DESCRIPTION OF COURSES

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AS 551 MATHEMATICAL METHODS IN STATISTICS                       (4L+0P)

Objective
This is another course that supports all other courses in Statistics / Agricultural Statistics. The students would be exposed to the advances in linear algebra and matrix theory. This would prepare them to study their main courses that involve knowledge of linear algebra and matrix algebra.

Theory

UNIT I
Linear Algebra: Group, ring, field and vector spaces, sub-spaces, basis, Gram Schmidt’s Orthogonalization, Galois field - Fermat’s theorem and primitive elements. Linear transformations.

UNIT II
Real Analysis: Convergence and divergence of infinite series, use of comparison tests - D’Alembert’s Ratio - test, Cauchy’s nth root test, Raabe’s test, Kummer’s test, Gauss test. Absolute and conditional convergence. Riemann integration, concept of Lebesgue integration, power series, Fourier, Laplace and Laplace -Steiltjes’ transformation, multiple integrals.

UNIT III
Matrix Algebra: unitary, similar, hadamard, circulant, helmert’s matrices. Kronecker and hadamard product of matrices. Sub-matrices and partitioned matrices, permutation matrices, full rank factorization. Equations having many solutions.

UNIT IV
Generalized inverses, Moore-Penrose inverse, applications of g-inverse. Spectral decomposition of matrices, Differentiation and integration of matrices, Quadratic forms. Graph theory: Concepts and applications. Fuzzy set theory.

Suggested Readings