Syllabus for M. Sc. Mathematics Written Test
- Functions of One Variable: Limit, continuity, differentiation,
Rolle’s Theorem, Mean value theorem, Taylor's theorem, Maxima and minima
- Functions of Two Real Variables: Limit, continuity, partial derivatives,
differentiability, maxima and minima, Method of Lagrange multipliers, Homogeneous
functions including Euler’s theorem.
- Integral Calculus: Integration as the inverse process of differentiation,
definite integrals and their properties, Fundamental theorem of integral calculus.
Double and triple integrals, change of order of integration. Calculating surface
areas and volumes using double integrals and applications. Calculating volumes using
triple integrals and applications.
- Differential Equations: Ordinary differential equations of the
first order of the form y'=f(x,y). Bernoulli’s equation, exact differential equations,
integrating factor, Orthogonal trajectories, Homogeneous differential equations-separable
solutions, Linear differential equations of second and higher order with constant
coefficients, method of variation of parameters. Cauchy-Euler equation.
- Vector Calculus: Scalar and vector fields, gradient, divergence,
curl and Laplacian. Scalar line integrals and vector line integrals, scalar surface
integrals and vector surface integrals, Green's, Stokes and Gauss theorems and their
applications.
- Group Theory: Groups, subgroups, Abelian groups, non-abelian groups,
cyclic groups, permutation groups; Normal subgroups, Lagrange's Theorem for finite
groups, group homomorphisms and basic concepts of quotient groups (only group theory).
- Linear Algebra: Vector spaces, Linear dependence of vectors, basis,
dimension, linear transformations, matrix representation with respect to an ordered
basis, Range space and null space, rank-nullity theorem; Rank and inverse of a matrix,
determinant, solutions of systems of linear equations, consistency conditions. Eigenvalues
and eigenvectors. Cayley-Hamilton theorem. Symmetric, skew-symmetric, hermitian,
skew-hermitian, orthogonal and unitary matrices.
- Real Analysis: Interior points, limit points, open sets, closed
sets, bounded sets, connected sets, compact sets; completeness of R, Power series
(of real variable) including Taylor’s and Maclaurin’s, domain of convergence, term-wise
differentiation and integration of power series.
Syllabus for M. Sc. Physics Written Test
- Vector calculus: Coordinate systems in two and three dimensions,
Dot product, Cross product, Gradient, Divergence, Curl, Line integral, Surface integral,
Volume integral.
- Classical Mechanics: Kinematics, Force, Momentum, Work and Energy,
Collisions in Center-of-mass frame, Angular momentum, Torque, Rigid body motion,
Central force motion, Harmonic oscillator, and Non-inertial Frame Of Reference.
- Electrodynamics: Basic concepts of electrostatics, Gauss’s law
and its application, basic concepts of magnetostatics, electromotive force, Faraday’s
law, Maxwell’s equations, Electromagnetic waves.
- Quantum Mechanics: Wave particle duality, Photoelectric effect,
Black body radiation, Compton effect, Concepts of wave packets, Heisenberg uncertainty
principle and its application, wave function, Time dependent and independent Schrödinger
equation and its application in one dimension.
- Heat and Thermodynamics: Thermodynamic properties, Energy, work,
heat, laws of thermodynamics and their applications.
- Special Theory of Relativity: Michelson Morley Experiment, Lorentz
Transformations, Time Dilation and Length contraction.
- Solid State Physics: Crystal binding, Crystal structure, Electrical,
thermal and optical properties of solid.
- Optics: Wave equation, Plane waves, Electromagnetic waves, Standing
waves, Interference, Diffraction, Lasers
M.Tech. / MS in Computer Science & Engineering (CSE)
Syllabus for written examination of M.Tech. / M.S. admission in Computer Science
& Engineering
- Computer Programming: Fundamental programming constructs, Decision
Making and control statements, Arrays, Strings, Functions, Recursion, Dynamic memory
allocation, Composite data types (Structures and Unions)
- Discrete Mathematical Structures: Boolean algebra, Propositional
and first order logic, Sets, Relations, Functions, Partial orders and lattices,
Groups and Rings, Trees, Graphs (Connectivity, Matching, Coloring), Combinatorics
(Counting, Recurrence relations, Generating functions)
- Data Structures: Time and Space complexity of algorithms, Asymptotic
analysis, Big O and other notations, Stacks, Queues, Linked lists (Singly, Doubly
and Circular), Trees, Binary search trees, AVL tree, Heaps, Hashing and Graphs
- Algorithms: Complexity analysis, Searching, Sorting, Algorithm
design techniques (Greedy, Dynamic programming and Divide‐and‐conquer), Graph search,
Minimum spanning tree, Shortest path
- Computer Organization and Architecture: Machine instructions and
addressing modes. ALU, Data‐path and Control unit, Instruction pipelining, Memory
hierarchy (Cache, Main memory and Secondary storage), I/O interface (Interrupt and
DMA mode)
- Operating Systems: Processes, Threads, Inter‐process communication,
Concurrency and Synchronization, Deadlock, CPU scheduling, Memory management and
Virtual memory
- Database Management Systems: ER‐model, Relational model, Relational
algebra, Tuple calculus, SQL, Integrity constraints, Normal forms, File organization,
Indexing, Transactions and Concurrency control
- Computer Networks: OSI and TCP/IP Model, Ethernet and WiFi, Access
Control, Flow and Error control, Network devices, Switching, IPv4, IPv6, Routing
algorithms, TCP/UDP and sockets, Congestion control, Application layer protocols
(DNS, SMTP, POP, FTP, HTTP)
- Theory of Computation:Regular expressions and finite automata,
Context-free grammars and push-down automata, Regular and context-free languages,
Turing machine and Undecidability
M.Tech. / MS in Electronics & Communication Engineering (ECE)
Syllabus of written exam for M.Tech. / MS admission (ECE)
- Digital Design: Number Systems & Codes, Boolean Algebra and Minimization
Techniques, Digital CMOS Logic, Combinatorial Circuits & Systems, Sequential Circuits
& Systems, Finite State Machines.
