| Re: MSc mathematics from Osmania University distance education
Yes Osmania University Distance Education offer MSc Mathematics course.
As you want to do MSC Mathematics from Osmania University Distance Education so you want to get information about this course so here I am giving you same:
MSC Mathematics:
Duration:
2 Years
Eligibility:
Candidate must have bachelor’s degree in same relevant discipline from a recognized University.
Course Structure:
Unit I
Automaphisms- Conjugacy and G-sets- Normal series solvable groups-
Nilpotent groups. (Pages 104 to 128 of [1] )
Unit II
Structure theorems of groups: Direct product- Finitly generated abelian
groups- Invariants of a finite abelian group- Sylow’s theorems- Groups of
orders p2,pq . (Pages 138 to 155)
Unit III
Ideals and homomsphism- Sum and direct sum of ideals, Maximal and prime
ideals- Nilpotent and nil ideals- Zorn’s lemma (Pages 179 to 211).
Unit-IV
Unique factorization domains - Principal ideal domains- Euclidean domains-
Polynomial rings over UFD- Rings of traction.(Pages 212 to 228)
DEPARTMENT OF MATHEMATICS
OSMANIA UNIVERSITY
M.Sc. (Applied Mathematics)
Semester I
AM – 102T Paper-II
Real Analysis
Unit I
Metric spaces- Compact sets- Perfect sets- Connected sets
Unit II
Limits of functions- Continuous functions- Continuity and compactness
Continuity and connectedness- Discontinuities – Monotone functions.
Unit III
Rieman- Steiltjes integral- Definition and Existence of the Integral- Properties
of the integral- Integration of vector valued functions- Rectifiable waves.
Unit-IV
Sequences and series of functions: Uniform convergence- Uniform
convergence and continuity- Uniform convergence and integration- Uniform
convergence and differentiation- Approximation of a continuous function by a
sequence of polynomials.
Text Books:
[1] Principles of Mathematical Analysis (3rd Edition)
(Chapters 2, 4, 6 )
by
Mc Graw-Hill Internation Edition
DEPARTMENT OF MATHEMATICS
OSMANIA UNIVERSITY
M.Sc. (Applied Mathematics)
Semester I
AM –103T Paper-III
Complex Analysis
Unit I
Regions in the complex plane- Functions of a complex variable- Mappings by
exponential functions- Limits- Continuity- Derivatives- Cauchy-Riemans
equations- Sufficient conditions for differentiation- Polar coordinates.
Unit II
Analytic functions- Uniquely determined analytic functions- Reflection
principle- The exponential function- The logarithmic function- Complex
exponents- Trigonometric functions- Hyperbolic functions- Inverse
trigonometric- Hyperbolic functions.
Unit III
Derivatives of functions w(t)- Definite integrals of functions w(t)- Contours-
Contour integrals- Upper bounds for moduli of contour integrals- Anti
derivatives.
Unit-IV
Cauchy-Goursat theorem and its proof- Simply and multiply connected
domains- Cauchy’s integral formula- Derivatives of analytic functions-
Liouville’s theorem and fundamental theorem of algebra- Maximum modulus
principle.
Text Books:
[1] Complex Variable and Application (8th Edition)
by
James Ward Brown,
Ruel V-churchill
DEPARTMENT OF MATHEMATICS
OSMANIA UNIVERSITY
M.Sc. (Applied Mathematics)
Semester I
AM –104T Paper-IV
Mechanics
Unit I
Dynamics of systems of Particles:- Introduction - Centre of Mass and Linear
Momentum of a system- Angular momentum and Kinetic Energy of a system,
Mechanics of Rigid bodies- Planar motion:- Centre of mass of Rigid bodysome
theorem of Static equilibrium of a Rigid body- Equilibrium in a uniform
gravitational field- Rotation of a Rigid body about a fixed axis.
Unit II
Moment of Inertia:- calculation of moment of Inertia Perpendicular and
Parallel axis theorem- Physical pendulum-A general theorem concerning
Angular momentum-Laminar Motion of a Rigid body-Body rolling down an
inclined plane (with and without slipping).
Unit III
Motion of Rigid bodies in three dimension-Angular momentum of Rigid body
products of Inertia, Principles axes-Determination of principles axes-
Rotational Kinetic Energy of Rigid body- Momentum of Inertia of a Rigid
body about an arbitrary axis- The momental ellipsoid - Euler’s equation of
motion of a Rigid body.
