Osmania University Msc Maths Syllabus

I completed my Bsc from Rajasthan University as a regular student. Now I want to take admission in Osmania University as Non colligate student so I want to know the Osmania University distance education Msc Maths syllabus?

Hello sir, Im doing MSC in Maths from Osmania University. I want Msc Maths Syllabus. Is there any one can provide me Osmania University Msc Maths Syllabus?

[pawan]

At Osmania university M.Sc. Mathematics is a postgraduate programme of two years, sub divided into four semesters.

The main objective of this course is to give first-hand knowledge in advanced applied mathematics and forefront research experience.

The basic eligibility criteria set for this course is a Bachelors degree in any discipline with mathematics as the main subject, from any recognized university or board.


Osmania University Msc Maths Syllabus:

Sem. I

Advanced Abstract Algebra
Unit I
Direct product of groups (External and Internal). Isomorphism theorems - Diamond isomorphism theorem, Butterfly Lemma, Conjugate classes, Sylows theorem, p-sylow theorem.

Commutators, Derived subgroups, Normal series and Solvable groups, Composition series, Refinement theorem and Jordan-Holder theorem for infinite groups.

Polynomial rings, Euclidean rings. Modules, Sub-modules, Quotient modules, Direct sums and Module Homomorphisms. Generation of modules, Cyclic modules.

Field theory - Extension fields, Algebraic and Transcendental extensions, Separable and inseparable extensions, Normal extensions. Splitting fields. Galois theory - the elements of Galois theory, Fundamental theorem of Galois theory

Galois theory - the elements of Galois theory, Fundamental theorem of Galois theory, Solvalibility by radicals.

Sem. I
Real Analysis
Unit I
Algebra and algebras of sets, Algebras generated by a class of subsets, Borel sets, Lebesgue measure of sets of real numbers, Measurability and Measure of a set, Existence of Non-measurable sets, Measurable functions. Realization of nonnegative measurable function as limit of an increasing sequence of simple functions.

Realization of non-negative measurable function as limit of an increasing sequence of simple functions. Structure of measurable functions, Convergence in measure, Egoroff's theorem.

Weierstrass's theorem on the approximation of continuous function by polynomials, Lebesgue integral of bounded measurable functions, Lebesgue theorem on the passage to the limit under the integral sign for bounded measurable functions.

Summable functions, Space of square summable functions. Fourier series and coefficients, Parseval's identity, Riesz-Fisher Theorem.Lebesgue integration on R2.

Lebesgue integration on R2, Fubini's theorem. Lp-spaces, Holder-Minkowski inequalities. Completeness of Lp-spaces.

Sem. I
Advanced Differential Equations
Unit I
Non-linear ordinary differential equations of particular forms. Riccati's equation -General solution and the solution when one, two or three particular solutions are known. Total Differential equations.

Partial differential equation of first order formulation and classification of partial differential equations, Lagranges linear equation, particular forms of non linear partial differential equations, Charpits method.

Linear Partial differential equations with constant coefficients. Homogeneous and non- Homogeneous equation. Partial differential equation of second order with variable coefficients- Monge's method,

Classification of linear partial differential equation of second order, Cauchy's problem, Method of separation of variables, Laplace, Wave and diffusion equations, Canonical forms.

Linear homogeneous boundary value problems. Eigen values and eigen functions. Strum-Liouville boundary value problems. Orthogonality of eigen functions. Reality of eigen values.

Sem. I
Differential Geometry-I

Unit I
Theory of curves- Space curves, Tangent, Contact of curve and surface, Osculating plane, Principal normal and Binormal, Curvature, Torsion, Serret- Frenet's formulae.

II
Osculating circle and Osculating sphere, Existence and Uniquenss theorems, Bertrand curves, Involute, Evolutes.

III
Ruled surface, Developable surface, Tangent plane to a ruled surface. Necessary and sufficient condition that a surface =f () should represent a developable surface.

IV
Metric of a surface, First, second and third fundamental forms. Fundamental magnitudes of some important surfaces, Orthogonal trajectories. Normal curvature, Meunier's theorem,.

V
Principal directions and Principal curvatures, First curvature, Mean curvature, Gaussion curvature. Umbilics. Radius of curvature of any normal section at an umbilic on z = f(x,y). Radius of curvature of a given section through any point on z = f(x,y). Lines of curvature, Principal radii, Relation between fundamental forms. Asymptotic lines,

Sem. I
Dynamics of a Rigid body

Unit I
D'Alembert's principle. The general equations of motion of a rigid body. Motion of centre of inertia and motion relative to centre of inertia. Motion about a fixed axis: Finite forces (Moment of effective forces about a fixed axis of rotation, angular momentum, kinetic energy of a rotating body about a fixed line. Equation of Motion of the body about the Axis of Rotation, Principle of Conservation of energy. The compound pendulum (Time of a Complete Oscillation, Minimum time of oscillation), Centre of percussion.

II
Motion of a rigid body in two dimensions: Equations of motion in two dimensions, Kinetic energy of a rigid body, Moment of Momentum, Rolling and sliding Friction, Rolling of a sphere on a rough inclined plane , Sliding of a Rod, Sliding and Rolling of a Sphere on an inclined plane, Sliding and Rolling of a sphere on a fixed sphere. Equations of motion of a rigid body under impulsive forces, Impact of a rotating Elastic sphere on a fixed horizontal Rough plane. Change in K.E. due to the action of impulse.

III
Motion in three dimensions with reference to Euler's dynamical and geometrical equations. Motion under no forces, Motion under impulsive forces. Conservation of momentum (linear and angular) and energy for finite as well as impulsive forces.

IV
Lagrange's equations for holonomous dynamical system, Energy equation for conservative field, Small oscillations, Motion under impulsive forces. Motion of a top.

V
Hamilton's equations of motion, Conservation of energy, Hamilton's principle and principle of least action

For more details here i am giving link Osmania University Msc Maths Syllabus
osmania.ac.in/Syllabus2016/PGCBCSSyllabus2016/Syllabus/d)_Faculty_of_Science/Mathematics_PG.pdf