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  #2  
Old January 24th, 2014, 03:36 PM
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Default Re: MSc mathematics entrance exam Syllabus

Yes sure, here I am providing you the MSc mathematics entrance exam Syllabus of Delhi University. You can use this syllabus in your examination preparations.

SECTION 1
• Elementary set theory, Finite, countable and uncountable sets, Real number
system as a complete ordered field, Archimedean property, supremum,
infimum.

• Sequence and series, Convergence, limsup, liminf.

• Bolzano Weierstrass theorem, Heine Borel theorem.

• Continuity, Uniform continuity, Intermediate value theorem, Differentiability,
Mean value theorem, Maclaurin’s theorem and series, Taylor’s series.

• Sequences and series of functions, Uniform convergence.

• Riemann sums and Riemann integral, Improper integrals.

• Monotonic functions, Types of discontinuity.

• Functions of several variables, Directional derivative, Partial derivative.

• Metric spaces, Completeness, Total boundedness, Separability, Compactness,
Connectedness.

SECTION 2

• Eigenvalues and eigenvectors of matrices, Cayley-Hamilton theorem.

• Divisibility in Z, congruences, Chinese remainder theorem, Euler’s -
function.

• Groups, Subgroups, Normal subgroups, Quotient groups, Homomorphisms,
Cyclic groups, Permutation groups, Cayley’s theorem, Class equations, Sylow
theorems.

• Rings, Fields, Ideals, Prime and Maximal ideals, Quotient rings, Unique
factorization domain, Principal ideal domain, Euclidean domain, Polynomial
rings and irreducibility criteria.

• Vector spaces, Subspaces, Linear dependence, Basis, Dimension, Algebra of
linear transformations, Matrix representation of linear transformations,
Change of basis, Inner product spaces, Orthonormal basis.

SECTION 3

• Existence and Uniqueness of solutions of initial value problems for first order
ordinary differential equations, Singular solutions of first order ordinary
differential equations, System of first order ordinary differential equations,
General theory of homogeneous and non-homogeneous linear ordinary
differential equations, Variation of parameters, Sturm Liouville boundary
value problem, Green’s function.

• Lagrange and Charpit methods for solving first order PDEs, Cauchy problem
for first order PDEs, Classification of second order PDEs, General solution of
higher order PDEs with constant coefficients, Method of separation of
variables for Laplace, Heat and Wave equations.

• Numerical solutions of algebraic equations, Method of iteration and Newton-
Raphson method, Rate of convergence, Solution of systems of linear
algebraic equations using Guass elimination and Guass-Seidel methods, Finite
differences, Lagrange, Hermite and Spline interpolation, Numerical
integration, Numerical solutions of ODEs using Picard, Euler, modified Euler
and second order Runge-Kutta methods.

• Velocity, acceleration, motion with constant and variable acceleration,
Newton’s Laws of Motion, Simple Harmonic motion, motion of particle
attached to elastic string, motion on inclined plane, motion of a projectile,
angular velocity and acceleration, motion along a smooth vertical circle, work,
energy and impulse, Collision of elastic bodies, Bodies falling in resisting
medium, motion under action of central forces, central orbits, planetary
motion, moment of inertia and couple, D’Alembart’s principle.

• Equilibrium of particle and a system of particles, Mass centre and centres of
gravity, Frictions, Equilibrium of rigid body, work and potential energy.
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Last edited by Sashwat; January 24th, 2014 at 06:43 PM.
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  #3  
Old February 2nd, 2015, 01:35 PM
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Default Re: MSc mathematics entrance exam Syllabus

Hi can you please provide me the syllabus of M.Sc mathematics entrance exam of Devi Ahilya Vishwavidyalaya?
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  #4  
Old February 2nd, 2015, 01:37 PM
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Join Date: Apr 2013
Default Re: MSc mathematics entrance exam Syllabus

Ok, as you want the syllabus of M.Sc mathematics entrance exam of Devi Ahilya Vishwavidyalaya so here I am providing you.

DAV M.Sc mathematics syllabus
Analysis
Riemann integral. Integrability of continuous and monotonic functions, The fundamental theorem of
integral calculus, Mean value theorems of integral calculus. Partial derivation and differentiability of
real-valued functions of two variables. Schwarz and t Young’s theorem. Implicit function theorem.
Improper integrals and their convergence, Comparison tests, Abel’s and Dirichlet’s tests, Frullani’s
integral. Integral as a function of a parameter Continuity, derivability and integrability of an integral of a
function of a parameter. Fourier series of half and full intervals.
Complex numbers as ordered pair. Geometric representation of Complex numbers. Stereographic
projection. Continuity and differentiability of Complex functions. Analytic functions. Cauchy-Riemann
equations. Harmonic functions. Mobius transformations. Fixed point. Cross ratio. Inverse points and
critical mappings. Conformal mappings.
Definition and examples of metric spaces. Neighborhood. Limit points. Interior points. Open and closed
sets. Closure and interior. Boundary points. Sub-space of a metric space. Cauchy sequences.
Completeness. Cantor’s intersection theorem. Contraction principle. Real numbers as a complete ordered
field. Dense subsets. Baire Category theorem. Separable, second countable and first countable spaces.
Continuous functions. Extension theorem. Uniform continuity. Compactness. Sequential compactness.
Totally bounded spaces. Finite intersection property. Continuous functions and compact sets.
Connectedness.
Algebra & Linear Algebra
Group – Automorphism, inner automorphisms, automorphism groups, Congjugacy relation and
centraliser, Normaliser, Counting principle and the class equation of a finite group, Cauchy’s theorem
and Sylow’s theorems for finite abelian groups and non abelian groups.
Ring theory – Ring homonorphism, Ideals and Quotient Rings, Field of Quotients of an Integral Domain.
Euclidean Rings, polynomial Rings, Polynomials over the Rational Field, Polynomial Rings over
Commutaive Rings, Unique factorization domain.
Definition and examples of vector spaces. Subspaces. Sum and direct sum of subspaces. Linear span.
Linear dependence, independence and their basic properties. Finite dimensional vector spaces. Existence
theorem for bases. Invariance of the number of elements of a basis set. Dimension. Existence of
complementary subspace of a subs pace of a finite dimensional vector space. Dimension of sums of
subspaces. Quotient space and its dimension.
Linear transformations and their representation as matrices. The algebra of linear transformations. The
rank nullity theorem. Change of basis. Dual space. Bidual space and natural isomorphism. Adjoint of a
linear transformation. Eigenvalues and eigenvector of a linear transformation. Diagonalisation. Bilinear,
Quadratic and Hermitian forms.
Inner Product Spaces, Cauchy-Schwarz inequality Orthogonal vectors. Orthogonal Complements.
Orthonormal sets and bases. Bessel’s inequality for finite dimensional spaces. Gram – Schmidt
Orthogonalization process.




Contact Details

Devi Ahilya Vishwavidyalaya
RNT Marg, Near Central Mall, Nalanda Campus, South Tukoganj, Chhoti Gwaltoli, Indore, Madhya Pradesh 452001 ‎
0731 252 1887

Map location

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