Semester II

This module aims at preparing students about the formulation of different Mathematical problems in form  of nonlinear systems and their analysis. The intent of this module is to present several of the important existence theorems for solutions of various types of problems associated with differential equations and provide qualitative and quantitative descriptions for solutions. At the same time we develop numerical methods of analysis of different problems which have applications in many other areas of mathematics, as well.

The main focus of this course will be based  on formulation of simple and multiple regression models, give an account of the principle of least squares; carry out tests of linear hypothesis, perform validation of a regression model, select the important explanatory variables and to interpret the results .

The module of Operations Research and optimisation is design to equip the leaners with knowledge and practical skills enabling him confidently 

(1) To model real life problems using mathematical tools;

(2)  To solve real life problems using Linear and nonlinear programming tools;

(3) To use IT tools (Operations Research or other mathematical software) as a support while solving problems. These include the utilisation of software: R, Python, Excel or TORA.

The module aims to provide the students with a solid background of inferential statistics. It is intended to impart the core of statistical inference: estimation and hypothesis testing. It covers

1. Random sample and sampling distribution;
2. Point estimators and methods of estimation;
3. Estimation with confidence interval;
4. Hypothesis testing on population parameters;
5. Inference for simple linear regression;
6. Analysis of Variance (ANOVA);
7. Bayesian inference;
8. Applications with R.

The following open access book may be used to supplement lectures handout.

https://www.degruyter.com/view/title/534115?tab_body=toc-62810

 Mathematical Modelling

  This Course aims at preparing students about the formulation of different Mathematical Models  and gives them an idea of solving the Models.  The intent of this course is to present several of the important existence theorems for solutions of various types of problems associated with differential equations and provide qualitative and quantitative descriptions for solutions.

Mathematical Modelling: Simple Situations requiring Mathematical Modelling, The Technique of Mathematical Modelling, Modelling Through Trigonometry, Geometry, Ordinary Differential Equations, Modelling through a System of ODEs, Mathematical Modelling Through ODE of 2^nd Order, Mathematical Modelling through Difference Equations, Mathematical Modelling Through PDEs. Application to infectious diseases.

 Learning Outcomes

Upon Completion of this Module students, should have a reasonable understanding of:

• the definitions and terms related to the Module aims as well as the Course Contents.
• the statements , proofs and implications of the basic results.
• should be able to present  simple arguments and conclusions using Mathematical modelling arguments with clarity.