Math: Advanced

Updated: July 2024

Introduction

Here Be Dargons

From this point on, all material is higher education. Do not worry if it's to peculiar, puzzling, perplexing, or perspiring. This is a resource for harder challenges, to add depth for difficult topics in robotics. Tackling the mathematics of AI and Machine Learning, Calculus, Optical Systems, Statistics, and so so much more.

These topics are lightly covered for the curious and idle minds. The folks who are hungry for more, and are looking for a challenge. You have been warned. 💀

Linear Algebra

Here we expand on the Vector and Matrix sections from prior articles. These have been testing the waters of an incredibly important field in math called Linear Algebra.


Dot Product
Cross Product
Basic Transformations
Matrix Transformations
Homogenous Coordinates

Calculus

This is merely the fundamentals of calculus. Understanding the relationship between a derivative, integral, and the math behind curves.


Derivatives
Integrals

Physics

This is a short section on what builds on top of early physics.


Energy
Work

Statistics

This is a section on continuous statistics and probabilities.


Standard Deviation
Normal Distribution
Probability Density
Cumulative Distribution

Machine Learning

This is a section that tackles Machine Learning, distinct from AI. While tightly coupled they are not the same thing. AI is an incredibly scenario dependent problem space, and difficult to generalize in a useful way. Machine Learning is a tool that greatly enables AI to function, and is easier to document.


Regression
Classification
Linear Regress/Class
Convolutional Neural Net

Camera Systems

This is a section on optics. How a camera works, what a lens does, and why calibration is incredibly important. This does not get into the quantum world. Almost everything discussed will be at the geometric level.


Lens Systems
Focal Points
Intrinsic Matrix
Sensor Arrays