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;
asymptotic.
Graph Theory:
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 Simpsons rules.
Calculus:
Calculus:
Limit,
Continuity & differentiability, Mean value Theorems, Theorems of integral
calculus, evaluation of definite & improper integrals, Partial derivatives,
Total derivatives, maxima & minima.
2. 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 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 approach, 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:
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 languages (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:
Computer Networks:
ISO/OSI
stack, LAN technologies (Ethernet, Token ring), Flow and error control
techniques, Routing algorithms, Congestion 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.
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