ENGINEERING MATHEMATICS
Mathematical Logic: Propositional Logic;
First Order Logic.
Probability: Conditional Probability; Mean,
Median, Mode and Standard Deviation; Random
Variables; Distributions; uniform, normal,
exponential, Poisson, Binomial.
Set Theory & Algebra: Sets; Relations;
Functions; Groups; Partial Orders; Lattice;
Boolean Algebra.
Combinatorics: Permutations; Combinations;
Counting; Summation; generating functions;
recurrence relations; asymptotics.
Graph Theory: Connectivity; spanning trees;
Cut vertices & edges; covering;
matching; independent sets; Colouring;
Planarity; Isomorphism.
Linear Algebra: Algebra of matrices,
determinants, systems of linear equations,
Eigen values and Eigen vectors.
Numerical Methods: LU decomposition for
systems of linear equations; numerical
solutions of non linear algebraic equations
by Secant, Bisection and Newton-Raphson
Methods; Numerical integration by
trapezoidal and Simpson's rules.
Calculus: Limit, Continuity &
differentiability, Mean value Theorems,
Theorems of integral calculus, evaluation of
definite & improper integrals, Partial
derivatives, Total derivatives, maxima &
minima.
FORMAL LANGUAGES AND AUTOMATA
Regular Languages: finite automata, regular
expressions, regular grammar.
Context free languages: push down automata,
context free grammars
COMPUTER HARDWARE
Digital Logic: Logic functions,
minimization, design and synthesis of
combinatorial and sequential circuits,
number representation and computer
arithmetic (fixed and floating point)
Computer organization: Machine instructions
and addressing modes, ALU and data path,
hardwired and microprogrammed control,
memory interface, I/O interface (interrupt
and DMA mode), serial communication
interface, instruction pipelining, cache,
main and secondary storage
SOFTWARE SYSTEMS
Data structures and Algorithms: the notion
of abstract data types, stack, queue, list,
set, string, tree, binary search tree, heap,
graph, tree and graph traversals, connected
components, spanning trees, shortest paths,
hashing, sorting, searching, design
techniques (greedy, dynamic, divide and
conquer), asymptotic analysis (best, worst,
average cases) of time and space, upper and
lower bounds, intractability
Programming Methodology: C programming,
program control (iteration, recursion,
functions), scope, binding, parameter
passing, elementary concepts of object
oriented programming
Operating Systems (in the context of Unix):
classical concepts (concurrency,
synchronization, deadlock), processes,
threads and interprocess communication, CPU
scheduling, memory management, file systems,
I/O systems, protection and security
Information Systems and Software
Engineering: information gathering,
requirement and feasibility analysis, data
flow diagrams, process specifications,
input/output design, process life cycle,
planning and managing the project, design,
coding, testing, implementation,
maintenance.
Databases: relational model, database
design, integrity constraints, normal forms,
query languages (SQL), file structures
(sequential, indexed), b-trees, transaction
and concurrency control
Data Communication: data encoding and
transmission, data link control,
multiplexing, packet switching, LAN
architecture, LAN systems (Ethernet, token
ring), Network devices: switches, gateways,
routers
Networks: ISO/OSI stack, sliding window
protocols, routing protocols, TCP/UDP,
application layer protocols & systems
(http, smtp, dns, ftp), network security
Web technologies: three tier web based
architecture; JSP, ASP, J2EE, .NET systems;
html, XML
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