## Syllabus & Subjects for Master of Science [M.Sc] (Mathematics):

 Name of the Subject Topics covered Real Analysis Basic topology, sequences and series, continuity, The Lebesgue Integral, Simple and Step Functions, the Lebesgue integral of step functions, Upper Functions, the Lebesgue integral of upper functions. Algebra Permutations and combinations, Sylow theorems, groups of order p square, PQ, polynomial rings, matrix rings Number Theory Divisibility, Euclidean theorem, Euler’s theorem, Arithmetic functions, roots, and indices. Topology Order of topology, the base for a topology, connected spaces, compact space of the real line, countability axioms, Probability Theory Nature of data and methods of compilation, representation of data, measures of central tendency, measuring the variability of data, tools of interpreting numerical data, like mean, median, quartiles, standard deviation, skewness and kurtosis, and correlation analysis Differential Geometry Tensors, curves with torsion, envelopes and developable surfaces, involutes, tangent planes, and fundamental magnitudes. Linear Programming Convex sets opened and closed half-spaces, sensitivity analysis, parametric programming, transportation problems. Complex Analysis Geometric representation of numbers, complex-valued functions, power series, trigonometric functions, Cauchy’s theorem for the rectangle, in a disk and its general form. Geometry Of Numbers Lattices, Hermite’s theory of minima of positive definite quadratic forms. Elasticity Analysis of strain, analysis of stress, Equations of Elasticity, Inverse and semi-inverse methods of solution, General Equations of the plane problems in polar coordinates Vector Analysis Scalar and vector point functions, Green’s and Stoke’s theorems, Curi-linear coordinates, the equation of motion and first integral. Field Theory Fields, the theorem of Galois theory, Cyclotomic extensions, Lagrange’s theorem on primitive elements, degree field extensions and all other forms and applications of fields, and solvability of polynomials by radicals

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