M.Phil in Mathematics
MPhil
In Satna
Description
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Type
MPhil
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Location
Satna
Facilities
Location
Start date
Start date
Reviews
Course programme
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 M.Phil in Mathematics.
M.Phil in Mathematics