Math

I came across an interesting approach to solving the problem of doubling the frequency in circuitry: use an analog multiplier. Indeed, if the incoming signal is a sine wave, then what could be simpler than multiplying the incoming signal by itself, i.e. …

An unsolved mystery in combinatorial number theory — Imagine 8 runners on a circular track of 1 unit length all running at different constant speeds and all starting from the same place. Will each runner be at least 1/8 units of the track away from every other runner at some point in time? Will each runner eventually become…

In this article, I will be introducing a field in mathematics known as calculus of variations which I explored in my IB Mathematics Internal Assessment. What is Calculus of Variations? To understand the intuition behind calculus of variations, it may help to consider a simple scenario where it would be used: finding the shortest path…

In the previous chapter, we introduced the idea of a vector space from a more intuitive and even geometric perspective. We said that a vector space is a set of objects that can be visualized as arrows and that interact with each other through an operation called addition. They can…

Table of contents Introduction Linear Regression: Concepts and Terminology Types of Linear Regression Evaluating Linear Regression Models Linear Regression in Practice Conclusion Introduction Linear regression is a fundamental concept in machine learning used to establish a relationship between a dependent variable and one or more independent variables. It is often the first algorithm used…

Many of my colleagues (both in the media and in academia) appear to know worryingly little about research on the limits and potential problems of AI. …

The most basic math guide I could come up with. — Note: Python will be used. This is not a comprehensive review of math Numbers Here are some different number systems: Natural numbers: Numbers such as 1, 2, 3, 4, 5, 6… so on. Only positive numbers here. Whole numbers: Same as the natural number, but zero is now added, so it’s…

“Spacetime tells matter how to move; matter tells spacetime how to curve.” The term “Relativity” was first discovered by Galileo Galilei. An example of this could be imagining yourself walking on the ground and a man is walking on the train beside you, now for the obvious reason his speed…

A comparison between more than two quantities (multitudes or magnitudes) of a different type. — The quantities being compared are called the “terms” of the rate. Multipart rates are also known as multi- term or multi- step rates. Multipart rates are usually written using the forward slash, /, to separate the terms: “𝑎 units / 𝑏 units / 𝑐 units…” As with rates, the forward…