Numerical Methods and Optimization in Python

About Numerical Methods and Optimization in Python

This course is about numerical methods and optimization algorithms in Python programming language.

We are NOT going to discuss ALL the theory related to numerical methods (for example how to solve differential equations etc.) - we are just going to consider the concrete implementations and numerical principles

The first section is about matrix algebra and linear systems such as matrix multiplication, gaussian elimination and applications of these approaches. We will consider the famous Google's PageRank algorithm. Then we will talk about numerical integration. How to use techniques like trapezoidal rule, Simpson formula and Monte-Carlo method to calculate the definite integral of a given function. The next chapter is about solving differential equations with Euler's-method and Runge-Kutta approach. We will consider examples such as the pendulum problem and ballistics. Finally, we are going to consider the machine learning related optimization techniques. Gradient descent, stochastic gradient descent algorithm, ADAGrad, RMSProp and ADAM optimizer will be discussed - theory and implementations as well.

IF YOU ARE NEW TO PYTHON PROGRAMMING THEN YOU CAN LEARN ABOUT THE FUNDAMENTALS AND BASICS OF PYTHON IN THA LAST CHAPTERS

Section 1 - Numerical Methods Basics

numerical methods basics

floating point representation

rounding errors

performance C, Java and Python

Section 2 - Linear Algebra and Gaussian Elimination

linear algebra

matrix multiplication

Gauss-elimination

portfolio optimization with matrix algebra

Section 3 - Eigenvectors and Eigenvalues

eigenvectors and eigenvalues

applications of eigenvectors in machine learning (PCA)

Google's PageRank algorithm explained

Section 4 - Interpolation

Lagrange interpolation theory

implementation and applications of interpolation

Section 5 - Root Finding Algorithms

solving non-linear equations

root finding

Newton's method and bisection method

Section 6 - Numerical Integration

numerical integration

rectangle method and trapezoidal method

Simpson's method

Monte-Carlo integration

Section 7 - Differential Equations

solving differential-equations

Euler's method

Runge-Kutta method

pendulum problem and ballistics

Section 8 - Numerical Optimization (in Machine Learning)

gradient descent algorithm

stochastic gradient descent

ADAGrad and RMSProp algorithms

ADAM optimizer explained

IF YOU ARE NEW TO PYTHON PROGRAMMING THEN YOU CAN LEARN ABOUT THE FUNDAMENTALS AND BASICS OF PYTHON IN THA LAST CHAPTERS

Thanks for joining my course, let's get started!