What you would learn in Numerical Methods and Optimization in Python course?
This course focuses on mathematical methods and optimization algorithms within Python, the programming language.
The first part is about linear systems and matrix algebra like matrix multiplication and gaussian elimination and the application of these techniques. We will examine the well-known page rank algorithm developed by Google. PageRank algorithm.
We will discuss numerical integration. Techniques to use such as the trapezoidal rule Simpson formula and the Monte-Carlo technique to determine the definitive integral.
The next chapter will solve differential equations using Euler's method and the Runge-Kutta method. We will examine instances like the pendulum problem and ballistics.
We will also continue to examine optimization methods based on machine learning. The gradient descent stochastic gradient descent algorithm, ADAGrad, RMSProp, and ADAM optimizer will be reviewed the theory and its implementation.
Part 1: Numerical Methods Fundamentals
Basics of numerical methods
floating-point representation
rounding errors
efficiency C, Java and Python
Section 2 Linear Algebra and Gaussian Elimination
Section 3 - Eigenvectors and Eigenvalues
eigenvectors and eigenvalues
applications of eigenvectors in machine-learning (PCA)
Google's PageRank algorithm explained
4. Interpolation
Section 5 The Root Finding Algorithms
Section 6 Numerical Integration
7. Section 7 - Differential Equations
Section 8 Numerical Optimization (in Machine Learning)
gradient descent algorithm
stochastic gradient descent
ADAGrad as well as RMSProp algorithms
ADAM optimizer explained
Course Content:
- Learn about linear systems and Gaussian elimination
- Understand eigenvectors and eigenvalues
- Learn about Google's PageRank algorithm.
- Know the concept of the importance of numerical integration
- Know Monte-Carlo simulations
- Know differential equations, Euler's method as well as Runge-Kutta's method
- Know about machine learning-related algorithmic optimization (gradient descent stochastic gradient descent ADAM optimizer, etc.)
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