calculate and approximate the aggregate claim
distribution for short term insurance contracts.
UNIT 3 : Explain the concept of ruin for a risk model – Calculate the adjustment coefficients and state Lundberg’s
inequality – Describe the effect on the probability of ruin of changing parameter values and of simple reinsurance
arrangements.
UNIT 4 : Describe and apply the fundamental concepts of credibility theory – Describe and apply the fundamental concepts
of simple experience rating systems – Describe and apply techniques for analyzing a delay(or run-off) triangle and
projecting the ultimate position
UNIT 5 : Explain the fundamental concepts of a generalized linear model(GLM), and describe how a GLM may be applied.
Books for Study and Reference :
Institute of Actuaries Acted. Study Materials.
Hossack, Ian B; Pollard, John H; Zenhwirth, Benjamin (1999) : Introductory Statistics
with applications in General Insurance, Cambridge University Press. 2nd ed.
Klugman, Stuart A. et al. (1998) : Loss Models: from data to decisions, John Wiley
Daykin Chris, D; Pentikainen, Teivo; Pesonen, Martti (1994) : Practical Risk theory for
Actuaries, Chapman & Hall.
MSI C217
LIFE CONTINGENCIES – II
UNIT 1 : Gross premiums and provisions
UNIT 2 : Profit Testing
UNIT 3 : Determining provisions using profit testing
UNIT 4 : Factor affecting mortality & selections
UNIT 5 : Single figure indices
Books for Study and Reference:
Institute of Actuaries ActEd. Study Materials.
Benjamin, B. Pollard, J.H. (1993) : The analysis of mortality and other actuarial
statistics, Faculty and Institute of Actuaries, 3rd ed.
Gerber, Hans U. (1997) : Life insurance Mathematics, Springer, Swiss Association of
Actuaries, 3rd ed.
Booth, Philip M et al., (1999) : Modern Actuarial Theory and Practice, Chapman &
Hall.
Bowers, Newton L.et al (1997):Actuarial Mathematics, Society of Actuaries, 2nd ed.
MSI C218
FINANCIAL ECONOMICS
UNIT 1: Introduction to Financial Economics: - Recap of Utility Theory. The Efficient Markets Hypothesis: The three forms of
EMH - The Evidence for or against each form of EMH.
UNIT 2: Measures of Investment Risk: - Measures of Risk - Relationship between Risk measures and Utility Functions.
UNIT 3: Portfolio Theory: - Portfolio Theory - Benefits of Diversification.
UNIT 4: Models of Asset Returns: - Multifactor Models - The Single Index Model.
UNIT 5: Asset Pricing Models: - The Capital Asset Pricing Models (CAPM) – Limitations of CAPM – Arbitrage Pricing Theory
(APT).
Books for Study and Reference :
61
Institute of Actuaries ActEd , CT8 Study material.
Panjer, Harry, H. (1998) : Financial economics : with applications to investments,
insurance and pensions. The Actuarial foundations.
MSI C219 JOINT LIFE AND PENSION BENEFITS
UNIT 1 : Simple annuities and assurances involving two lives.
UNIT 2 : Contingent and reversionary benefits
UNIT 3 : Competing risks
UNIT 4 : Multiple decrement tables
UNIT 5 : Pension benefits
Books for Study and Reference:
Institute of Actuaries ActEd. Study Materials.
Benjamin, B. Pollard, J.H. (1993) : The analysis of mortality and other actuarial
statistics, Faculty and Institute of Actuaries, 3rd ed.
Booth, Philip M et al., (1999) : Modern Actuarial Theory and Practice, Chapman &
Hall.
Gerber, Hans U. (1997) : Life insurance Mathematics, Springer, Swiss Association of
Actuaries, 3rd edition
MSI C212
CORPORATE FINANCIAL MANAGEMENT
UNIT 1 : Foundations of Finance : Time value of Money – NPV, IRR, and other Measures – Valuation of Common
Stocks and Bonds.
UNIT 2 : Investment Analysis : Modern theory of Finance – Capital Budgeting Decision Rule – Capital Budgeting and
Cash Flow Analysis – Capital Budgeting and Risk.
UNIT 3 : Variance Analysis – Importance of variance analysis – Material variance, labour variance, overhead variance.
Working capital management – Factors determining working capital – Calculation of working capital.
UNIT 4 : Financial Planning : Financial Statements and Ratio Analysis – Short-term Financial Decisions – Long-term
Financial Decisions.
UNIT 5 : Special Topics : Mergers and Acquisitions and Corporate Governance – Options and Corporate Finance.
Books for Study and Reference :
Brealey, Myers and Marcus : Fundamentals of Corporate Finance, McGraw Hill.
Ross, Westerfield and Jordan : Fundamentals of Corporate Finance, Tata McGraw Hill.
Van Home and Wachowicz : Fundamentals of Financial Management, Prentice Hall
India.
MSI C213 COMPUTATIONAL LABORATORY – II
Objectives :

To provide exposure to Mathematical / Statistical software focusing more on writing source codes.

To analyse the given data by identifying appropriate tools.
Mathematical and Statistical Packages Exercises. S Plus/ SAS/ MAPLE/
MATHEMATICA/ MATLAB
2.
4.
5.
Data Analysis : Identifying the statistical tool and analysing the data using the appropriate tools.(S PLUS/ SAS)
Symbolic manipulation using MAPLE/ MATHEMATICA
Exercises based on the subjects taught in III & IV semesters.
(ie. Survival Analysis – Stochastic Models etc.)
Simulation study depending upon the requirement of the problem. (MATLAB)
62
MSI C214
PROJECT & VIVA VOCE
Objectives :

To provide written, oral and visual presentation skills

To develop team work.
Course Outline : Based on the interest of the students, they can choose their team and seminar topic. It can also an
individual work. During the term, students will meet periodically the faculty to discuss different stages of the seminar.
They are required to give three seminar presentations.
Project Work/ Internship :
Objectives : To develop student’s abilities to solve applied industrial and actuarial problems in a longer time frame
than in usual in other courses. Students will learn how to search for known results and techniques related the project
work. The students will present their project results as a written document and verbally.
