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  #2  
23rd August 2018, 09:55 AM
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Re: Madras University Business Statistics

Can you provide me the M.Sc. (Master in Science) in Statistics Program Syllabus offered by Department of Statistics of University of Madras?
  #3  
23rd August 2018, 09:56 AM
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Join Date: Aug 2012
Re: Madras University Business Statistics

The M.Sc. (Master in Science) in Statistics Program Syllabus offered by Department of Statistics of University of Madras is as follows:

MSI C121 Statistical Mathematics


Unit I: Metric Space open, closed sets Intervals (rectangles), Real valued Continuous functions-Discontinuities - compact sets, Bolzano Weirstrass theorem, Heine Borel theorem.

Unit II: Derivatives - maxima and minima - Riemann integral & Riemann Stieltjes integral with respect an increasing integrator properties of R.S. integral. Functions of several variables, constrained and unconstrained maxima minima of functions, partial and total derivatives

Unit III: Basic properties of matrices (orthogonal, idempotent, kronecker product, projection operators etc); Linear dependence, independence and rankof a matrix; characteristic roots and polynomial, multiplicity of characteristic roots ;Cayley Hamilton theorem; inverse of a matrix and determinants;

Unit IV: Reduction of matrices, Echelon form, Hermite canonical form, diagonal reduction, rank factorization, triangular reduction Jordan form; Symmetric matrices and its properties; Decomposition like, singular value decomposition, spectral decomposition, Cholesky decomposition etc.

Unit V: Matrix differentiation; Generalized inverse and its propeties, Moore-Penrose inverse ; Application of g-inverse; Quadratic forms, classification, definiteness, index and signature, extremum; transformation and reduction of quadratic form; applications of quadratic forms.

REFERENCES:

Rudin, Walter (1976) : Principles of Mathematical Analysis, McGraw Hill.
Apostol, T.M. (1985) : Mathematical Analysis, Narosa, Indian Ed.
Royden, H.L.(1995) : Real analysis, 3ed., Prentice Hall of India.
Rangachari,M.S.(1996) : Real Analysis, Part 1, New Century Book House.
Ash, R.B. (1972) : Real analysis and probability, Academic press.
Biswas, S. (1984) : Topics in Algebra of Matrices, Academic Publications.
David, A.Harville(1997) : Matrix algebra from a statisticians perspective, Springer.
Hoffman, K. and Kunze, R. (1971) : Linear Algebra, 2nd ed. Prentice Hall, Inc.
Graybill, F.A. (1983) : Matrices with application in Statistics, 2nd ed. Wadsworth.
Rao, C.R. & Bhimasankaran, P.(1992) : Linear algebra, Tata McGraw Hill Pub. Co. Ltd.
Searle, S.R. (1982) : Matrix Algebra useful for Statistics, John Wiley and Sons, Inc.


here i am giving link of M.Sc.in Statistics Syllabus Department of Statistics of University of Madras
unom.ac.in/uploads/department/syllabus/66_msc-statistics-syllabus-2013-14.pdf


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