Vidyasagar University Syllabus
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Vidyasagar University Syllabus
MSC Semester – I:
Mathematical
Computation

Propositional logic: Syntax, semantics, valid, satisfiable and
unsatisfiable formulas, encoding and examining the validity of some logical
arguments. Proof techniques: forward proof, proof by contradiction,
contrapositive proofs, proof of necessity and sufficiency.

Sets, relations and functions: Operations on sets, relations and
functions, binary relations, partial ordering relations, equivalence
relations, principles of mathematical induction

Size of a set: Finite and infinite sets, countable and uncountable
sets, Cantor's diagonal argument and the power set theorem,
SchroederBernstein theorem.

Introduction to counting: Basic counting techniques  inclusion and
exclusion, pigeonhole principle, permutation, combination, summations.
Introduction to recurrence relation and generating function.

Algebraic structures and morphisms: Algebraic structures with one
binary operation  semigroups, monoids and groups, congruence relation and
quotient structures. Free and cyclic monoids and groups, permutation groups,
substructures, normal subgroups. Algebraic structures with two binary operations
 rings, integral domains and fields. Boolean algebra and Boolean ring

Introduction to graphs: Graphs and their basic properties  degree,
path, cycle, subgraphs, isomorphism, Eulerian and Hamiltonian walks, graph
coloring, planar graphs, trees.

Advanced
Computer Architecture

Overview of von Neumann architecture: Instruction set architecture;
The Arithmetic and Logic Unit, The Control Unit, Memory and I/O devices and
their interfacing to the CPU; Measuring and reporting performance; CISC and
RISC processors

Pipelining: Basic concepts of pipelining, data hazards, control
hazards, and structural hazards; Techniques for overcoming or reducing the
effects of various hazards.

Hierarchical Memory Technology: Inclusion, Coherence and locality
properties; Cache memory organizations, Techniques for reducing cache misses;
Virtual memory organization, mapping and management techniques, memory
replacement policies.

Instructionlevel parallelism: Concepts of instructionlevel
parallelism (ILP), Techniques for increasing ILP; Superscalar,
superpipelined and VLIW processor architectures; Vector and symbolic
processors; Case studies of contemporary microprocessors

Multiprocessor Architecture: Taxonomy of parallel architectures;
Centralized sharedmemory architecture, synchronization, memory consistency,
interconnection networks; Distributed sharedmemory architecture, Cluster
computers

Non von Neumann Architectures: Data flow Computers, Reduction
computer architectures, Systolic Architectures.

Computer Networks

Introduction to networks and layered architecture. Data communication
concepts, transmission media and topology, multiplexing

Circuit switching and packet switching, data link layer, layer 2
switches and ATM switches, SONET/SDH.

Medium access control. CSMA CD, TDMA, FDMA, CDMA. Network layer and
addressing, IP version 4 and 6. Routing algorithms. Transmission layer, TCP
and UDP. Congestion control techniques. WAN, ATM. Internetworking. Wireless
communications. Network management and security

Computer
Graphics

Graphics hardware and display devices; graphics primitives: drawing
lines and curves; 2d and 3d transformations; segments and their applications;
generating curves, surfaces and volumes in 3d, wireframe models, Bezier and
spline curves and surfaces

Geometric modeling: elementary geometric algorithms for polygons,
boundary representations, constructive solid geometry, spatial data
structures; hidden surface and line elimination

Rendering: shading, light models, realistic image synthesis techniques,
textures and imagebased rendering; video games and computer animation.
Laboratory: Programming for generating lines, curves and rendered surfaces

Interactive graphics programming: modeling and updating objects in an
object hierarchy, video games, computer animation and realistic image
synthesis.

Programming environments: OpenGL (or equivalent), Java graphics
environments, X windows (or equivalents).

Multimedia

Introduction to Multimedia System: Architecture and components,
Multimedia distributed processing model, Synchronization, Orchestration and
Quality of Service (QOS) architecture.

Audio and Speech: Data acquisition, Sampling and Quantization, Human
Speech production mechanism, Digital model of speech production, Analysis and
synthesis, Psychoacoustics, low bit rate speech compression, MPEG audio
compression.

Images and Video: Image acquisition and representation, Composite
video signal NTSC, PAL and SECAM video standards, Bilevel image compression
standards: ITU (formerly CCITT) Group III and IV standards, JPEG image
compression standards, MPEG video compression standards

Multimedia Communication: Fundamentals of data communication and
networking, Bandwidth requirements of different media, Real time constraints:
Audio latency, Video data rate, multimedia over LAN and WAN, Multimedia
conferencing.