Prerequisite : Completion of the course duration of first two semesters.
Course Outline :
The faculty will propose an array of problems in industrial / actuarial studies. Students may choose a problem
from this list or propose of their own provided a faculty member / Guide approves it. This work may also be carried
out as an internship programme.
On completion of the project work, each student is expected to



Submit a written document describing the results, mathematical developments, background material,
bibliographical search etc.
Present orally in a seminar setting of the work done in the thesis
Submit the software (if relevant) with appropriate documentation.
The students will meet regularly with the project guide / adviser to work out problems that appear and adjust the
goals and time frame accordingly.
MSI E201 OBJECT ORIENTED PROGRAMMING WITH C++
UNIT 1 : Principles of object oriented programming – beginning with C++ - Token, Expressions and Control structures.
UNIT 2 : Functions in C++ - Classes and objects.
UNIT 3 : Constructors and Destructors – operator overloading and type conversions
UNIT 4 : Inheritance : Extending classes – Pointers, Virtual Functions and Polymorphism.
UNIT 5 : Console I/O operations – working with files – object oriented systems development – Templates and
Exception handling.
Books for Study and Reference :
Balagurusamy (1999) : Object oriented programming with C++, Tata McGraw Hill
Company Ltd., New Delhi, 16th reprinting.
Hubbard, J.R. (2000) : Programming with C++ 2nd ed., McGraw Hill, New York.
MSI E202
PRINCIPLES OF ECONOMICS
UNIT 1 : Market Mechanism – Supply and Demand interaction – Determination of equilibrium Elasticity of demand and
Supply – Rational utility and consumption choice – Insurance system and its impact on Welfare.
63
UNIT 2 : Costs Revenue and output – Market structure – short and long run equilibrium in different markets – perfect
competition, Monopoly, Monopolistic competition.
UNIT 3 : Macro Economics – Concepts of GDP, GNP, NNP – methods of calculating National Income – problems –
difficulties and uses of National Income Analysis. Propensity to consume – multiplier – determinants of consumption.
UNIT 4 : Monetary and Fiscal policy – Government intervention – financial markets – exchange rates – International
trade – Balance of payments.
UNIT 5 : Inflation types – interest rate and exchange rate – types of unemployment – public sector finances in an
industrial economy.
Books for study and Reference :
Stonier and Hague : Economic Theory
Kovtsoyiannis : Modern micro economics ELBS publications.
Samuelson Paul & Norhaus William (1998) : Economics, McGraw Hill.
Allen, R.G.D. : Mathematical analysis for Economics, Macmillan.
Panjer, Harry, H.(ed)(1998) : Financial Economics with applications to investments,
Insurance and pension. The Actuarial foundation
MSI E204
NUMERICAL METHODS
UNIT 1 : Numerical coumputing and computers – Solving non-linear equations.
UNIT 2 : Solving set of equations.
UNIT 3 : Interpolation and curve fitting.
UNIT 4 : Numerical differentiation and Numerical integration.
UNIT 5 : Numerical solution of ordinary differential equations.
Books for Study and Reference :
Gerald, C.F. and Wheatley, P.O. (1994) : Applied Numerical Analysis, Addison Wesley,
New York, 5th Ed.
Press, W.B., Flannery, S. Teuddsky and Vetterling, W. (1989) : Numerical Recipes in C :
The art of Scientific computing. Rev. 1st ed., Cambridge University Press.
Rice, John, R. (1983) : Numerical Methods, Software and Analysis, McGraw Hill,
New York.
Atkinson, K.E. (1978) : An introduction to Numerical Analysis, Wiley & Sons,
New York.
Sastry, S.S. (1987) : Introductory methods of numerical analysis, Prentice Hall of India,
New Delhi, (10th printing).
MSI E205
FINANCE AND FINANCIAL REPORTING
UNIT 1 : Introduction to Finance – Functions of Financial Management – Scope – Organisation – Sources of funds – Long term –
Medium term and Short term – Financial risks.
UNIT 2 : Company Management – Types of business entity – pros and cons of limited company – legal documentation –
corporate and personal taxation.
UNIT 3 : Capital structure – Net Income approach Net operating Income approach – M M approach Traditional
approach – average and personal tax of the investors – concept of cost of capital – factors affecting cost of capital –
specific and overall cost of capital.
UNIT 4 : Dividend decision and valuation of the firm – Determinants and constraints of a dividend policy – Financial
Institution – IDBI, ICICI, IFCI, UTI, Commercial Banks, Insurance companies etc.
UNIT 5 : Financial reporting – Accounting principles – types – basic financial statement – kinds of reports – Nature of
reports – guiding principles of reporting – necessary steps for good reporting.
Books for Study and Reference :
Samuels, J.M., Wilkes, F.M., Brayshaw, R.E. (1995) : Management of company finance,
64
International Thomson, 6th ed.
Brealey, Richard, A. (1999) : Principles of Corporate finance, McGraw Hill, 6th ed.
Holmes, Geoffrey, Sugden, Alan (1999) : Interpreting company reports and accounts,
Prentice Hall, 7th ed.
Pandey, I.M. : Financial Management.
Prasannachandra : Financial Management
Kuchhal : Financial Management
Moshal : Management Accounting
Institute of Actuaries ActEd , Study Material :
MSI E207 RESOURCE OPTIMIZATION PRINCIPLES
UNIT 1 : Linear programming problems - model formulation and graphical solution – various types of solutions – simplex
method of solving linear programming –duality principles – dual simplex method.
UNIT 2 : Artificial variable techniques Big M method – two phase method – assignment problem – transportation
problem – MODI method of finding optimal solutions.
UNIT 3 : Sequencing problem – replacement problems – game theory – zero sum games – graphical method – solution
of games by LPP.
UNIT 4 : Decision analysis – components of decision making – decision making without probabilities – maximum –
minimax regret – Hurwicz and equal likelihood criterion – decision making with probabilities – expected value –
expected opportunity loss criterion.
