Propositional Logic; First Order Logic.
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;
Permutations; Combinations; Counting; Summation; generating
functions; recurrence relations; asymptotics.
Connectivity; spanning trees; Cut vertices & edges;
covering; matching; independent sets; Colouring; Planarity;
Algebra of matrices, determinants, systems of linear
equations, Eigen values and Eigen vectors.
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.
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:
finite automata, regular expressions, regular grammar.
Context free languages:
push down automata, context free grammars
Logic functions, minimization, design and synthesis of
combinatorial and sequential circuits, number representation
and computer arithmetic (fixed and floating point)
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
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, Algorithm
design by induction), asymptotic analysis (best, worst,
average cases) of time and space, upper and lower bounds,
Basic concepts of complexity classes – P, NP, NP-hard,
Scope, binding, parameter passing, recursion, C programming
– data types and declarations, assignment and control flow
statements, 1-d and 2-d arrays, functions, pointers,
concepts of object-oriented programming - classes, objects,
inheritance, polymorphism, operator overloading.
Operating Systems (in the context of Unix): classical concepts (concurrency, synchronization, deadlock),
processes, threads and inter process communication, CPU
scheduling, memory management, file systems, I/O systems,
protection and security, shell programming.
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.
E-R diagrams, relational model, database design, integrity
constraints, normal forms, query languages (SQL), file
structures (sequential, indexed), b-trees, transaction and
Data Communication and Networks:
ISO/OSI stack, transmission media, data encoding,
multiplexing, flow and error control, LAN technologies
(Ethernet, token ring), network devices – switches,
gateways, routers, ICMP, application layer protocols – SMTP,
POP3, HTTP, DNS, FTP, Telnet, network security – basic
concepts of public key and private key cryptography, digital
Proxy, HTML, XML, basic concepts of cgi-bin programming.