Statistics and Optimization Algorithms

 Tentative

Participants will be equipped with standard techniques in descriptive and inferential Statistics and will be able to use these techniques in decision making

Participants will be equipped with standard techniques for solving various Mathematical problems numerically

Participants will be familiar with linear and non linear Optimization techniques and applications

MM-004-Numerical Methods:

1: Preliminaries of Computing: Errors, Taylor series approximations Solutions of algebraic and transcendental equations, system of nonlinear equations

2: Interpolation: Finite difference operators, Lagrange’s and Newton’s Interpolation, Error in interpolation

3 Numerical differentiation & Integration: Methods based on interpolation, finite differences, methods with error analysis, Trapezoidal and Simpson’s rule, Gauss quadrature method with error analysis

4: Solution of systems of Linear Equations: Direct Methods: Gaussian elimination method, Iterative methods, Solutions of Initial Value Problems

MM-005: Statistical Methods

1: Descriptive Statistics (Review)

2: Probability Distributions

3: Population and sample, sampling techniques,

4: Statistical Inference: Types of Hypothesis, hypothesis testing, Rejection and Non-rejection regions, Type-I and Type-II errors, Correlation and Regression

MM-006: Optimization

Linear Optimization

1: Linear Programming Problem (LPP): Sensitivity Analysis, Duality

Theory: Dual LPPs, Dual-Primal relationship, Results on duality, Relevant

Applications.

2:Transportation Problem (TP) and Assignment Problem (AP)

Nonlinear Optimization

1: Motivation and Background

2: Single Variable Optimization

3: Multivariable Unconstrained optimization

4: Multivariable Constrained optimization