UNIT 5 : Network flow models – shortest route problem – project management – the CPM and PERT Networks.
Books for Study and Reference :
Sharma, J.K. (1997) : Operations Research, Theory and applications, Macmillan.
Taha, H.A. (1996) : Operations Research, 5th edition, Prentice Hall of India, New York.
MSI E208 DATA ANALYSIS USING R & SAS
Prerequisite: compulsory knowledge in Advanced Statistical Inference and Survival Analysis
UNIT 1 : Graphs, Diagrams , Descriptive Statistics and Data Exploration Techniques
UNIT 2 : Bivariate Data Analysis, Multivariate Data Analysis
UNIT 3 : Non parametric Tests
UNIT 4 : Statistical Models ,Time series Analysis
UNIT 5 : Simulation Techniques
*****
65
STATISTICS
An independent Department of Statistics started functioning in 1941 and became a full fledged Department of
study and research from 1975 under the leadership of
Prof. K.N.Venkataraman. The Department offers Masters
M.Phil. and Ph.D. programmes. The Department also offers P.G. Course in Actuarial Science, a self-supportive course
under University Industry Community Interaction Centre (UICIC) of the University .
.
66
STATISTICS
(Course Proposals for the academic year 2007 – 2008)
A – CORE COURSES
Title of the Course
C/E/S
L
Subject Code
T
P
C
I SEMESTER
MSI C101
MSI C102
MSI C103
MSI C104
UOM S001
Real Analysis
Linear Algebra
Distribution Theory
Measure Theory
Elective 1
Elective 2
Soft Skill
C
C
C
C
E
E
S
3
3
3
3
2
2
1
1
1
1
1
1
0
0
0
0
0
0
4
4
4
4
3
3
2
Probability Theory
Sampling Theory
Statistical Estimation Theory
Practical – I (Calculator Based)
Elective 3
Elective 4
Soft Skill
C
C
C
C
E
E
S
3
3
3
2
2
2
1
1
1
0
1
1
0
0
0
0
0
0
4
4
4
2
3
3
2
Multivariate Analysis
Testing Statistical Hypotheses
Design & Analysis of Experiments
Elective 5
Soft Skill
Internship
C
C
C
E
S
S
3
3
3
2
1
1
1
1
0
0
0
0
4
4
4
3
2
2
C
C
C
C
C
E
S
3
0
0
0
3
2
1
0
0
6
1
1
0
2
2
0
0
0
4
2
2
6
4
3
2
II SEMESTER
MSI C105
MSI C106
MSI C107
MSI C108
UOM S002
III SEMESTER
MSI C109
MSI C110
MSI C111
UOM S003
UOM I001
IV SEMESTER
MSI C112
MSI C113
MSI C114
MSI C115
MSI C116
UOM S004
Statistical Quality Management
Practical – II (Calculator Based)
Practical – III (Software Based)
Project Work / Dissertation
Reliability and Survival Analysis
Elective 6
Soft Skill
B – ELECTIVE COURSES :
Subject
Code
MSI E101
MSI E102
MSI E103
MSI E104
MSI E106
MSI E107
MSI E108
MSI E109
MSI E110
MSI S111 *
MSI S112 *
Title of the Course
L
T
P
C
Operations Research
Actuarial Statistics
Statistical Genetics
Markov Chain and its Applications
Statistical Methods for Epidemiology
Stochastic Modeling
Non parametric inference
Data Mining Tools
Bayesian Inference
Statistics for Social Sciences
Bio-Statistics
3
3
3
3
3
3
3
3
3
3
3
0
0
0
0
0
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3
3
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3
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3
* TO OTHER DEPARTMENTS ONLY
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MSI C101
Real Analysis
Pre-requisite : Undergraduate level Mathematics.
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3
1
0
4
Guest Faculty
Unit I : Recap of elements of set theory; introduction to real numbers, introduction to
n-dimensional Euclidian space;
open and closed intervals (rectangles), compact sets, Bolzano – Weirstrass theorem, Heine – Borel theorem.
Unit II : Sequences and series; their convergence. Real valued functions, continuous functions; uniform continuity,
sequences of functions, uniform convergence ; power series and radius of convergence.
Unit III : Differentiation, maxima – minima of functions; functions of several variables, constrained maxima – minima of functions.
Unit IV : Riemann integral & Riemann – Stieltjes integral with respect an increasing integrator – properties of R.S.
integral –integrators of bounded variation.
Unit V : Multiple integrals and their evaluation by repeated integration, change of variables in multiple integration.
Uniform convergence in improper integrals, differentiation under the sign of integral – Leibnitz rule.
REFERENCES :
Apostol, T.M. (1985) : Mathematical Analysis, Narosa, Indian Ed.
Bartle,R.G., Sherbert, D.R.(1982) : introduction to Real analysis.
Malik, S.C.(1985) : Mathematical analysis, Wiley Eastern Ltd.
Royden, H.L.(1995) : Real analysis, 3ed., Prentice Hall of India.
Rudin, Walter (1976) : Principles of Mathematical Analysis, McGraw Hill.
Rangachari,M.S.(1996) : Real Analysis, Part 1, New Century Book House.
MSI C102
Linear Algebra
Pre-requisite : Undergraduate level Mathematics.
C
3
1
0
4
Ms. M.R. Sindhumol
Unit 1 : Vector spaces, Linear dependence, linear independence, basis and diversion of vector space, inner product Gram Schmidt
orthogonalization, linear transformations, projection operators, null space and nullity.
Unit II : Matrix algebra, rank and inverse of a matrix, determinants, characteristic roots, characteristic polynomial, Cayley Hamilton
theorem, multiplicity of characteristic roots, idempotent matrix.
Unit III : Reduction of matrices, Echelon form, Hermite canonical form, diagonal reduction, rank factorization, triangular reduction
Jordan form, pairs of symmetric matrices, singular value decomposition, spectral decomposition.
Unit IV : Kronecker product of matrices matrix differentiation, generalized inverse, Moore-Penrose inverse and properties of ginverse, Application of g-inverse.
