A look into cartesian, spherical, and cylindrical coordinate systems. — This article is part of the series Mathematics for Quantum Mechanics. The Importance of Different Coordinate Systems Though most of us are familar with Cartesian coordinates, some quantum mechanical problems simplify greatly if calculated in a different coordinate system. The three main coordinate systems for modeling objects in three dimensions are Cartesian, spherical, and cyclindrical. …

A brief look into partial derivatives. — This article is part of the series Mathematics for Quantum Mechanics. If you have not read this article on derivatives of a single variable, I recommend you do that before reading this page. In quantum mechanics the quantities we are interested in deriving will often depend on more than one…

It is tradition when learning a new programming language that the very first program run prints the phrase “Hello World”. This article will walk you through how to write this customary program in four different programming languages: C++, Rust, Python, and Julia. C++ The C++ implementation of Hello World will be…

A brief introduction to cloud computing concepts. — Cloud computing is a pretty broad field but in general it is a collections of software and hardware that can be accessed entirely over the internet. Its main characteristics are that its on-demand, meaning that you get the resources you request when you request them, its pay-as-you-go, which means that…

This article presents a Python implementation of the algorithm presented in the paper Neural Networks Based Approach for Computing Eigenvectors and Eigenvalues of Symmetric Matrix by Zhang Yi and Yan Fu. Introduction Below is an algorithm for a neural network that can be used to find the smallest or largest eigenvectors…

A quick guide to derivatives with practice problems — This article is part of the series Mathematics for Quantum Mechanics. What is a Derivative? Geometrically speaking, given a function y(x), the derivative of the function is the slope of that function at the point x. From a physical standpoint, it is more useful to think of the slope of a curve in terms…

Regression algorithms are not as common in machine learning as their more fancy counterparts such as neural networks, but in the right contexts they can still be powerful predictive models. A benefit of using the regression algorithms over other machine learning models like neural networks is their simplicity. The mathematics…

Introduction Many machine learning courses and books start off with linear regression and there are a few reasons for this: 1. Linear regression is one of the most basic machine learning algorithms, but it contains all of the basic ingredients of a machine learning algorithm. 2. Linear regression has analytical expressions for its…