Unit IV
Lagrange Mechanics:-Generalized Coordinates-Generalized forces-Lagrange’s
Equations and their applications-Generalized momentum-Ignorable
coordinates-Hamilton’s variational principle-Hamilton function-Hamilton’s
Equations- Problems-Theorems.
Text Book:
[1] G.R.Fowles, Analytical Mechanics, CBS Publishing, 1986.
DEPARTMENT OF MATHEMATICS
OSMANIA UNIVERSITY
M.Sc. (Applied Mathematics)
Semester I
AM – 105T Paper- V
Mathematical Methods
Unit I
Existence and Uniqueness of solution of
dx
dy
= f(x,y). The method of successive
approximation- Picard’s theorem- Sturm-Liouville’s boundary value problem.
Partial Differential Equations: Origins of first-order PDES-Linear equation of firstorder-
Lagrange’s method of solving PDE of Pp+Qq = R – Non-Linear PDE of order
one-Charpit method- Linear PDES with constant coefficients.
Unit II
Partial Differential Equations of order two with variable coefficients- Canonical form
Classification of second order PDE- separation of variable method solving the onedimensional
Heat equation and Wave equation- Laplace equation.
Unit III
Power Series solution of O.D.E. – Ordinary and Singular points- Series solution about
an ordinary point -Series solution about Singular point-Frobenius Method.
Lagendre Polynomials: Lengendre’s equation and its solution- Lengendre Polynomial
and its properties- Generating function-Orthogonal properties- Recurrance relations-
Laplace’s definite integrals for Pn (x)- Rodrigue’s formula.
Unit-IV
Bessels Functions: Bessel’s equation and its solution- Bessel function of the first kind
and its properties- Recurrence Relations- Generating function- Orthogonality
properties.
Hermite Polynomials: Hermite’s equation and its solution- Hermite polynomial and
its properties- Generating function- Alternative expressions (Rodrigue’s formula)-
Orthogonality properties- Recurrence Relations.
Text Books:
[1] “Elements of Partial Differential Equations”, By Ian Sneddon, Mc.Graw-
Hill International Edition.
[2] “Text book of Ordinary Differential Equation”, By S.G.Deo, V. Lakshmi
Kantham, V. Raghavendra, Tata Mc.Graw Hill Pub. Company Ltd.
[3] “Ordinary and Partial Differential Equations”, By M.D. Raisingania,
S. Chand Company Ltd., New Delhi.
DEPARTMENT OF MATHEMATICS
OSMANIA UNIVERSITY
M.Sc. (Applied Mathematics)
Semester II
AM –201T Paper-I
Advanced Algebra
Unit I
Algebraic extensions of fields: Irreducible polynomials and Eisenstein
criterion- Adjunction of roots- Algebraic extensions-Algebraically closed
fields (Pages 281 to 299)
Unit II
Normal and separable extensions: Splitting fields- Normal extensions-
Multiple roots- Finite fields- Separable extensions (Pages 300 to 321)
Unit III
Galois theory: Automorphism groups and fixed fields- Fundamental theorem
of Galois theory- Fundamental theorem of Algebra (Pages 322 to 339)
Unit-IV
Applications of Galoes theory to classical problems: Roots of unity and
cyclotomic polynomials- Cyclic extensions- Polynomials solvable by radicals-
Ruler and Compass constructions. (Pages 340-364)
Text Books:
[1] Basic Abstract Algebra- S.K. Jain, P.B. Bhattacharya, S.R. Nagpaul.
Reference Book:
Topics in Algrbra
By
I. N. Herstein
DEPARTMENT OF MATHEMATICS
OSMANIA UNIVERSITY
M.Sc. (Applied Mathematics)
Semester II
AM –202T Paper-II
Advanced Real Analysis
Unit I
Algebra of sets- Borel sets- Outer measure- Measurable sets and Lebesgue
measure- A non-measurable set- Measurable functions- Little word’s three
principles.
Unit II
The Rieman integral- The Lebesgue integral of a bounded function over a set
of finite measure- The integral of a non-negative function- The general
Lebesgue integral.
Unit III
Convergence in measure- Differentiation of a monotone functions- Functions
of bounded variation.
