One Stop GATE Forum: Gate Syllabus of INFORMATION TECHNOLOGY

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   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.

                                    

                                    FORMAL LANGUAGES AND AUTOMATA

                                    

                                    Regular Languages: finite automata, regular
                                    expressions, regular grammar.

                                    

                                    Context free languages: push down automata,
                                    context free grammars

                                    

                                    COMPUTER HARDWARE

                                    

                                    Digital Logic: Logic functions,
                                    minimization, design and synthesis of
                                    combinatorial and sequential circuits,
                                    number representation and computer
                                    arithmetic (fixed and floating point)

                                    

                                    Computer organization: Machine instructions
                                    and addressing modes, ALU and data path,
                                    hardwired and microprogrammed control,
                                    memory interface, I/O interface (interrupt
                                    and DMA mode), serial communication
                                    interface, instruction pipelining, cache,
                                    main and secondary storage

                                    

                                    SOFTWARE SYSTEMS

                                    

                                    Data structures and Algorithms: the notion
                                    of abstract data types, stack, queue, list,
                                    set, string, tree, binary search tree, heap,
                                    graph, tree and graph traversals, connected
                                    components, spanning trees, shortest paths,
                                    hashing, sorting, searching, design
                                    techniques (greedy, dynamic, divide and
                                    conquer), asymptotic analysis (best, worst,
                                    average cases) of time and space, upper and
                                    lower bounds, intractability

                                    

                                    Programming Methodology: C programming,
                                    program control (iteration, recursion,
                                    functions), scope, binding, parameter
                                    passing, elementary concepts of object
                                    oriented programming

                                    

                                    Operating Systems (in the context of Unix):
                                    classical concepts (concurrency,
                                    synchronization, deadlock), processes,
                                    threads and interprocess communication, CPU
                                    scheduling, memory management, file systems,
                                    I/O systems, protection and security

                                    

                                    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.

                                    

                                    Databases: relational model, database
                                    design, integrity constraints, normal forms,
                                    query languages (SQL), file structures
                                    (sequential, indexed), b-trees, transaction
                                    and concurrency control

                                    

                                    Data Communication: data encoding and
                                    transmission, data link control,
                                    multiplexing, packet switching, LAN
                                    architecture, LAN systems (Ethernet, token
                                    ring), Network devices: switches, gateways,
                                    routers

                                    

                                    Networks: ISO/OSI stack, sliding window
                                    protocols, routing protocols, TCP/UDP,
                                    application layer protocols & systems
                                    (http, smtp, dns, ftp), network security

                                    

                                    Web technologies: three tier web based
                                    architecture; JSP, ASP, J2EE, .NET systems;
                                    html, XML

                                    

MA -
                                    MATHEMATICS

                                    

                                    Linear Algebra: Finite dimensional vector
                                    spaces. Linear transformations and their
                                    matrix representations, rank; systems of
                                    linear equations, eigenvalues and
                                    eigenvectors, minimal polynomial, Cayley-Hamilton
                                    theorem, diagonalisation, Hermitian, Skew-Hermitian
                                    and unitary matrices. Finite dimensional
                                    inner product spaces, self-adjoint and
                                    Normal linear operators, spectral theorem,
                                    Quadratic forms.

                                    

                                    Complex Analysis: Analytic functions,
                                    conformal mappings, bilinear
                                    transformations, complex integration:
                                    Cauchy's integral theorem and formula,
                                    Liouville's theorem, maximum modulus
                                    principle, Taylor and Laurent's series,
                                    residue theorem and applications for
                                    evaluating real integrals.

                                    

                                    Real Analysis: Sequences and series of
                                    functions, uniform convergence, power
                                    series, Fourier series, functions of several
                                    variables, maxima, minima, multiple
                                    integrals, line, surface and volume
                                    integrals, theorems of Green, Stokes and
                                    Gauss; metric spaces, completeness,
                                    Weierstrass approximation theorem,
                                    compactness. Lebesgue measure, measurable
                                    functions; Lebesgue integral, Fatou's lemma,
                                    dominated convergence theorem.

