Notes

Propositional Logic; First Order Logic.
Probability
:
Conditional Probability; Mean, Median, Mo
de and Standard Deviation; Random
Variables; Distributions; uniform, normal, exponential, Poisson, Binomial.
Set Theory & Algebra
:
Sets; Relations; Functions; Groups;
Partial Orders; Lattice; Boolean
Algebra.
Combinatory
:
Permutations; Combinations; Counting; Summation; generating functions;
recurrence relations; asymptotics.
Graph Theory
:
Connectivity; spanning trees; Cut ve
rtices & edges; covering; matching;
independent sets; Colouring; Planarity; Isomorphism.
Linear Algebra
:
Algebra of matrices, determinants, syst
ems 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, Bise
ction 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.
COMPUTER
SCIENCE
AND
INFORMATION
TECHNOLOGY
Digital Logic:
Logic functions, Minimization, Design and synthesis of combinational and
sequential circuits; Number representation and computer arithmetic (fixed and floating point).
Computer Organization and Architecture:
Machine instructions and addressing modes, ALU
and data-path, CPU control design, Memory interface, I/O interface (Interrupt and DMA mode),
Instruction pipelining, Cache and main memory, Secondary storage.
Programming and Data Structures:
Programming in C; Functions, Recursion, Parameter
passing, Scope, Binding; Abstract data types,
Arrays, Stacks, Queues, Linked Lists, Trees,
Binary search trees, Binary heaps.
Algorithms:
Analysis, Asymptotic notation, Notions of space and time complexity, Worst and
average case analysis; Design: Greedy appro
ach, Dynamic programming, Divide-and-conquer;
Tree and graph traversals, Connected components, Spanning trees, Shortest paths; Hashing,
Sorting, Searching. 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.
Theory of Computation:
Regular languages and finite automata, Context free languages and
Push-down automata, Recursively enumerable sets and Turing machines, Undecidability.
Compiler Design:
Lexical analysis, Parsing, Syntax directed translation, Runtime environments,
Intermediate and target code generation, Basics of code optimization.
Operating System:
Processes, Threads, Inter-process communication, Concurrency,
Synchronization, Deadlock, CPU scheduling, Memory management and virtual memory, File
systems, I/O systems, Protection and security.
Databases:
ER-model, Relational model (relational algebra, tuple calculus), Database design
(integrity constraints, normal forms), Query langua
ges (SQL), File structures (sequential files,
indexing, B and B+ trees), Transactions and concurrency control.
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.
Computer Networks:
ISO/OSI stack, LAN technologies (Ethernet, Token ring), Flow and error
control techniques, Routing algorithms, Conges
tion control, TCP/UDP and sockets, IP(v4),
Application layer protocols (icmp, dns, smtp, pop, ftp, http); Basic concepts of hubs, switches,
gateways, and routers. Network security – basic concepts of public key and private key
cryptography, digital signature, firewalls.
Web technologies
: HTML, XML, basic concepts of client-server computing.