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what are the full syllabus for the entrance exam of m.s.,ph.d (mathematics) in the pondicherry university..?

what is the syllabus for msc mathemtics entrance exam ?

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what is the syllabus for msc mathemtics entrance exam ?

**Syllabus for M.Sc Mathematics::-

a)Real Analysis:- Basic topology, continuity, sequences and series, The
Lebesgue Integral, Lebesgue integral of step functions,
Lebesgue integral of upper functions, Simple and Step
Functions, Upper Functions.

b)Algebra:- Permutations and combinations, groups of order p square, Sylow
theorems, PQ, polynomial rings, matrix rings.


c) Number Theory :- Divisibility, Euler’s theorem, Euclidean theorem, roots and
indices, Arithmetic functions.

d)Field Theory :- The theorem of Galois theory, Lagrange’s theorem on
primitive elements, Cyclotomic extensions, degree field
extensions and all other forms and applications of fields.

e)Linear Programming:- Opened and closed half-spaces, Convex Sets,
sensitivity analysis, transportation problems,
parametric programming.

f)Probability Theory :-Nature of data and methods of compilation, measures of
central tendency, representation of data, measuring the
variability of data, tools of interpreting numerical data e.g
mean, median, quartiles, standard deviation.

g)Complex Analysis :-Power series, trigonometric functions, Geometric
representation of numbers, complex-valued functions,
Cauchy’s theorem for rectangle, disk and its general form.

*** Entrance exam name:-

1)BITSAT
2)IIT JAM
3)CMI
4)NEST
5)CUSCUT CAT
6)CUCET