Unit V : Quadratic forms, classification, definiteness, index and signature, extremum of quadratic forms, reduction of quadratic
form, transformation, applications of quadratic forms.
REFERENCES :
Bellman, R. (1970) : Introduction to Matrix Analysis, 2nd ed. McGraw Hill.
Biswas, S. (1984) : Topics in Algebra of Matrices, Academic Publications.
David, A.Harville(1997) : Matrix algebra from a statistician’s perspective, Springer.
Hadley, G. (1987) : Linear Algebra, Narosa Publishing House.
Hoffman, K. and Kunze, R. (1971) : Linear Algebra, 2nd ed. Prentice Hall, Inc.
Graybill, F.A. (1983) : Matrices with application in Statistics, 2nd ed. Wadsworth.
Rao, C.R. & Bhimasankaran, P.(1992) : Linear algebra, Tata McGraw Hill Pub. Co. Ltd.
Searle, S.R. (1982) : Matrix Algebra useful for Statistics, John Wiley and Sons, Inc.
MSI C103
Distribution Theory
Pre-requisite : Undergraduate level Mathematics.
C
3
1
0
4
Guest Faculty
Unit I : Brief review of distribution theory, functions of random variables and their distributions using Jacobian of transformation,
Laplace and Caushy distribution, lognormal distribution, gamma, logarithmic series.
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Unit II : Bivariate normal, Bivariate exponential, Bivariate Poisson, Compound, truncated and mixture of distributions,
concepts of convolution.
Unit III : Sampling distributions, non-central chi-square distribution, t and F distributions and their properties,
distributions of quadratic forms under normality and related distribution theory – Cochran’s and James theory.
Unit IV : Order statistics their distributions and properties, Joint and marginal distributions of order statistics, extreme value and
their asymptotic distributions, approximating distributions of sample moment, delta method.
Unit V : Kolmogorov Smirnov distributions, life distributions, exponential, Weibull and extreme value distributions Mills ratio,
distributions classified by hazard rate.
REFERENCES :
Gibbons(1971) : Non-parametric inference, Tata McGraw Hill.
Rohatgi, V.K. and Md. Whsanes Saleh, A.K.(2002) : An introduction to probability & Statistics, John Wiley and Sons.
Rao, C.R. (1973) : Linear statistical inference and its applications, 2ed, Wiley Eastern.
Mood,A.M. & Graybill, F.A. and Boes, D.C. : Introduction to the theory of statistics, McGraw Hill.
Johnson,S. & Kotz,(1972): Distributions in Statistics, Vol. I, II & III, Hougton & Miffin.
Dudewicz, E.J., Mishra, S.N.(1988) : Modern mathematical statistics, John Wiley.
Searle, S.R.(1971) : Linear models, John Wiley.
MSI C104
Measure Theory
Pre-requisite : Undergraduate level Mathematics.
C
3
1
0
4
Dr. G.Gopal/Guest Faculty
Unit I : Sets and set functions, Algebra of sets, limits of sequence of sets, classes of sets : Ring, Field, Field and monotone classes,
Generated classes.
Unit II : Measure functions, properties of measure functions, Outer measure, extension and completion of measures
signed measures, Hahn Decomposion theorem.
Unit III : Lebesgue, Stieltjes measures, examples, measurable functions, approximation theorems.
Unit IV : Measure integration, properties of measure integrals, Monotone convergence theorem and dominated convergence
theorem, Fatou’s lemma.
Unit V : Absolute continuity, Radon Nikodymn theorem, singularity, Lebesgue Decomposion theorem, Fubini’s theorem,
convergence types for measurable functions (almost everywhere, in mean and their inter-relationships).
REFERENCES :
Munroe, M.E. (1971) : Measure and integration, 2nd ed. Addision Wesley.
Ash, R.B. (1972) : Real analysis and probability, Academic press.
Kingman, J.F.C. and Taylor, J. (1973) : Introduction to measure and probability, Cambridge University Press.
Royden, H.L. (1968) : Real analysis, 2nd ed. Macmillan.
Loeve, M. (1960) : Probability theory, Van Nostrand.
Halmos, P.R. (1974) : Measure theory, East-West.
De Barr, G. (1987) : Measure theory and integration, Wiley Eastern.
MSI C105
Probability Theory
Pre-requisite : Measure Theory.
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3
1
0
4
Dr.G.Gopal/ Guest Faculty
Unit I : Events, sample space, different approaches to probability, random variables and random vector, Distribution
functions of random variables and random vector, Expectation and moments, basic, Markov, Chebyshev’s, Holder’s,
Minkowski’s and Jensen’s inequalities.
Unit II : Independence of sequence of events and random variables, conditional probability, conditional expectation,
smoothing properties, Tail-sigma field, 0-1 law of Borel and Kolmogorov, Hew itt-Savage 0-1 law.
Unit III : Characteristic functions and their properties, inversion formula, convergence of random variables, convergence
in probability, almost surely, in the r-th mean and in distribution, their relationships, convergence of moments, Helly-Bray
theorem, continuity theorem and convolution of distributions.
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Unit IV : Convergence of series of random variables, three-series theorem, Khintchines weak law of large numbers,
Kolmogorov inequality, strong law of large numbers.
Unit V : Central limit theorem, statement of CLT, Lindeberg, Levy and Liapounov forms with proof and Lindeberg
Feller’s form examples.
REFERENCES :
Bhat, B.R. (1985) : Modern probability theory, 2nd ed. Wiley Eastern.
Chow, Y.S. and Teicher, H. (1979) : Probability theory, Springer Verlag.
Ash Robert, B. (1972) : Real analysis and probability, Academic Press. 3 rd ed.
Chung, K.L. et al : A course in probability theory, Academic press.
V.K.Rohatgi etal(2002) : An introduction to probability and statistics, John Wiley.
Parthasarthy, K.R. (1977) : Introduction to probability and measure, MacMillan Co., Breiman, L. (1968) : Probability,
Addison Wesley.
MSI C106
Sampling theory
Pre-requisite : Undergraduate level Mathematics.
