__
Engineering Mathematics:__

**
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; Coloring; 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, evaluation of 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; NPcompleteness.

**
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
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, B and 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.