Gate 2012 Computer Science Engineering(CSE) Syllabus
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 Engineering
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 env ironments,
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