C
3
1
0
4
Dr.M.R.Srinivasan
Unit I : Review of basic finite population sampling techniques SRS, Stratified, Systematic sampling, related results on
estimation, allocation problem in stratification sampling, efficiency of systematic over stratified and SRS.
Unit II : Varying probabilities, PPS WR/WOR ordered and un-ordered estimator, selection of samples Horowitz Thompson, Desraj,
Rao Hartley-Cochran estimators.
Unit III : Sampling with supplementary information, Ratio and regression estimators and related results.
Unit IV : Multi stage and multiphase sampling, two stage sampling with equal number of second stage under-double
sampling cluster sampling.
Unit V : Non sampling errors, errors in surveys (Types of Errors), Observational errors (Measurement and related results,
Incomplete samples (Non-response Politz and summary randomized response technique, Introduction to Jackknife and bootstrap
techniques.
REFERENCES :
Cochran, W.G. (1977) : Sampling Techniques 3rd ed., Wiley.
Des Raj and Chandak (1988) : Sampling Theory, Narosa.
Murthy, M.N. (1977) : Sampling theory and methods. Statistical publishing society, Calcutta.
Sukhatme & Sukhatme (1984) : Sampling theory of surveys with applications. ISAS.
Singh, D. and Chaudhary, F.S. (1986) : Theory and Analysis of Sample Survey Designs, New Age International
Publishers.
MSI C107
Statistical Estimation Theory
Pre-requisite : Probability Theory.
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3
1
0
4
Dr.G.Gopal
Unit I : Sufficient statistics, Neyman, Fisher Factorisation theorem, the existence and construction of minimal sufficient statistics,
Minimal sufficient statistics and exponential family, sufficiency and completeness, sufficiency and invariance.
Unit II : Unbiased estimation : Minimum variance unbiased estimation, locally minimum variance unbiased estimators,
Rao Blackwell – theorem.Completeness- Lehmann Scheffe theorems, Necessary and sufficient condition for unbiased
estimators
Unit III : Cramer- Rao lower bound, Bhattacharya system of lower bounds in the 1-parameter regular case. Chapman Robbins inequality.
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Unit IV : Maximum likelihood estimation, computational routines, strong consistency of maximum likelihood estimators,
Asymptotic Efficiency of maximum likelihood estimators, Best Asymptotically Normal estimators, Method of moments.
Unit V : Bayes’ and minimax estimation : The structure of Bayes’ rules, Bayes’ estimators for quadratic and convex loss functions,
minimax estimation, interval estimation.
REFERENCES :
V.K.Rohatgi etal(2002) : An introduction to probability and statistics, John Wiley.
Lehmann, E.L. (1983) : Theory of point estimation, John Wiley.
Zacks, S. (1971) : The theory of statistical inference, John Wiley.
Rao, C.R. (1973) : Linear statistical inference and its applications, Wiley Eastern, 2 nd ed.
Ferguson, T.S. (1967) : Mathematical statistics, A decision theoretic approach, Academic press, New York and London.
Lindley, D.V. (1965) : Introduction to probability and statistics, Part 2, Inference, Cambridge University Press.
MSI C108
Practical – I (Calculator Based)
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2
0
0
2
All Faculty
4
Guest Faculty
Practical Exercises based on MSI C102, MSI C103, MSI C106 and MSI C107
MSI C109
Multivariate Analysis
Pre-requisite : Distribution theory.
C
3
1
0
Unit I : Random sampling from a multivariate normal distribution. Maximum likelihood estimators of parameters. Distribution of
sample mean vector. Wishart matrix – its distribution and properties. Distribution of sample generalized variance.
Unit II : Null and non-null distribution of simple correlation coefficient. Null distribution of partial and multiple
correlation coefficient. Distribution of sample regression coefficients. Application in testing and interval estimation.
Distribution of sample intra – class correlation – coefficient in a random sample from a symmetric multivariate normal
distribution. Application in testing and interval estimation.
Unit III : Null distribution of Hotelling’s T2 statistics. Application in tests on mean vector for one and more multivariate
normal populations and also on equality of the components of a mean vector in a multivariate normal population.
Unit IV : Multivariate linear regression model – estimation of parameters, tests of linear hypotheses about regression coefficients.
Likelihood ratio test criterion. Multivariate Analysis of variance (MANOVA) of one-and two-way classified data.
Unit V : Classification and discrimination procedures for discrimination between two multivariate normal populations –
sample Discriminant function, tests associated with Discriminant functions, probabilities of misclassification and their
estimation, classification into more than two multivariate normal populations.
Principal components, Dimension reduction, Canonical variables and canonical correlation – definition, use, estimation
and computation.
REFERENCES :
Anderson, T.W. (1983) : An introduction to multivariate statistical analysis. 2nd ed.Wiley. (study)
Giri, N.C. (1977) : Multivariate statistical inference, Academic press.
Kshirsagar, A.M. (1972) : Multivariate analysis, Marcel Dekker.
Morrison, D.F. (1976) : Multivariate statistical methods, 2nd ed. McGraw Hill.(study)
Muirhead, R.J. (1982) : Aspects of multivariate statistical theory, Wiley.
Rao, C.R. (1973) : Linear Statistical Inference and its applications, 2nd ed. Wiley.
Seber, G.A. (1984) : Multivariate observations, Wiley.
Sharma, S. (1996) : Applied multivariate techniques, Wiley.
Srivastava, M.S. and Khatri, C.G. (1979) : An introduction to multivariate statistics. North Holland.
Johnson,R.& Wichern(1992) : Applied multivariate statistical analysis, Prentice Hall, 3ed.(study).
MSI C110
Testing Statistical Hypotheses
Pre-requisite : Probability Theory .
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3
1
0
4
Dr.G.Gopal
Unit I : Uniformly most powerful tests, the Neyman-Pearson fundamental Lemma, Distributions with monotone likelihood
ratio.Problems
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Unit II : Generalization of the fundamental lemma, two sided hypotheses, testing the mean and variance of a normal
distribution.
