# GATE Computer Science and Information Technology Syllabus 2015

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**GATE 2015 Computer Science and Information Technology Syllabus ( CS )**

**Engineering Mathematics Syllabus**

**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.

**Combinatory :** 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 Information Technology Syllabus**

**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. Asymptotic analysis ( best, worst, average cases ) of time and space, upper and lower bounds, Basic concepts of complexity classes P, NP, NP – hard, NP – complete.

**Theory of Computation :** Regular languages and finite automata, Context free languages and Push – down automata, Recursively enumerable sets and Turing machines, Undecidability.

**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.

**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.

**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. Network security basic concepts of public key and private key Cryptography, Digital Signature, Firewalls.

**Web Technologies :** HTML, XML, basic concepts of Client / Server computing.

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