MA in LPU

I get admission in MA in Mathematics course at LPU university . I requires syllabus of the course . Will you please provide here syllabus of the course ?

[Kiran Chandar]

As you want I am here providing you syllabus of MA in Mathematics course of LPU university.

Syllabus for MA in Mathematics:
FIRST YEAR
Real analysis
Complex analysis and differential geometry
Abstract algebra
Statistics

SECOND YEAR
Linear algebra
Topology
Differential and integral equation
Measure theory and functional analysis

MA in Mathematics syllabus

Linear Algebra:
Finite dimensional vector spaces; Linear transformations and their matrix
representations, rank; systems of linear equations, eigen values and eigen vectors,
minimal polynomial, Cayley-Hamilton Theroem, diagonalisation, Hermitian, Skew-
Hermitian and unitary matrices; Finite dimensional inner product spaces, Gram-Schmidt
orthonormalization process, self-adjoint operators.
Complex Analysis:
Analytic functions, conformal mappings, bilinear transformations; complex integration:
Cauchy's integral theorem and formula; Liouville's theorem, maximum modulus
principle; Taylor and Laurent's series; residue theorem and applications for evaluating
real integrals.
Real Analysis:
Sequences and series of functions, uniform convergence, power series, Fourier series,
functions of several variables, maxima, minima; Riemann integration, multiple integrals,
line, surface and volume integrals, theorems of Green, Stokes and Gauss; metric
spaces, completeness, Weierstrass approximation theorem, compactness; Lebesgue
measure, measurable functions; Lebesgue integral, Fatou's lemma, dominated
convergence theorem.
Ordinary Differential Equations:
First order ordinary differential equations, existence and uniqueness theorems, systems
of linear first order ordinary differential equations, linear ordinary differential equations of
higher order with constant coefficients; linear second order ordinary differential
equations with variable coefficients; method of Laplace transforms for solving ordinary
differential equations, series solutions; Legendre and Bessel functions and their
orthogonality.
Algebra:
Normal subgroups and homomorphism theorems, automorphisms; Group actions,
Sylow's theorems and their applications; Euclidean domains, Principle ideal domains
and unique factorization domains. Prime ideals and maximal ideals in commutative
rings; Fields, finite fields.
Functional Analysis:
Banach spaces, Hahn-Banach extension theorem, open mapping and closed graph
theorems, principle of uniform boundedness; Hilbert spaces, orthonormal bases, Riesz
representation theorem, bounded linear operators.
Numerical Analysis:
Numerical solution of algebraic and transcendental equations: bisection, secant method,
Newton-Raphson method, fixed point iteration; interpolation: error of polynomial
interpolation, Lagrange, Newton interpolations; numerical differentiation; numerical
integration: Trapezoidal and Simpson rules, Gauss Legendre quadrature, method of
undetermined parameters; least square polynomial approximation; numerical solution of
systems of linear equations: direct methods (Gauss elimination, LU decomposition);
iterative methods (Jacobi and Gauss-Seidel); matrix eigenvalue problems: power
method, numerical solution of ordinary differential equations: initial value problems:
Taylor series methods, Euler's method, Runge-Kutta methods.
Partial Differential Equations:
Linear and quasilinear first order partial differential equations, method of characteristics;
second order linear equations in two variables and their classification; Cauchy, Dirichlet
and Neumann problems; solutions of Laplace, wave and diffusion equations in two
variables; Fourier series and Fourier transform and Laplace transform methods of
solutions for the above equations.
Mechanics:
Virtual work, Lagrange's equations for holonomic systems, Hamiltonian equations.
Topology:
Basic concepts of topology, product topology, connectedness, compactness,
countability and separation axioms, Urysohn's Lemma.
Probability and Statistics:
Probability space, conditional probability, Bayes theorem, independence, Random
variables, joint and conditional distributions, standard probability distributions and their
properties, expectation, conditional expectation, moments; Weak and strong law of
large numbers, central limit theorem; Sampling distributions, UMVU estimators,
maximum likelihood estimators, Testing of hypotheses, standard parametric tests based
on normal, X2 , t, F - distributions; Linear regression; Interval estimation.

Linear programming:
Linear programming problem and its formulation, convex sets and their properties,
graphical method, basic feasible solution, simplex method, big-M and two phase
methods; infeasible and unbounded LPP's, alternate optima; Dual problem and duality
theorems, dual simplex method and its application in post optimality analysis; Balanced
and unbalanced transportation problems, u -u method for solving transportation
problems; Hungarian method for solving assignment problems.


Calculus of Variation and Integral Equations:
Variation problems with fixed boundaries; sufficient conditions for extremum, linear
integral equations of Fredholm and Volterra type, their iterative solutions.