Unit III : Unbiased ness for hypotheses testing, similarly and completeness, UMP unbiased tests for multi parameter
exponential families, comparing two Poisson or Binomial populations, testing the parameters of a normal distribution
(unbiased tests), comparing the mean and variance of two normal distributions.
Unit IV : Symmetry and invariance, maximal invariance, most powerful invariant tests.
Unit V : SPRT procedures, likelihood ratio tests, locally most powerful tests, the concept of confidence sets, non parametric tests.
REFERENCES :
V.K.Rohatgi etal(2002) : An introduction to probability and statistics, John Wiley.
Lehmann, E.L. (1986) : Testing of statistical hypothesis, John Wiley.
Ferguson, T.S. (1967) : Mathematical statistics, A decision theoretic approach, Academic press.
Rao, C.R. (1973) : Linear statistical inference and its applications, Wiley Eastern, 2 nd ed.
Gibbons, J.D. (1971) : Non-parametric statistical inference, McGraw Hill.
MSI C111
Design and Analysis of Experiments
Pre-requisite : Matrix algebra & Linear models.
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3
1
0
4
Dr.M.R.Srinivasan
Unit I : Linear models, classification, linear estimators, Gauss-Markov theorem, BLUE, test of general linear hypothesis, fixed,
mixed and random effects models.
Unit II : Review of basic designs: CRD, RBD, LSD, Orthogonal latin squares, Hyper Graeco Latin squares – analysis of variance –
analysis of covariance – multiple comparisons – multiple range tests - Missing plot technique – general theory and applications.
Unit III : General factorial experiments, factorial effects; best estimates and testing the significance of factorial effects ;
study of 2 and 3 factorial experiments in randomized blocks; complete and partial confounding. Fractional replication
for symmetric factorials. Sprip plot and split block experiments.
Unit IV : General block design and its information matrix (C), criteria for connectedness, balanced and orthogonality; intrablock
analysis (estimability, best point estimates / interval estimates of estimable linear parametric functions and testing of linear
hypotheses) : BIBD – recovery of interblock information; Youden design – intrablock analysis.
Unit V : Response surface methodology - first order and second order rotatable designs, applications: clinical trials.
REFERENCES :
Das, M.N. and Giri, N. (1979) : Design and analysis of experiments, Wiley Eastern.
John, P.W.M. (1971) : Statistical design and analysis of experiments, Macmillan.
Montgomery, C.D. (2001) : Design and analysis of experiments, John Wiley, New York.
Friedman, L.M., Furberg, C.D., Demets, D.L.(1998) : Fundamentals of clinical trials, Springer.
Robert, O., Kuelhl(2000) : Design of experiments. Statistical principles of research design and analysis, Duxbury.
Federer, W.T.(1963) : Experimental design; Theory and application, Oxford & IBH publishing Co.
Doshi, D.D. (1987) : Linear estimation and design of experiments, Wiley Eastern Ltd.
MSI C112
Statistical Quality Management
Pre-requisite : Undergraduate level Statistics.
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3
1
0
4
Ms.M.R.Sindhumol
Unit I : Concept of quality – definition and standardization of quality – Functional elements of TQM, quality movements
in India, quality circle, quality audit, Direct and indirect quality costs, measurement and analysis – Pareto and Ishikawa
diagrams, ISO 9000 series.
Unit II : General theory and review of control charts for attribute and variable data; O.C. and A.R.L. of control charts; Moving
average and exponentially weighted moving average charts; Cu-sum charts using V-masks and Economic design of X-bar chart.
Unit III : Acceptance sampling plans for attribute inspection ; single, double and sequential sampling plans and their properties.
Plans for inspection by variables for one-sided and two-sided specifications; Mil-Std and IS plans.
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Unit IV : continuous sampling plans for Dodge type and Wald-Wolfiwitz type and their properties, chain sampling plan..
Unit V : Capability indices Cp, Cpk and Cpm; estimation, confidence intervals and tests of hypotheses relating to
capability indices for Normally distributed characteristics. Use of Design of Experiments in SPC, factorial experiments.
REFERENCES :
Montgomery, D.C. (2001) : Introduction to Statistical Quality Control, John Wiley.
Ott,E.R. (1975) : Process quality control, McGraw Hill.
Grant, L. and Leavenworth, S. (1996) : Statistical quality control, McGraw Hill.
Murthy, M.N. (1989) : Excellence through quality & reliability, Applied statistical centre.
Thomas P.Ryan(2000) : Statistical methods for quality improvement 2ed., John Wiley.
MSI C113
Practical – II (Calculator Based)
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0
0
2
2
Ms. M.R. Sindhumol
Practical Exercises based on MSI C109, MSI C110, MSI C111, MSI C112 and MSI C113
MSI C114
Practical – III (Software Based)
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0
0
2
2
Dr. M.R. Srinivasan
Use Statistical packages like SPSS, MINITAB / S-PLUS for solving statistical problems in Core and Electives. Exercises
will be prepared by the faculty in-charge.
MSI C115
Project Work / Dissertation
MSI C116
Reliability and Survival Analysis
Pre-requisite : Probability Theory.
C
0
6
0
6
All Faculty
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3
1
0
4
Dr. G.Gopal
Unit I : Introduction to Survival concepts, Survival functions and hazard rates, concepts of Type I, Type II, Random and other types of
censoring, likelihood in these cases.
Unit II : Life distributions-exponential Weibull, Gamma, Lognormal, Pareto, Linear failure rate, estimation / testing under censoring setup.
Unit III : Life tables, failure rate, mean residual life and their elementary properties.
Unit IV : Estimation of survival functions-actuarial estimator, Product – limit (Kaplan-Meier) estimator, properties.
Unit V : Cox proportional hazards regression models with one and several covariates, exponential, Weibull, lognormal regression.
REFERENCES :
Miller,R.G.(1981) : Survival analysis, John Wiley.
Collet, D.(1984) : Statistical analysis of life time data.
Despande,J.V., Gore, A.P. and Shanbhogue, A.(1995) : Statistical analysis of non normal data, Wiley Eastern.
Cox, D.R. and Oakes, D.(1984) : Analysis of survival data, Chapman & Hall, New York.
