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May 20th, 2017 07:36 PM
Re: Syllabus of PhD entrance exam in Delhi University

October 2nd, 2015 12:48 PM
Re: Syllabus of PhD entrance exam in Delhi University

As you want I am here giving you syllabus for M.Phil/Ph.D (Mathematics) Entrance Test of Delhi University.

Syllabus :

Section I – Analysis:

Finite, countable and uncountable sets, bounded and unbounded sets, Archimedean property,
ordered field, completeness of ℝ, sequence and series of functions, uniform convergence,
Riemann integrable functions, improper integrals, their convergence and uniform convergence,
Fourier series. Partial and directional derivatives, Taylor’s series, implicit function theorem, line
and surface integrals, Green’s theorem, Stoke’s theorem.
Elements of metric spaces, convergence, continuity, compactness, connectedness,
Weierstrass’s approximation theorem, completeness, Baire’s category theorem, Bolzano-
Weirstrass theorem, compact subsets ofℝ , Heine-Borel theorem,
Lebesgue outer measure, Lebsegue measure and Lebsegue integration, Riemann and
Lebesgue integrals.
Complex numbers, analytic functions, Cauchy-Riemann equations, Riemann sphere and
stereographic projection, lines, circles, crossratio, Mobius transformations, line integrals,
Cauchy’s theorems, Cauchy’s theorem for convex regions, Morera’s theorem, Liouville’s
theorem, Cauchy’s integral formula, zero-sets of analytic functions, exponential, sine and cosine
functions, power series representation, classification of singularities, conformal mapping,
contour integration, fundamental theorem of algebra.
Banach spaces, Hahn-Banach theortem, open mapping and closed graph theorem, principle of
uniform boundedness, boundedness and continuity of linear transformations, dual spaces,
embedding in the second dual, Hilbert spaces, projections, orthonormal bases, Riesz
representation theorem, Bessel’s inequality, Parseval’s identity.
Elements of Topological spaces, continuity, convergence, homeomorphism, compactness,
connectedness, separation axioms, first and second countability, separability, subspaces, product

Section II – Algebra:

Space of n-vectors, linear dependence, basis, linear transformations, algebra of matrices, rank
of a matrix, determinants, linear equations, characteristic roots and vectors.
Vector spaces, subspaces, quotient spaces, linear dependence, basis, dimension, the algebra of
linear transformations, kernel, range, isomorphism,linear functional, dual space, matrix
representation of a linear transformation, change of bases, reduction of matrices to canonical
forms, inner product spaces, orthogonality, eigenvalues and eigenvectors, projections, triangular
form, Jordan form, quadratic forms, reduction of quadratic forms.
Groups, subgroups, normal subgroups, quotient groups, homomorphisms, cyclic groups,
permutation groups, Cayley’s theorem, Symmetric groups, alternating groups, simple groups.
conjugate elements and class equations of finite groups, Sylow’s theorem, solvable groups,
Jordan-Holder theorem, direct products, structure theorem for finite abelian groups.
Rings, Ideals, prime and maximal ideals, quotient ring, integral domains, Euclidean domains,
principal ideal domains, unique factorization domains,polynomial rings, chain conditions on
rings,fields, quotient fields, finite fields, characteristic of field, field extensions, elements of
Galois theory, solvability by radicals, ruler and compass construction.
Section III- Differential Equations and Mechanics:
First order ODE, singular solutions, initial value problems of first order ODE, general theory of
homogeneous and non-homogeneous linear ODEs, variation of parameters, Lagrange’s and
Charpit’s methods of solving first order PDEs, PDEs of higher order with constant coefficients.
Existence and uniqueness of solution ( , ) dy
dx f x y = , Green’s function, Sturm-Liouville boundary
value problems, Cauchy problems and characteristics, classification of second order PDE,
separation of variables for heat equation, wave equation and Laplace equation,
Equation of continuity in fluid motion, Euler’s equations of motion for perfect fluids, two
dimensional motion, complex potential, motion of sphere in perfect liquid and motion of liquid
past a sphere, vorticity, Navier-Stoke’s equations of motion for viscous flows, some exact

University of Delhi
New Delhi, Delhi 110021

October 2nd, 2015 12:48 PM
Re: Syllabus of PhD entrance exam in Delhi University

Can you please provide here syllabus for M.Phil/Ph.D (Mathematics) Entrance Test of Delhi University ?
June 2nd, 2014 05:58 PM
Re: Syllabus of PhD entrance exam in Delhi University

As you want to get the entrance exam syllabus to get admission in PhD in Delhi University so here is the information of the same for you:

I want to tell you that please specify the PhD subject for which you want to get the entrance exam syllabus

PhD in Delhi University is offered in these subjects:
Buddhist Studies
Computer Science
Development Communication & Extension
Fabric & Apparel Science
Food & Nutrition
ome Science
Human Development & Childhood Studies
Library Information Science
Operational Research
Political Science
Resource Management & Design Application
Social Work
Adult Continuing Education & Extension

Here for your reference I am giving you the entrance exam syllabus of PhD in Computer Science of DU:

Programming Fundamentals
A Brief History of C
C is middle-level Language
The Form of a C Program
Variables, Data Types, Operator & Expression
Data Declaration & Definition
Operator & Expression
C as a Structured Language
Console input and output
Formatted Input/ Output
Control Statement
Nested switch
Iteration Statements for loop
Memory Organization
Pointer Arithmetic
Array & String
Complier Vs Interpreters
Arguments & local variables
Storage Class & Scope
Declaration and Initializing Structure
Preprocessor Directive Macro Substitution
File handling
Void Pointer
Bitwise Operator
Graphics In C

Data Structures
Introduction To Data Structure
Implementation of Data Structure
Array as Data Structure
Polynomial Representation Using Arrays
Sparse Matrices
Drawback of Sequential Storage
Implementation of Linked List
Other Operation & Applications
Generalized Linked List
Operation on Stack
Static & Dynamic Implementation of a Stack
Operation on a Queue
Static & Dynamic Implementation of Queue
Tree Terminology
Binary Search Tree Traversal

Database Management System
Database and Need for DBMS
Views of data-schemas and instances
Database Design using ER model
Relational Model
Relational Database design
Storage and File Structure
Transaction And Concurrency control
Crash Recovery and Backup
Security and privacy

Divide And Conquer
Greedy Method
Dynamic Programming
Branch and Bound

Computer Networks
Introduction to Networking
Common Network Architecture
The OSI Reference Model
Local Area Networks
Broad Band Networks
IP Addressing & Routing
Domain Network Services
Network Applications
Network Security

Operating Systems
Operating system functions and characteristics
Real time systems
Methodologies for implementation of O/S service system
Functions of the system
File access and allocation methods
Structured Organizations
Storage allocation methods
Virtual memory concepts
Hardware Management
Deadlock detection and recovery

Contact Details:
University of Delhi
University Rd,
New Delhi,
Delhi 110007 ‎
011 2766 7853 ‎

Map Location:
June 2nd, 2014 11:45 AM
Syllabus of PhD entrance exam in Delhi University

I want to get admission in PhD in Delhi University and for that I need to get the entrance exam syllabus so can you provide me that as it is very urgent for me?

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