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# gate2016

## Virtual Calculator for GATE 2016

**For GATE CSE**

- The only real use of calculator is multiplication and division, so don’t worry too much using this.
- Base, matrix, integral options are not available as in Casio 991, but they are not needed if you study the problems as per theory.

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## GATE CSE 2016 Syllabus

### GATE 2017 syllabus is no change from GATE 2016. The changes given below were for GATE 2016 syllabus.

## Contents

## Discrete Mathematics

- Propositional and first order logic.
- Sets, relations, functions, partial orders and lattices. Groups.
- Graphs: connectivity, matching, coloring.
- Combinatorics: counting, recurrence relations, generating functions.

Boolean Algebra moved to Digital Logic.

Permutations; Combinations removed from Combinatorics but being basic and counting being there this does not really matter.

asymptotics removed, but basics are in asymptotic analysis part of Algorithms

spanning trees; Cut vertices & edges; covering; independent sets; Planarity; Isomorphism removed. But based on other topics this just means Planarity and isomorphism are removed (spanning trees are already in algorithms)

## Linear Algebra

LU decomposition added here from Numerical methods which was removed as a whole otherwise.

## Calculus

Theorems of integral calculus, evaluation of definite & improper integrals, Partial derivatives, Total derivatives removed and Integration added. So, this would mean we can expect only simple integration questions.

## Probability

- Random variables.
- Uniform, normal, exponential, poisson and binomial distributions.
- Mean, median, mode and standard deviation.
- Conditional probability and Bayes theorem.

Bayes theorem newly added but it was implicitly part of conditional probability

## Digital Logic

- Boolean algebra.
- Combinational and sequential circuits. Minimization.
- Number representations and computer arithmetic (fixed and floating point).

**Boolean algebra**added to here from set theory & algebra

## Computer Organization and Architecture

- Machine instructions and addressing modes.
- ALU, data‐path and control unit.
- Instruction pipelining.
- Memory hierarchy: cache, main memory and secondary storage;
- I/O interface. (Interrupt and DMA mode)

Memory interface part is removed. So, questions on RAM would not be there.

## Programming and Data Structures

- Programming in C. Recursion.
- Arrays, stacks, queues, linked lists, trees, binary search trees, binary heaps, graphs.

**Functions, Parameter passing, Scope, Binding; Abstract data types**removed. But most of these are part of runtime environments in compilers (see Draggon book Runtime Environments chapter) anyway.**Graphs**added here.

## Algorithms

- Searching, sorting, hashing.
- Asymptotic worst case time and space complexity.
- Algorithm design techniques: greedy, dynamic programming and divide‐and‐conquer.
- Graph search, minimum spanning trees, shortest paths.

Space and time complexity restricted to only worst case.

Connected components removed here, but they are in Graph theory anyway

Tree and graph traversals removed. But these are implied in Data Structure portion and other algorithm portions.

Basic concepts of complexity classes – P, NP, NP-hard, NP-complete removed. So, their definitions need not be studied but reduction is there in Theory of Computation anyway.

## Theory of Computation

- Regular expressions and finite automata.
- Context-free grammars and push-down automata.
- Regular and context-free languages, pumping lemma.
- Turing machines and undecidability.

pumping lemma newly added. So, questions based on pumping length or some examples can be asked.

Recursively enumerable sets removed but Turing machines are there. So, this should not really matter.

## Compiler Design

- Lexical analysis, parsing, syntax-directed translation.
- Runtime environments.
- Intermediate code generation.

target code generation, Basics of code optimization removed. This is quite a good removal for students. Questions like register allocation, optimizations like code motion etc. would not be there

## Operating System

- Processes, threads, inter‐process communication, concurrency and synchronization.
- Deadlock.
- CPU scheduling.
- Memory management and virtual memory.
- File systems. Disks is also under this

**I/O systems, Protection and security**removed. Rarely questions like size of graphic card required etc have been asked.

## Databases

- ER‐model. Relational model:relational algebra, tuple calculus,SQL.
- Integrity constraints,
- normal forms.
- File organization, indexing (e.g., B and B+ trees).
- Transactions and concurrency control.

No change

## Computer Networks

- Concept of layering. LAN technologies (Ethernet).
- Flow and error control techniques,
- switching.
- IPv4/IPv6,
- routers and routing algorithms (distance vector, link state).
- TCP/UDP and sockets, congestion control.
- Application layer protocols (DNS, SMTP, POP, FTP, HTTP).
- Basics of Wi-Fi.
- Network security: authentication, basics of public key and private key cryptography, digital signatures and certificates, firewalls.

**IPv6**added**Token Ring**removed**Basics of Wi–Fi**added**Basic concepts of hubs, switches, gateways, and routers**removed**Subnetting**is an important part under IP.

## General Aptitude

- No change in Numerical Ability as well as Verbal Ability.

## Removals

Except LU decomposition, all portions of Web Technologies, IS & Software Engineering and Numerical Methods are removed.

**Web technologies:** HTML, XML, basic concepts of client-server computing.

**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

**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.

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