Thursday, August 5, 2010



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;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 Simpson’s rules.

Calculus: Limit, Continuity & differentiability, Mean value Theorems, Theorems of integral calculus, evaluationof definite & improper integrals, Partial derivatives, Total derivatives, maxima & minima.


Theory of Computation: Regular languages and finite automata, Context free languages and Push-down
automata, Recursively enumerable sets and Turing machines, Undecidability; NP completeness.

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 datapath, 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 approach, Dynamic programming, Divide-and-conquer; Tree and graph traversals,
Connected components, Spanning trees, Shortest paths; Hashing, Sorting, Searching.

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, Band B+ trees),
Transactions and concurrency control.

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.


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