Mathematical Logic: Propositional
Logic; First Order Logic.
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.
Combinations; Counting; Summation; generating functions; recurrence relations;
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
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
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
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
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, operator overloading.
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
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,
Databases: 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 signature, firewalls
Web technologies: Proxy,
HTML, XML, basic concepts of cgi-bin programming.