# Ph. D Statistics

North Eastern Hill UniversityPrice on request

Price on request

Price on request

£ 295 - (Rs 25,163)

+ VAT

Free

## Important information

- PhD
- Shillong

Starts | Location |
---|---|

On request |
ShillongNorth-Eastern Hill University, Umshing Mawkynroh Shillong 793022, Meghalaya , 793022, Meghalaya, India See map |

## Course programme

Recap of elements of set theory; Introduction to real numbers. Introduction to ndimensional Euclidian space; open and closed intervals (rectangles), compact sets,

Bolzano – Weirstrass theorem, Heine – Borel theorem. Sequences and series; their convergence.

UNIT – II : Real valued function; continuous functions, uniform continuity. Differentiation; maxima

– minima of functions, functions of several variables, constrained maxima – minima of functions, mean value theorem, Taylor’s theorem, differentiation under the sign of

integral – Leibnitz rule.

UNIT – III : Fields, vector spaces, subspaces, linear dependence, basis and dimension of a vector space, completion theorem, linear equations. Vector spaces with an inner

product, Gram-Schmidt ortghogonalization process, orthonormal basis and

orthogonal projection of a vector.

UNIT – IV : Linear transformations, algebra of matrices, row an column spaces of a matrix, elementary matrices, determinants, rank and inverse of a matrix, partitioned matrices, Kronecker product. Real quadratic forms, positive definite matrix. Characteristic roots and vectors, Cayley – Hamilton theorem, minimal polynomial, similar matrices.

UNIT – V : Difference table. Methods of interpolation; Lagrange’s interpolation formula, Newton’s

divided difference formula. Numerical differentiation based on Newton’s and

Lagrange’s formula. Numerical integration; Trapezoidal, Simpson’s one-third and

three-eighth formula for numerical integration.