**UNIVERSITY OF DELHI (DEPARTMENT OF OPERATIONAL RESEARCH)**

**Eligibility::**

**Conditions for Admission to M.Sc. Part-I in Operational Research and M.A. /M.Sc. Part-I in Applied Operational Research, 2013-2014**

Examination passed | Percentage Required |
---|---|

Any Master’s Degree examination of the University of Delhi or an examination recognized as equivalent thereto with atleast two papers in Mathematics/ Computer Science/ Statistics/ Operational Research at graduation/ higher level. | 55% marks in aggregate |

OR | |

Any Bachelor’s Degree examination under 10+2+3 scheme of examination of the University of Delhi or an examination recognized as equivalent thereto with atleast two papers in Mathematics/ Computer Science/ Operational Research/ Statistics. | 55% marks in aggregate |

**Note:**

1. The candidates who are appearing in the final year examination of the degree on the basis of which admission is sought are also eligible to apply.

2. Applicants who have graduated under 10+2+3 scheme or an equivalent scheme are eligible for admission.

__MCA ENTRANCE EXAM PATTERN__

__MCA ENTRANCE EXAM PATTERN__

Admission Procedure:

(A) MCA

Mode – I

50% of the seats are filled on the basis of merit in the B.Sc. (H) Computer Science Examinations of University of Delhi. The students seeking admission under this mode must apply for admission by the last date mentioned in this bulletin.

Mode-II

Remaining 50% seats shall be filled through an entrance test conducted by the Department of Computer Science followed by interview. The entrance test will consist of two tests Test I will be objective type and Test II will consist of subjective type questions.

Note: If M is the number of seats in a particular category, answer sheets of Test II shall be evaluated only for the top 6M scorers of Test I in that category and top 3M scorers of Test II shall be called for the interview.

There shall be 80% weightage for the entrance test (only Test II) and 20% weightage for the interview. In the event of any shortfall of admission under mode-I, the remaining seats will be added to the quota for the candidates seeking admission through Mode II. If a candidate is shortlisted for admission in both the modes, he/she will be admitted through mode I only. Future withdrawals will not change the mode of admission of a candidate already admitted.

(B) MSc (Computer Science) Entrance Exam

Mode-I

50% of the seats are filled on the basis of merit in the B.Sc. (H) Computer Science Examinations of University of Delhi. The students seeking admission under this mode must apply for admission by the last date mentioned in this bulletin.

Mode-II

For admission against the remaining 50% seats in the M.Sc. Computer Science course, the candidates are required to take the Admission Tests which will consist of two parts:

Test I : Objective type questions.

Test II : Comprehensive questions.

Students with 40% marks in Part-I will qualify for Part-II. A relaxation of 5% will be provided to the candidates belonging to SC/ST category.

For preparing the final merit list 60% weightage will be given to the score in the Admission Test (Test-II only) and 40% weightage will be given to the score of the qualifying examination (i.e. Bachelor’s level).

In the event of any shortfall of admission under mode-I, the remaining seats will be added to the quota for the candidates seeking admission through Mode II. If a candidate is shortlisted for admission in both the modes, he/she will be admitted through mode I only. Future withdrawals will not change the mode of admission of a candidate already admitted.

Number of Seats for MCA/M.Sc. (Computer Science):

The number of sanctioned seats in each of the programs MCA/M.Sc. (Computer Science) is 46.

Distribution of 23 seats under each of the modes I and II is as follows

SC | 3 |

ST | 2 |

OBC | 6 |

Unreserves | 12 |

Total | 23 |

Admission Procedure for PG Operation Research:

M.Sc. Operational Research and/or M.A./ M.Sc. Applied Operational Research

a. Common Entrance Test

It will consist of written test, group discussion and interview.

i. Written Test (80%) :

It will be of 3 hrs. duration with multiple choice questions. There will be negative marking for every wrong answer. It will consist of two parts :

Part-I : General Aptitude (20%) : General English, Comprehension, Logic, Analytical ability and Reasoning.

i. Part-II :Quantitative Aptitude (60%): Questions from Mathematics, Statistics, Operational Research and Computer Science.

ii. Group Discussion (10%)

iii. Interview (10%)

Based on the performance in written test, a consolidated merit list consisting of 3 times of the number of seats available for admission in each course would be prepared for group discussion and interview.

Note: In all cases the decision of the Mathematical Sciences Courses Admission Committee will be final and binding on the candidates.

__SYLLABUS__

__SYLLABUS__

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

Syllabus for entrance test is given below:

**Mathematics:** Mathematics at the level of B. Sc. 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. Correct usage of English Language and Reading comprehension.

**The syllabus for the M.Sc. (Computer Science) Entrance Test would be as follows:**

**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.

**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 Fdistributions, test of significance based on t, Chi-square and Fdistributions.