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Syllabus


Name of the SubjectTopics Covered
Real AnalysisBasic topology, sequences and series, continuity, The Lebesgue Integral, Simple and Step Functions, Lebesgue integral of step functions, Upper Functions, Lebesgue integral of upper functions.
AlgebraPermutations and combinations, Sylow theorems, groups of order p square, PQ, polynomial rings, matrix rings
Number TheoryDivisibility, Euclidean theorem, Euler’s theorem, Arithmetic functions, roots and indices.
TopologyOrder of topology, Base for a topology, connected spaces, compact space of the real line, countability axioms,
Probability TheoryNature 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 GeometryTensors, curves with torsion, envelopes and developable surfaces, involutes, tangent planes and fundamental magnitudes.
Linear ProgrammingConvex Sets, Opened and closed half-spaces, sensitivity analysis, parametric programming, transportation problems.
Complex AnalysisGeometric representation of numbers, complex-valued functions, power series, trigonometric functions, Cauchy’s theorem for rectangle, in a disk and its general form.
Geometry of NumbersLattices, Hermite’s theory on minima of positive definite quadratic forms.
ElasticityAnalysis 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 AnalysisScalar and vector point functions, Green’s and Stoke’s theorems, Curi-linear coordinates, the equation of motion and first integral.
Field TheoryFields, 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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