Gross, A.J. and Clark, V.A.(1975) : Survival distribution: Reliability applications in the Biomedical sciences, John Wiley and Sons.
Elandt-Johnson,R.E. Johnson, N.L. : Survival models and data analysis, John Wiley & sons.
Kalbfleish, J.D. and Prentice R.L.(1980) : The statistical analysis of failure time data, John Wiley.
ELECTIVES
MSI E101
Operations Research
3
0
0
3
Guest Faculty
Pre-requisite : Open to all – Offered in the First Semester.
Unit I : Linear programming – Simplex and Revised simplex method. Duality in LPP – sensitivity Analysis – Bounded variable Techniques –
parametric and integer programming problems – Game theory – different methods of solving game problems.
Unit II : Application of LPP – Transportation problem – Assignment problem – characteristic of queuing model – M/M/1 and M/M/C
queuing model.
Unit III : Network analysis- PERT and CPM-Simulation- Monte-Carlo Techniques.
REFERENCES :
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Handy Taha (1992) : Operations Research, An Introduction, Prentice Hall.
Hiller Lieberman (1995) : Introduction to Opearations Research, McGraw Hill.
J.K.Sharma(1997) : Operations Research. Theory and Applications, Macmillan.
MSI E102
Actuarial Statistics
3
0
0
3
Guest Faculty
Pre-requisite : Open to all – Offered in the Second Semester
Unit I : Mortality : Gompertz - Makeham laws of mortality - life tables.
Annuities : Endowments, Annuities, Accumulations, Assurances, Family income benefits.
Unit II : Policy Values : Surrender values and paid up policies, industrial assurances, Joint life and last survivorship, premiums.
Unit III : Contingent Functions : Contingent probabilities, assurances. Decrement tables.
Pension funds : Capital sums on retirement and death, widow’s pensions, benefits dependent on marriage.
REFERENCES :
Study Material, 104-Survival Models, Actuarial Society of India.
Hooker,P.F., Longley, L.H.-Cook (1957) : Life and other contingencies, Cambridge.
Alistair Neill(1977) : Life contingencies, Heinemann professional publishing.
Hosack,I.B., Pollard, J.H. and Zehnwirth, B.(1999) : introductory statistics with applications in general insurance, Cambridge University.
MSI E103
Statistical Genetics
3
0
0
3
Dr.M.R.Srinivasan
Unit I : Bio-assays - response relationship - Transformation - probit and logits - Feller's theorem. Symmetric and Asymmetric assays.
Unit II : Mating designs - random mating - Hardy and Weinberg equilibrium. Inbreeding - segregation and linkage analysis.
Unit III : Estimation of gene frequencies - inheritance - heritability- repeatability - selection index - diallel and triallel crosses.
REFERENCES :
Falconer, D.S.(1981) : Introduction to quantitative genetics, Longman.
Bruce, S.Wein(1990) : Genetic data analysis, Sinauer associates.
Keneth Lange(1997): Mathematical and statistical methods for genetic analysis, Springer.
MSI E104
Markov Chain and its Applications
3
0
0
3
Guest Faculty
Unit I : Markov Chains - classification of states, Determination of higher order transition probabilities, stability of a
Markov system, limiting behavior.
Unit II : Kolmogorov forward and backward differential equations. Poisson processes - birth and death processes
and applications.
Unit III : Branching process and its applications.
REFERENCES :
J.Medhi(1982) : Stochastic processes, Wiley Eastern.
Cinlar, E.(1975) : Introduction to stochastic processes, Prentice Hall.
Samuel Karlin and Howard M.Taylor(1975) : A first course in Stochastic processes Vol.I, Academic Press
Bhat,B.R.(2000) : Stochastic models : Analysis and Applications, New Age International.
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MSI E106
Statistical Methods for Epidemiology
3
0
0
3
Dr.M.R.Srinivasan
Unit I : Measures of disease frequency : Mortality / morbidity rates, incidence rates, prevalence rates. Source of mortality / morbidity
statistics – hospital records, vital statistics records. Measures of secrecy or validity : sensitivity index, specificity index. Measure of reliability.
Epidemiologic concepts of diseases : Factors which determine the occurrence of diseases, models of transmission of infection, incubation
period, disease spectrum and herd immunity.
Unit II : Observational studies in Epidemiology : Retrospective (case control) & prospective (cohort or longitudinal) studies. Measures of
association : Relative risk, attributable risk. Statistical techniques used in analysis : Cornfield and Garts method, Mantel – Haenszel method.
Conditional and unconditional matching. Analysis of data from matched samples, logistic regression approach.
Experimental Epidemiology : Clinical and community trials Statistical techniques: Methods for comparison of two treatments. Crossover
design with Garts and McNemars test. Randomization in a clinical trials, sequential methods in clinical trials, clinical life tables, assessment
of survivability in clinical trials.
Unit III : Mathematical modeling in Epidemiology : (deterministic and stochastic) simple epidemic model, generalized epidemic model,
Read-Frost and Green-wood models, models for carrier borne and host vector diseases. Estimation of latent and infectious periods,
geographical spread of the disease, simulation of an epidemic.
REFERENCES :
Kahn, H.A., Sempose, C.T.(1989) : Statistical methods in Epidemiology, Oxford University press.
Daley, D.J., Gani, J.(1999) : Epidemic modeling an introduction, Cambridge.
MSI E107
Stochastic Modelling
3
0
0
3
Dr.G.Gopal
Unit I : Basic concepts of Stochastic Processes and their classifications - Markov chain and its applications - Markov processes and
applications.
Unit II : Time Series models : Concepts, analysis and applications.
Gauss Weiner processes - Levy processes. Brownian Motion.
Unit III : Monte Carlo simulations of stochastic processes.
REFERENCES :
J.Medhi(1982) : Stochastic processes, Wiley Eastern.
Cinlar, E.(1975) : Introduction to stochastic processes, Prentice Hall.
Samuel Karlin and Howard M.Taylor(1975) : A first course in Stochastic processes Vol.I, Academic Press
Bhat,B.R.(2000) : Stochastic models : Analysis and Applications, New Age International.