                                    

                                    Ordinary Differential Equations: First order
                                    ordinary differential equations, existence
                                    and uniqueness theorems, systems of linear
                                    first order ordinary differential equations,
                                    linear ordinary differential equations of
                                    higher order with constant coefficients;
                                    linear second order ordinary differential
                                    equations with variable coefficients, method
                                    of Laplace transforms for solving ordinary
                                    differential equations, series solutions;
                                    Legendre and Bessel functions and their
orthogonality, Sturm Liouville system,
                                    Greeen's functions.

                                    

                                    Algebra: Normal subgroups and homomorphisms
                                    theorems, automorphisms. Group actions,
                                    sylow's theorems and their applications
                                    groups of order less than or equal to 20,
                                    Finite p-groups. Euclidean domains,
                                    Principal ideal domains and unique
                                    factorizations domains. Prime ideals and
                                    maximal ideals in commutative rings.

                                    

                                    Functional Analysis: Banach spaces, Hahn-Banach
                                    theorems, open mapping and closed graph
                                    theorems, principle of uniform boundedness;
                                    Hilbert spaces, orthonormal sets, Riesz
                                    representation theorem, self-adjoint,
                                    unitary and normal linear operators on
                                    Hilbert Spaces.

                                    

                                    Numerical Analysis: Numerical solution of
                                    algebraic and transcendental equations;
                                    bisection, secant method, Newton-Raphson
                                    method, fixed point iteration,
                                    interpolation: existence and error of
                                    polynomial interpolation, Lagrange, Newton,
Hermite(osculatory)interpolations; numerical
                                    differentiation and integration, Trapezoidal
                                    and Simpson rules; Gaussian quadrature;
(Gauss-Legendre and Gauss-Chebyshev), method
                                    of undetermined parameters, least square and
                                    orthonormal polynomial approximation;
                                    numerical solution of systems of linear
                                    equations: direct and iterative methods, (Jacobi
                                    Gauss-Seidel and SOR) with convergence;
                                    matrix eigenvalue problems: Jacobi and
                                    Given's methods, numerical solution of
                                    ordinary differential equations: initial
                                    value problems, Taylor series method,
                                    Runge-Kutta methods, predictor-corrector
                                    methods; convergence and stability.

                                    

                                    Partial Differential Equations: Linear and
                                    quasilinear first order partial differential
                                    equations, method of characteristics; second
                                    order linear equations in two variables and
                                    their classification; Cauchy, Dirichlet and
                                    Neumann problems, Green's functions;
                                    solutions of Laplace, wave and diffusion
                                    equations in two variables Fourier series
                                    and transform methods of solutions of the
                                    above equations and applications to physical
                                    problems.

                                    

                                    Mechanics: Forces in three dimensions,
                                    Poinsot central axis, virtual work,
                                    Lagrange's equations for holonomic systems,
                                    theory of small oscillations, Hamiltonian
                                    equations;

                                    

                                    Topology: Basic concepts of topology,
                                    product topology, connectedness,
                                    compactness, countability and separation
                                    axioms, Urysohn's Lemma, Tietze extension
                                    theorem, metrization theorems, Tychonoff
                                    theorem on compactness of product spaces.

                                    

                                    Probability and Statistics: Probability
                                    space, conditional probability, Bayes'
                                    theorem, independence, Random variables,
                                    joint and conditional distributions,
                                    standard probability distributions and their
                                    properties, expectation, conditional
                                    expectation, moments. Weak and strong law of
                                    large numbers, central limit theorem.
                                    Sampling distributions, UMVU estimators,
                                    sufficiency and consistency, maximum
                                    likelihood estimators. Testing of
                                    hypotheses, Neyman-Pearson tests, monotone
                                    likelihood ratio, likelihood ratio tests,
                                    standard parametric tests based on normal,
                                    X2 ,t, F-distributions. Linear regression
                                    and test for linearity of regression.
                                    Interval estimation.

