Statistical Mathematics

Paper Code: 
DSTT 701(B)
Credits: 
6
Contact Hours: 
90.00
Max. Marks: 
100.00
Objective: 

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.

 

Students will be able to:

Course

Learning outcomes (at course level

Learning and teaching strategies

Assessment Strategies

Paper Code

Paper Title

DSTT 701 (B)

Statistical Mathematics

 

CO 87: Learn the concept of a vector space, base and dimension of vector space and linear transformation of vectors.

 

CO 88: Use the concept of matrices, rank, characteristic roots, Cayley Hamilton theorem and applications.

 

CO 89: Define special matrices and solve problems related to Quadratic forms.

 

CO 90: Identify the concept of sequence, series, continuity and differentiability of real numbers and maxima-minima of functions.

 

CO 91: Learn numerical methods related to differentiation, integration and finding numerical solution of nonlinear equations and ordinary differential equations.

Approach in teaching:

 

 

Interactive Lectures,

Group Discussion,

Classroom Assignment

Problem Solving Sessions

 

 

Learning activities for the students:

 

Assignments

Seminar

Presentation

Subject based Activities

 

Classroom Quiz

Assignments

Class Test

Individual Presentation

 

 

 

12.00
Unit I: 

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 transformations (elementary properties).

12.00
Unit II: 

Matrix: Basic terminology, row and column space, Echleon form, determinants, rank and inverse of matrix, characteristics roots and vectors, Caley- Hamilton Theorem and applications.

12.00
Unit III: 

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.

12.00
Unit IV: 

Real analysis: sequence and their convergence, real valued function, continuous function, discontinuity: Borel covering theorem, Boundness theorem and moistest theorem, differentiation, maxima and minima of one variable function.

12.00
Unit V: 

Numerical integration, trapezoidal, Simpsons 1/3 and 3/8 rule, solution of system of linear equations: Gauss estimation, Jacobi, Gauss-Seidel method. Numerical solution of nonlinear equations: Bisection method, Regula-Falsi method, Method of Iteration, Newton Rapson method. Numerical solution of ordinary differential equation: Runge-Kutta method.

Essential Readings: 
  • Apostol, T.M. (1985): Mathematical Analysis, Narosa Publishing House.
  • Burkill,J.C.(1980):A first Course in Mathematical Analysis, Vikas Publishing House.
  • Cournat, R.and John, F. (1965): Introduction to Calculus and Analysis, John Wiley.
  • Khuri,A.l(1983): Advanced Calculus with Applications in Statistics, John Wiley.
References: 

SUGGESTED READINGS:

  • Miller,K.S.(1957): Advanced Real Calculus, Harper, New York.
  • Sastry S.S. (1987): Introductory Methods of Numerical Analysis, Prentice Hall.
  • Saxena,H.C (1980).: Calculus of Finite Difference, S. Chand & Co.
  • Searle, S.R.(1982): Matrix Algebra Useful for Statistics, John Wiley
  • Shanti Narayan,(1998):A Textbook of Matrices , S. Chand & Co, 12 th revised edition.
  • Harville, DA. (1997): Matrix Algebra from a Statistician’s Perspective, Springer.
  • Searle, SR. (1982). Matrix Algebra Useful for Statistics, John Wiley.
  • Rao, A.R. and Bhimasankaram, P(1992) : Linear algebra, Tata –McGraw-Hill Publishing Co. Ltd.
  • Rao,C.R., Mithra,S.K. (1971) : Generalized inverse of matrices and its applications, John Wiley & Sons Inc.

e-RESOURCES:

JOURNALS:

  • Sankhya The Indian Journal of Statistics, Indian Statistical Institute
  • Aligarh Journal of Statistics, Department of Statistics and Operations Research, Aligarh
  • Muslim University
  • Afrika Statistika, Saint-Louis Senega University
  • International Journal of Statistics and Reliability Engineering, Indian Association for Reliability
  • and Statistic
  • Journal of the Indian Society for Probability and Statistics, Indian Society for Probability and
  • Statistics
  • Journal of the Indian Statistical Association, Indian Statistical Association
  • Statistica, Department of Statistical Sciences Paolo Fortunato, University of Bologna
  • Statistics and Applications, Society of Statistics, Computer and Applications
  • Stochastic Modeling and Applications, MUK Publications and Distributions
Academic Year: 
2023-2024
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