MSI E108
Non parametric Inference
3
0
0
3
Dr.M.R.Srinivasan
Unit I : Rank tests for comparing two treatments, Wilcoxon ranksum tests, Asymptotic null distribution of Wilcoxon statistics, Siegel-Tukey
and Smirnov tests, power of Wilcoxon rank, sum tests, Asymptotic power, comparison with students t-test, estimating the treatment effect.
Unit II : Block comparison for two treatments, sign test for paired comparisons, Wilcoxon signed rank test, a balanced design for paired
comparisons, power of sign and Wilcoxon signed rank tests and their comparisons.
Comparison of more than two treatments, the Kruskal, Wallis test, 2 x t contingency table, comparing several treatments with a control,
ranking several treatments.
Unit III : Randomised complete blocks, Friedman, Cochran, McNemar tests, Aligned ranks. Tests of randomness and independence, testing
against, trend, testing for independence, zxt contingency tables.
REFERENCES :
Lehmann, E.L.(1975) : Non parameteric: Statistical methods based on Ranks, McGraw Hill.
Gibbons, J.D.(1971) : Non parametric Statistical inference, McGraw Hill.
Hajek, J. and Sidak, Z.(1967) : The theory of rank tests, Academic press.
Hollandar, M. and Wolfe, D.A.(1973) : Non parametric statistical methods, John Wiley.
Walsh, J.F.(1962) : Handbook of non parametric statistics, Van Nostrand.
Puri,M.L.(Ed.) (Bloomington1969)n (1972) : First international symposium on non parametric inference, Cambridge University press.
MSI E109
Data Mining Tools
3
75
0
0
3
Ms.M.R.Sindhumol
Unit I : Classification and clustering methods, decision trees.
Unit II : Introduction to databases, data warehouse, online analytical processing.
Unit III : Association rules, neural networks, regression models and trees.
REFERENCES :
Han,J and Kamber,M(2001) : Data mining: Concepts and techniques, Morgan Kautamann publishers.
Brieman, L. Friedman, J.H.,Olshen, R.A. and Stone,C.J.(1984) : Classification and regression trees; Wardsworth and Brooks.
Hestie, T.,Tibshirani,R. and Friedman,J.(2001) : The elements of statistical learning, Springer.
Johnston,R.R. & Wichern (1992):Applied multivariate Statistical analysis, Prentice Hall.
MSI E110
Bayesian Inference
3
0
0
3
Guest Faculty
Unit I : Bayesian point estimation : as a prediction problem from posterior distribution. Bayes estimators for (i) absolute error loss (ii) squared
error loss (iii) 0-1 loss. Generalization to convex loss functios. Evaluation of the estimate in terms of the posterior risk. theorem – prior and
posterior distributions. Conjugate priors and Jeffrey’s priors, examples.
Unit II : Bayesian interval estimation : Credible intervals. Highest posterior density regions. Interpretation of the confidence coefficient of an
interval and its comparison with the interpretation of the confidence coefficient for a classical confidence interval.
Unit III : Bayesian testing of hypotheses : Specification of the appropirate form of the prior distribution for a Bayesian testing of hypothesis
problem. Prior odd,s Posterior odds, Bayes factor for various types of testing hypothesis problems depending upon whether the null
hypothesis and the alternative hypothesis are simple or composite.
REFERENCES :
Berger,J.O. : Statistical decision theory and Bayesian analysis, Springler Verlag.
Robert, C.P. and Casella, G.Monte Carlo : Statistical methods, Springer Verlag.
Leonard, T. and Hsu, J.S.J. : Bayesian methods, Cambridge University press.
Degroot, M.H. : Optimal statistical decisions, McGraw Hill.
Bernando, J.M. and Smith, A.F.M. : Baysian theory, John Wiley and sons.
Robert, C.P. : The Bayesian choice : A decision theoretic motivation, Springer.
MSI S111
Statistics for Social Sciences
3
0
0
3
Dr.G.Gopal /
Guest Faculty
Unit I : Measures of central tendency and dispersion - coefficient of variation. Elements of probability theory Bayes theorem. Random variables - standard distributions and their properties, Binomial, Poisson, Uniform, Normal
Distributions.
Unit II : Elements of sampling theory - Simple and stratified and systematic sampling schemes. Multiple correlation
and Regression, Partial linear and Regression, Correlation and regression - Rank Correlation.
Unit III : Tests of significance based on Normal t, Chi square and F distributions. ANOVA - one-way and two-way
classifications.
REFERENCES :
John E.Freund(1999) : Mathematical statistics, Pearson education.
Rohatgi, V.K. (2001) : An introduction to probability and statistics, John Wiley.
Bhat,B.R. Srivenkataraman,T. and Rao Madheva K.S.(1997) : Statistics:A beginner’s text, Vol.II, New age international Pvt. LTd.
MSI S112
Bio-Statistics
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Dr.M.R.Srinivasan/
Ms.M.R.Sindhumol
Unit I : Frequency distribution - Diagrammatic representation - Measures of Central tendency - Dispersion - Probability
- Probability distribution - Binomial, Poisson & Normal Distribution.
Unit II : Elements of sampling theory – Simple, stratified and systematic sampling schemes. Applications in Biology
Correlation and Regression, Rank Correlation. Multiple correlation and Regression, Partial correlation.
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Unit III : Large Sample test - Small sample test - Student ‘t’, ‘F’ tests - Chi-Square test for independence and Goodness
of fit - Analysis of Variance. Non parametric Tests - Sign test, Run test, Median test, Two Sample Rank test.
REFERENCES :
Wayne,W.David(1987) : A foundation for analysis in Health Sciences 4 th ed., John Wiley and Sons.
Jerrold H.Zar ( 1984) : Bio statistical analysis, Prentice hall 2 nd ed.
Susan Milton, J.(1992) : Statistical methods in the biological and health sciences, McGraw Hill.
Jain,J.R.(1982) : Statistical techniques in quantitative genetics, Tata McGraw Hill.
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