                                    

                                    Linear Programming: Linear programming
                                    problem and its formulation, convex sets
                                    their properties, graphical method, basic
                                    feasible solution, simplex method, big-M and
                                    two phase methods, infeasible and unbounded
LPP's, alternate optima. Dual problem and
                                    duality theorems, dual simplex method and
                                    its application in post optimality analysis,
                                    interpretation of dual variables. Balanced
                                    and unbalanced transportation problems,
                                    unimodular property and u-v method for
                                    solving transportation problems. Hungarian
                                    method for solving assignment problems.

                                    

                                    Calculus of Variations and Integral
                                    Equations: Variational problems with fixed
                                    boundaries; sufficient conditions for
extremum, Linear integral equations of
                                    Fredholm and Volterra type, their iterative
                                    solutions. Fredholm alternative.

Author	Message
annu Newbie Joined: 03Apr2007 Online Status: Offline Posts: 19	Topic: Gate Syllabus of INFORMATION TECHNOLOGY Posted: 03Apr2007 at 10:54pm
	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. FORMAL LANGUAGES AND AUTOMATA Regular Languages: finite automata, regular expressions, regular grammar. Context free languages: push down automata, context free grammars COMPUTER HARDWARE Digital Logic: Logic functions, minimization, design and synthesis of combinatorial and sequential circuits, number representation and computer arithmetic (fixed and floating point) Computer organization: Machine instructions and addressing modes, ALU and data path, hardwired and microprogrammed control, memory interface, I/O interface (interrupt and DMA mode), serial communication interface, instruction pipelining, cache, main and secondary storage SOFTWARE SYSTEMS Data structures and Algorithms: the notion of abstract data types, stack, queue, list, set, string, tree, binary search tree, heap, graph, tree and graph traversals, connected components, spanning trees, shortest paths, hashing, sorting, searching, design techniques (greedy, dynamic, divide and conquer), asymptotic analysis (best, worst, average cases) of time and space, upper and lower bounds, intractability Programming Methodology: C programming, program control (iteration, recursion, functions), scope, binding, parameter passing, elementary concepts of object oriented programming Operating Systems (in the context of Unix): classical concepts (concurrency, synchronization, deadlock), processes, threads and interprocess communication, CPU scheduling, memory management, file systems, I/O systems, protection and security 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. Databases: relational model, database design, integrity constraints, normal forms, query languages (SQL), file structures (sequential, indexed), b-trees, transaction and concurrency control Data Communication: data encoding and transmission, data link control, multiplexing, packet switching, LAN architecture, LAN systems (Ethernet, token ring), Network devices: switches, gateways, routers Networks: ISO/OSI stack, sliding window protocols, routing protocols, TCP/UDP, application layer protocols & systems (http, smtp, dns, ftp), network security Web technologies: three tier web based architecture; JSP, ASP, J2EE, .NET systems; html, XML MA - MATHEMATICS Linear Algebra: Finite dimensional vector spaces. Linear transformations and their matrix representations, rank; systems of linear equations, eigenvalues and eigenvectors, minimal polynomial, Cayley-Hamilton theorem, diagonalisation, Hermitian, Skew-Hermitian and unitary matrices. Finite dimensional inner product spaces, self-adjoint and Normal linear operators, spectral theorem, Quadratic forms. Complex Analysis: Analytic functions, conformal mappings, bilinear transformations, complex integration: Cauchy's integral theorem and formula, Liouville's theorem, maximum modulus principle, Taylor and Laurent's series, residue theorem and applications for evaluating real integrals. Real Analysis: Sequences and series of functions, uniform convergence, power series, Fourier series, functions of