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 Basicsnumerical methods basicsfloating point representationrounding errorsperformance C, Java and PythonSection 2 - Linear Algebra and Gaussian Eliminationlinear algebramatrix multiplicationGauss-eliminationportfolio optimization with matrix algebraSection 3 - Eigenvectors and Eigenvalueseigenvectors and eigenvalues