P.hd in Mathematics

Paper I : Abstract Algebra and Basic Topology

Section - A
(Abstract Algebra)
1. Groups
2. Rings
3. Fields and Exdtension Fields

Section - B
(Basic Topology)
1. Preliminaries
2. Continuity and Homeomorphism
3. Product and Quotient Topology
4. Connectedness
Paper II : Real and Complex Analysis

Section - A
(Real Analysis)
1. Real and Complex Number System
2. Riemann - Stieltje's Integral
3. Some Special functions
4. Functions of several variables
5. Lebesgue Measure and integration

Section - B
(Complex Analysis)
1. Analysis Functions
2. Complex Integration
3. Conformal Representation
Paper III : Tensor Algebra and Different Geometry

Section - A
(Tensor Algebra)

Section - B
(Different Geometry)
1. Curves in space
2. Surface in E3
3. Intrinsic Geometry of Surface
4. Asymptotic Lines and Geodesics
Paper IV(a) : Fundamentals of Computer Science
1. Introduction
2. Data representation and digital arithmetic
3. Introduction to Operating Systems
4. Introduction to UNIX and Windows
5. Introduction to Computer Network and the Internet
Paper IV(b) : Numerical Analysis and Computer Programming

Section - A
1. Interpolation
2. Numerical Differentiation
3. Numerical Integration

Section - B
1. Difference Equations
2. Numerical Solution of Ordinary Differential Equations
3. Bernoulli and euler Polynomials and Numbers



M.A./M.Sc. Final
Paper I : Topology and Functional Analysis

Section - A
(Topology)
1. Separation Axioms
2. Compact spaces and Compactifications
3. Nets and Filters
4. Metric Spaces

Section - B
(Functional Analysis)
1. Normed Linear spaces
2. Main Results in Normed Linear spaces
3. Inner Product Spaces

Paper II : Differential and Integral Equations

Section - A
(Differential Equations)
1. Ordinary Linear Differential Equation
2. Partial Differential Equation
3. Fourier and Laplace Transforms

Section - B
(Integral Euations)
1. Definition and classification
2. Fredholm's integral equations
3. Volterra integral equations

Paper III : (Optional) Advanced Mechanics

Section - A

Section - B
Kinematics of rigid body

Section - C
Fluid Dynamics

Paper IV : (Optional) Advanced Statistics
1. Random variable
2. Continuous Probabiloty Distribution
3. Estimation Theory
4. Testing of hypothesis
5. Finite differences

Paper V : (Optional) Algebraic Topology

Paper VI : (Optional) Approximation Theory

Paper VII : (Optional) Computer Programming
1. Introduction
2. Control Structures
3. Arrays and Pointers
4. Structures and files
5. Introduction to OOPs and C++

Paper VIII : (Optional) Finsler Geometry
1. Finsler Space
2. Partial §-differentiation
3. Cartan's and Berwald's Covariant Differentiations
4. Theory of Curvature
5. Lie-Dirivation in Finsler space
6. Projective and conformal Transformations

Paper IX :(Optional) Fourier Analysis

Paper X : (Optional) H-Functions and their Applications
1. H-Functions and their elementary properties
2. Integrals and expansions involving the H-function of one variable
3. H-Functions of two variables
4. Contiguous recurrence relations and summation formulas for
H-function of two variables.
5. Integrals involving H-functions of two variables
6. Expansion formulas and generating relations for H-function of
two variables
7. Application of H-functions of one and two variables

Paper XI : (Optional) Hydrodynamics

Paper XII : (Optional) Measure Theory and Lebesgue Integration
1. Lebesgue Measure
2. The Lebesgue Integral
3. Differentiation and Integration
4. Measure and Integration
5. Outer Measure

Paper XIII : (Optional) Operations Research
1. Introduction
2. Linear Programming (L.P.)
3. Theory of Games
4. Transportation and Assignment Problems
5. Dynamic Programming
6. Inventory Problems
7. Replacement Problems
8. Queueing Theory

Paper XIV : (Optional) Riemannian Geometry
1. Tensor connexions
2. Riemannian Manifold(Vn)
3. Ricci's Coefficients of Rotation
4. Sub-Manifold and Hypersurfaces of a Vn
5. Sub-spaces and Hypersurfaces of an Euclidean space En
6. Lie Derivation in Vn

Paper XV : (Optional) Special Functions

Section - A
1. Gamma and Beta Functions
2. Hypergeometric and Generalized Hypergeometric functions
3. Bessel Functions
4. Generating Functions

Section - B
1. Legendre Polynomials
2. Hermite Polynomials
3. Laguerre Polynomials
4. Jacobi Polynomials

Paper XVI : (Optional) Theory of Relativity and Cosmolgy
1. Special Theory of Relativity
2. Relativistic Mechanics
3. Geometry of Space-time in (3+1) dimension
4. General Theory of Relativity
5. Cosmology

Paper XVII : (Optional) Transformation Geometry
1. Transformations in a Plane
2. Transformations in a space
3. Isometries
4. Groups of Transformations
5. Infinitesimal Transformations
6. Projective Transformations


The Course offers Doctoral Degree in Mathematics.