- Analog Electronics: Circuit Theorems and KCL/KVL, Op-amp, RC, RLC
Circuits, Physics of transistors, Characteristics and biasing of BJT, Small signal
(incremental) equivalent circuits, CE, CB and CC amplifiers, Difference Amplifier
Design, Oscillators and Filters: Bode plots, Clipping, Clamping and other Non-Linear
Op-Amp applications, Power supplies, DAC: Principles and Circuits, ADC: Principles
and Circuits.
- Signals and Systems: Linear time invariant (LTI) systems: Discrete
and continuous, Fourier representation of periodic signals, Fourier Transform of
aperiodic signals, Laplace and z-transform, Linear Feedback Systems.
- Digital Signal Processing: Transform analysis of LTI systems, Structures
for Discrete Time systems, FIR Filter Design Techniques, FFT, Multi-rate digital
Signal Processing, Adaptive signal Processing, Stochastic signals, Wiener Filtering,
LMS and RLS algorithms, spectral estimation.
- Basic Analog and Digital Communication: Bandwidth of AM/SSB/FM
analog signals, SNR of FM system, DM/ADM/PCM, signal-to-quantization noise ratio.,
PSK/DPSK/QAM /OFDM systems,BER and Q-function, Error correcting codes: Block codes
and convolutional codes
- Probability and matrices Algebra: Random variables, distribution,
mean and variance, Conditional probability, Bayes’s theorem, correlation, covariance,
Central limit theorem, Matrix multiplication,Gaussian elimination, Determinant,
Inverse of matrix, eigenvalues and eigen-vectors, matrix digonalization
MS in Communication and Computer Engineering (CCE)
Syllabus of written exam for MS admission (CCE)
- Digital Design: Number Systems & Codes, Boolean Algebra and Minimization
Techniques, Digital CMOS Logic, Combinatorial Circuits & Systems, Sequential Circuits
& Systems, Finite State Machines.
- Analog Electronics: Circuit Theorems and KCL/KVL, Op-amp, RC, RLC
Circuits, Physics of transistors, Characteristics and biasing of BJT, Small signal
(incremental) equivalent circuits, CE, CB and CC amplifiers, Difference Amplifier
Design, Oscillators and Filters: Bode plots, Clipping, Clamping and other Non-Linear
Op-Amp applications, Power supplies, DAC: Principles and Circuits, ADC: Principles
and Circuits.
- Signals and Systems: Linear time invariant (LTI) systems: Discrete
and continuous, Fourier representation of periodic signals, Fourier Transform of
aperiodic signals, Laplace and z-transform, Linear Feedback Systems.
- Digital Signal Processing: Transform analysis of LTI systems, Structures
for Discrete Time systems, FIR Filter Design Techniques, FFT, Multi-rate digital
Signal Processing, Adaptive signal Processing, Stochastic signals, Wiener Filtering,
LMS and RLS algorithms, spectral estimation.
- Basic Analog and Digital Communication: Bandwidth of AM/SSB/FM
analog signals, SNR of FM system, DM/ADM/PCM, signal-to-quantization noise ratio.,
PSK/DPSK/QAM /OFDM systems,BER and Q-function, Error correcting codes: Block codes
and convolutional codes
- Probability and matrices Algebra: Random variables, distribution,
mean and variance, Conditional probability, Bayes’s theorem, correlation, covariance,
Central limit theorem, Matrix multiplication,Gaussian elimination, Determinant,
Inverse of matrix, eigenvalues and eigen-vectors, matrix digonalization