# (Syllabus) GATE Examination (CS - COMPUTER SCIENCE AND ENGINEERING)

**Syllabus
: ****GATE
Examination (National Level Entrance Exam****)**

__CS
- COMPUTER SCIENCE AND ENGINEERING
__

**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; 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, 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; 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 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.