several variables, maxima, minima, multiple integrals, line, surface and volume integrals, theorems of Green, Stokes and Gauss; metric spaces, completeness, Weierstrass approximation theorem, compactness. Lebesgue measure, measurable functions; Lebesgue integral, Fatou's lemma, dominated convergence theorem. Ordinary Differential Equations: First order ordinary differential equations, existence and uniqueness theorems, systems of linear first order ordinary differential equations, linear ordinary differential equations of higher order with constant coefficients; linear second order ordinary differential equations with variable coefficients, method of Laplace transforms for solving ordinary differential equations, series solutions; Legendre and Bessel functions and their orthogonality, Sturm Liouville system, Greeen's functions. Algebra: Normal subgroups and homomorphisms theorems, automorphisms. Group actions, sylow's theorems and their applications groups of order less than or equal to 20, Finite p-groups. Euclidean domains, Principal ideal domains and unique factorizations domains. Prime ideals and maximal ideals in commutative rings. Functional Analysis: Banach spaces, Hahn-Banach theorems, open mapping and closed graph theorems, principle of uniform boundedness; Hilbert spaces, orthonormal sets, Riesz representation theorem, self-adjoint, unitary and normal linear operators on Hilbert Spaces. Numerical Analysis: Numerical solution of algebraic and transcendental equations; bisection, secant method, Newton-Raphson method, fixed point iteration, interpolation: existence and error of polynomial interpolation, Lagrange, Newton, Hermite(osculatory)interpolations; numerical differentiation and integration, Trapezoidal and Simpson rules; Gaussian quadrature; (Gauss-Legendre and Gauss-Chebyshev), method of undetermined parameters, least square and orthonormal polynomial approximation; numerical solution of systems of linear equations: direct and iterative methods, (Jacobi Gauss-Seidel and SOR) with convergence; matrix eigenvalue problems: Jacobi and Given's methods, numerical solution of ordinary differential equations: initial value problems, Taylor series method, Runge-Kutta methods, predictor-corrector methods; convergence and stability. Partial Differential Equations: Linear and quasilinear first order partial differential equations, method of characteristics; second order linear equations in two variables and their classification; Cauchy, Dirichlet and Neumann problems, Green's functions; solutions of Laplace, wave and diffusion equations in two variables Fourier series and transform methods of solutions of the above equations and applications to physical problems. Mechanics: Forces in three dimensions, Poinsot central axis, virtual work, Lagrange's equations for holonomic systems, theory of small oscillations, Hamiltonian equations; Topology: Basic concepts of topology, product topology, connectedness, compactness, countability and separation axioms, Urysohn's Lemma, Tietze extension theorem, metrization theorems, Tychonoff theorem on compactness of product spaces. Probability and Statistics: Probability space, conditional probability, Bayes' theorem, independence, Random variables, joint and conditional distributions, standard probability distributions and their properties, expectation, conditional expectation, moments. Weak and strong law of large numbers, central limit theorem. Sampling distributions, UMVU estimators, sufficiency and consistency, maximum likelihood estimators. Testing of hypotheses, Neyman-Pearson tests, monotone likelihood ratio, likelihood ratio tests, standard parametric tests based on normal, X2 ,t, F-distributions. Linear regression and test for linearity of regression. Interval estimation. Linear Programming: Linear programming problem and its formulation, convex sets their properties, graphical method, basic feasible solution, simplex method, big-M and two phase methods, infeasible and unbounded LPP's, alternate optima. Dual problem and duality theorems, dual simplex method and its application in post optimality analysis, interpretation of dual variables. Balanced and unbalanced transportation problems, unimodular property and u-v method for solving transportation problems. Hungarian method for solving assignment problems. Calculus of Variations and Integral Equations: Variational problems with fixed boundaries; sufficient conditions for extremum, Linear integral equations of Fredholm and Volterra type, their iterative solutions. Fredholm alternative. Post Resume: Click here to Upload your Resume & Apply for Jobs

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