**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.

COMPUTER SCIENCE AND ENGINEERING

**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.