# DU MCA Syllabus 2015

**Delhi University 2015 MCA Syllabus**

Delhi University Entrance Test shall have the following components : Mathematical Ability, Computer Science, Logical Reasoning and English Comprehension.

**DU 2015 MCA Syllabus**

**Mathematics :**Mathematics at the level of BSc program of the University of Delhi.**Computer Science :**Introduction to Computer organization including data representation, Boolean circuits and their simplification, basics of combinational circuits; C – programming : Data types including user defined data types, constants and variables, operators and expressions, control structures. Modularity : use of functions, scope, arrays.**Logical ability & English Comprehension :**Problem – solving using basic concepts of arithmetic, algebra, geometry and data analysis.**English Comprehension :**Correct usage of English Language and Reading comprehension.

**DU 2015 MSc Syllabus**

**I. Computer Science**

**Discrete Structures :**Sets, functions, relations, counting; generating functions, recurrence relations and their solutions; algorithmic complexity, growth of functions and asymptotic notations.**Programming, Data Structures and Algorithms :**Data types, control structures, functions / modules, object – oriented programming concepts : sub – typing, inheritance, classes and subclasses, etc. Basic data structures like stacks, linked list, queues, trees, binary search tree, AVL and B+ trees; sorting, searching, order statistics, graph algorithms, greedy algorithms and dynamic programming.**Computer System Architecture :**Boolean algebra and computer arithmetic, flip – flops, design of combinational and sequential circuits, instruction formats, addressing modes, interfacing peripheral devices, types of memory and their organization, interrupts and exceptions.

**Operating Systems :**Basic functionalities, multiprogramming, multiprocessing, multithreading, timesharing, real – time operating system; processor management, process synchronization, memory management, device management, file management, security and protection; case study : Linux.**Software Engineering :**Software process models, requirement analysis, software specification, software testing, software project management techniques, quality assurance.**DBMS and File Structures :**File organization techniques, database approach, data models, DBMS architecture; data independence, E – R model, relational data models, SQL, normalization and functional dependencies.**Computer Networks :**ISO – OSI and TCP / IP models, basic concepts like transmission media, signal encoding, modulation techniques, multiplexing, error detection and correction; overview of LAN / MAN / WAN; data link, MAC, network, transport and application layer protocol features; network security.

**II. Mathematics**

**Algebra :**Groups, subgroups, normal subgroups, cosets, Lagrange’s theorem, rings and their properties, commutative rings, integral domains and fields, sub rings, ideals and their elementary properties. Vector space, subspace and its properties, linear independence and dependence of vectors, matrices, rank of a matrix, reduction to normal forms, linear homogeneous and non – homogenous equations, Cayley – Hamilton theorem, characteristic roots and vectors. De Moivre’s theorem, relation between roots and coefficient of nth degree equation, solution to cubic and biquadratic equation, transformation of equations.

**Calculus :**Limit and continuity, differentiability of functions, successive differentiation, Leibnitz’s theorem, partial differentiation, Eider’s theorem on homogenous functions, tangents and normal, asymptotes, singular points, curve tracing, reduction formulae, integration and properties of definite integrals, quadrature, rectification of curves, volumes and surfaces of solids of revolution.**Geometry :**System of circles, parabola, ellipse and hyperbola, classification and tracing of curves of second degree, sphere, cones, cylinders and their properties.**Vector Calculus :**Differentiation and partial differentiation of a vector function, derivative of sum, dot product and cross product, gradient, divergence and curl.**Differential Equations :**Linear, homogenous and bi – homogenous equations, separable equations, first order higher degree equations, algebraic properties of solutions, Wronskian – its properties and applications, linear homogenous equations with constant coefficients, solution of second order differential equations. Linear non – homogenous differential equations, the method of undetermined coefficients, Euler’s equations, simultaneous differential equations and total differential equations.**Real Analysis :**Neighborhoods, open and closed sets, limit points and Bolzano Weiestrass theorem, continuous functions, sequences and their; properties, limit superior and limit inferior of a sequence, infinite series and their convergence. Rolle’s theorem, mean value theorem, Taylor’s theorem, Taylor’s series, Maclaurin’s series, maxima and minima, indeterminate forms.**Probability and Statistics :**Measures of dispersion and their properties, skewness and kurtosis, introduction to probability, theorems of total and compound probability, Bayes theorem random variables, and probability distributions and density functions, mathematical expectation, moment generating functions, cumulants and their relation with moments, binomial Poisson and normal distributions and their properties, correlation and regression, method of least squares, introduction to sampling and sampling distributions like Chi – square, t and F distributions, test of significance based on t, Chi – square and F distributions.

**III. English Comprehension : **

Correct usage of English language and reading comprehension.

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