Hypermedia presentation: Authoring and Publishing, Linear and
nonlinear presentation, Structuring Information, Different approaches of
authoring hypermedia documents, Hypermedia data models and standards.

Multimedia Information Systems: Operating system support for
continuous media applications: limitations is usual OS, New OS support, Media
stream protocol, file system support for continuous media, data models for
multimedia and hypermedia information, content based retrieval of
unstructured data.

Paper I (Theory)
Group A:
Mathematical Methods

Vector Analysis
Vector algebra, products, polar and axial vector, differentiation,
Gradient, Divergence and curl of vector and applications to simple problems,
Vector Integration: Line, Surface and Volume integral, Gauss' divergence
theorem, Stokes' theorem, Green’s theorem and related integral theorems,
Curvilinear coordinates.

Matrix:
Inverse of a matrix, Matrix algebra, Hermitian and Unitary matrices.
Similarity transformation, Diagonalisation of matrices with non degenerate Eigen
values, Eigen values and Eigen vectors.

Differential equations:
First order, second order
differential equations with constant coefficient, partial differential
equations and its solutions for simple problems with separation of variable
methods, Bessel, Legendre, Hermite polynomial differential equation,
generator recursion relation, Rodrigue formula, orthogonal properties,
Nonlinear Differential equation – Preliminary.

Laplace Transform and inverse Laplace Transform:
Definitions, Conditions for existence of Laplace transforms, Lerch's
theorem, important properties, Methods of finding transforms.

Fourier Analysis:
Fourier theorem, Fourier series, evaluation of coefficient, Analysis
of simple waveform using Fourier series, Fourier integrals, Relationship of
Fourier and Laplace transforms.

Complex Variable:
f(z) its limit and continuity, Derivative of f(z), Cauchy Riemann
equations, Analytic function, Harmonic functions, Orthogonal systems,
Applications to flow problem, Geometrical representation of f(z),Conformal
transformation, Integration of complex functions, Cauchy’s theorem.

GroupB:
Classical Mechanics

Conservation Principals (laws), constrained motion, degrees of
freedom, Generalized Coordinate, Generalized motion. Variational Principle
and Lagrangian formulation, Calculus of variation, delta variation, Euler
Lagrange differential equation, Conservative and non conservative systems,
Hamiltonian variational principal, Concept of Lagrange and equation of
motion, D Alembert’s principle

Rayleigh’s dissipation function, Conservation of momentums,
Conservation of Energy (Jacobi’s Integral), Concept of Symmetry, Homogeneity
and Isotropy, Hamiltonian formulation of Mechanics.

Group C:
Optics

Physical Optics:
Fermat's principle and its applications  Matrix method of Paraxial
optics. Magnification, Helmholtz Lagrange Laws, Cardinal points of an
optical systemthick lens and lens combinations, telephoto lenses, paraxial
approxin1ation. Aberration in images, Seidal aberration, Aplenetic points of
sphere, Ach romantic combination of lenses, oil immersion objectives, eye
pieces Ramsdan & Huygen.

Interference:
Interference of light waves,
spatial and temporal coherence, Young's experiment, intensity distribution,
Fresnel biprism, interference in thin film, Fringes of equal thickness and
equal inclination, Newton's ring.

Diffraction:
Diffraction of light waves, Fresnel and Fraunhofer class, Fresnel's
half period zones, explanation of rectilinear propagation of light, zone
plate, Fraunhofer diffraction due to single slit, double slit, grating.

GroupD:
Electrostatics and Magneto statics:

Electrostatics:
Introduction: Fundamental
relations of the electrostatics field, Gauss law, The potential function,
Field due to a continuous distribution of charge, Equipotential Surface,
Divergence theorem, Possion’s equation and Laplace equation, Capacitance,
Electrostatics Energy

Magneto statics:
Theories of the Magnetic Field, Magnetic Induction and Faradays law,
Magnetic flux density, Magnetic field strength and Magneto motive force,
Ampere’s work law, Permeability, Energy stored in Magnetic Field, Ampere’s
law for a current element, Volume distribution of current element and the
Dirac delta, Ampere’s law, Magnetic vector potential, Analogies between
Electric and Magnetic field.

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