Mathematical Logic: Propositional Logic; First Order Logic.
Probability: Conditional Probability; Mean, Median, Mode and Standard
Deviation; Random Variables; Distributions; uniform, normal, exponential,
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
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
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
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, NP-complete.
Programming Methodology: 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,
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, 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.
Databases: E-R diagrams, relational model, database design, integrity
constraints, normal forms, query languages (SQL), file structures
(sequential, indexed), b-trees, transaction and concurrency control.
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 signature, firewalls
Web technologies: Proxy, HTML, XML, basic concepts of cgi-bin programming.