Coming soon
Statistical Mathematics
This course is meant for students who do not have sufficient background of Mathematics. The students would be exposed to elementary mathematics that would prepare them to study their main courses that involve knowledge of Mathematics. The students would be exposed to the basic mathematical tools of real analysis, calculus, differential equations and numerical analysis.
Vector space, sub space, linear combination of vectors, linearly dependent and independent vectors, basis and dimension, linear transformations of vectors, nullity and rank of linear transformation (Sylvester Theorem), Algebra of linear transformation.
Matrix: Basic terminology, row and column space, Echleon form, determinants, rank and inverse of matrix, characteristics roots and vectors, algebraic and geometric multiplicity of a characteristic root, Caley- Hamilton Theorem and its applications.
Special matrices: idempotent, orthogonal and symmetrical, reduction of a real symmetric matrix to a diagonal form. Quadratic forms: definition, reduction and classification, simultaneously reduction of two quadratic forms, maxima- minima of ratio of quadratic form.
Real analysis: sequence and series and their convergence, real valued function, continuous function, uniform continuity, differentiation, maxima –minima of function, function of several variables, constrained maxima –minima of function.
Numerical differentiation and integration, trapezoidal, Simpsons 1/3 and 3/8 rule, Weddle’s rule, solution of system of linear equations: Gauss estimation, Jacobi, Gauss-Seidel method. Numerical solution of non linear equations: Bisection method, Regula-Falsi method, Method of Iteration, Newton Rapson method. Numerical solution of ordinary differential equation: Picard, Euler and modified Euler, Runge-Kutta method
Books Recommended/Reference Books
1. Apostol, T.M. (1985):Mathematical Analysis, Narosa Publishing House.
2. Burkill,J.C.(1980):A first Course in Mathematical Analysis, Vikas Publishing House.
3. Cournat, R.and John, F. (1965): Introduction to Calculus and Analysis, John Wiley.
4. Khuri,A.l(1983): Advanced Calculus with Applications in Statistics, John Wiley.
5. Miller,K.S.(1957): Advanced Real Calculus, Harper, New York.
6. Sastry S.S. (1987): Introductory Methods of Numerical Analysis, Prentice Hall.
7. Saxena,H.C (1980).: Calculus of Finite Difference, S. Chand & Co.
8. Searle, S.R.(1982): Matrix Algebra Useful for Statistics, John Wiley
9. Shanti Narayan,(1998):A Textbook of Matrices , S. Chand & Co.
10. Harville, DA. (1997): Matrix Algebra from a Statistician’s Perspective, Springer.
11. Searle, SR. 1982. Matrix Algebra Useful for Statistics, John Wiley.
12. Rao, A.R. and Bhimasankaram, P(1992) : Linear algebra, Tata –McGraw-Hill Publishing Co. Ltd.
13. Rao,C.R., Mithra,S.K. (1971) : Generalized inverse of matrices and its applications, John Wiley & Sons Inc.