Unit-IV
Differentiation of an integral- Absolute continuity- The Lp-spaces- The
Minkowski and Holder’s inequalities- Convergence and completeness.
Text Books:
[1] Real Analysis (3rd Edition)
(Chapters 3, 4, 5 )
by
H. L. Royden
Pearson Education (Low Price Edition)
DEPARTMENT OF MATHEMATICS
OSMANIA UNIVERSITY
M.Sc. (Applied Mathematics)
Semester II
AM –203T Paper- III
Advanced Complex Analysis
Unit I
Convergence of sequences and of series- Taylors series- Laurent’s series-
Absolute and uniform convergence of power series- Continuity of sums of
power series- Uniqueness of series representation.
Unit II
Residues- Cauchy’s residue theorem- Using a single residues the three types
of isolated singular points- Residues at poles- Zeroes of analytic functions-
Zeroes and poles- Behaviour of f near isolated singular points.
Unit III
Evaluation of improper integrals- Improper integrals from Fourier analysis-
Jordan’s lemma- Indented paths- Definite integrals involving sines and
cosines- Argument principle- Rouche’s theorem.
Unit-IV
Linear transformations- The transformation w =
z
1 mappings by w =
z
1 ,
Linear fractional transformations- An implicit form- Mapping of the upper
half plane- The transformation w = sin z, Mapping by z 2.
Text Books:
[1] Complex Variable and Application (8th Edition)
by
James Ward Brown,
Ruel V.churchill
Mc Graw Hall Int. Edition.
Reference:
[1] Complex Analysis
by
Serge Lang
Springer- Varlag
DEPARTMENT OF MATHEMATICS
OSMANIA UNIVERSITY
M.Sc. (Applied Mathematics)
Semester-II
AM –204T Paper- IV
Fluid Mechanics
Unit I
General orthogonal curvilinear coordinates - Kinematics - Lagrangian and
Eulerian methods - Equation of continuity - Boundary surface - Stream lines,
Path lines and Streak lines - Velocity potential - Irrotational and rotational
motions - Vortex lines
Unit II
Equation of motion - Lagrange's and Euler's equation of motion - Bernoulli's
theorem - Stream functions - Irrotational motion in two-dimensions - Complex
velocity potential sources – Sinks, doublets and their images - Milne-
Thompson Circle theorem
Unit III
Two dimensional irrotational motion produced by motion of Circular, Co-axial
and elliptic cylinders in an infinite mass of liquid - Theorem of Blasius motion
of a sphere through a liquid at rest at infinity - Liquid streaming past a fixed
sphere.
Unit IV
Stress components in a real fluid - Relation between rectangular components
of stress - Connection between stresses and gradient of velocity - Navier-
Stoke’s equations of motion - Plane Poiseulle and couette flows between two
parallel plates.
Text Books:
[1] W.H. Besaint and A.S.Ramsay, A Treatise on Hydromechanics, Part-II.
CBS Publishers, Delhi, 1988.
[2] F.Chorlton, Text book of Fluid Dynamics, CBS Publishers, Delhi, 1985.
DEPARTMENT OF MATHEMATICS
OSMANIA UNIVERSITY
M.Sc. (Applied Mathematics)
Semester-II
AM –205T Paper- V
Integral Transforms
UNIT –I
Laplace Transforms-Existence theorem-Laplace transforms of derivatives and
integrals – shifting theorems- Transform of elementary functions-Inverse
Transformations-Convolution theorem-Applications to ordinary and Partial
differential equations.
UNIT-II
Fourier Transforms- Sine and cosine transforms-Inverse Fourier Transforms(Infinite
and Finite Transforms)-Applications to ordinary and Partial differential equations .
UNIT-III
Hankel Transforms- Hankel Transform of the derivatives of a function.- Application
of Hankel Transforms in boundary value problems-The finite Hankel Transofrm.
UNIT-IV
Mellin Transforms-The Mellin inversion theorem- some elementary properties of
Mellin Transforms and Mellin Transfroms of derivatives – Mellin Integrals-
Convolution Theorem.
Text Books:-
1). R.V.Churchill, “Operational Mathematics”.
2). A.R.Vasishta and R.K.Guptha, “Integral Transforms”
For full syllabus here is the attachment:
Address:
Osmania University
Osmania University Main Rd,
Hyderabad, Telangana 500007
040 2768 2363
Map:
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