Trans-Finite Ordinals

Axioms of Set Theory Now, in my other articles, I have introduced rigorous mathematics to people who may not be familiar with it. Today, the rigor will be stepped up 10 fold. So, now, let me introduce you to the idea of axioms: We have already discussed axioms in the topic of Topology and VectorSpaces, but […]

GR Article II: MultiLinear Algebra

This article assumes knowledge of abstract VectorSpaces, discussed in this article. Now, onto the difficulties. Dual VectorSpace Say we have two VectorSpaces and . Then, we define: Here, we assume that the tilde (the little squiggle) above the arrow means linear, or in many cases, multilinear. This has a VectorSpace structure, where Now, we define […]

Plasma Oscillations – “Langmuir Wave” approximation derivation

In a previous article we established an approximate estimate for the frequency of oscillations in a “cold plasma” because of small disturbances in the arrangement of the electrons and ions. In this article we will establish a much better model for oscillations in a plasma, which takes into consideration the fact that Plasmas tend to be […]

Inside the CPU – Instruction cycles

One of the most widely taught processes of a computer is the instruction cycle (fetch-decode-execute cycle), yet it seems to be one that causes a lot of headache with students. Instead of finding a way to memorise all the acronyms and orders, how about we clearly explain why each process happens, rather than simply what […]

GR Article I: Topology

Topology Open intervals; something you may have thought was useless or underwhelmingly unimportant. But, in actuality, they have helped built one of the major fields in Modern Mathematics, and has propelled the world of physics, and General Relativity, to the way you see it now. I am taking about how it founded the world of […]

Linear Algebra: Derivation of formula for the inverse of a matrix and Cramer’s rule

In this article I shall attempt to derive a formula for the inverse of a matrix, and from there derive Cramer’s rule. I feel that many textbooks and courses on linear algebra (especially at high-school level) present matrices and their corresponding formulas and definitions without giving any hint of where these ideas came from, and […]

Calculus Proof of Centripetal Acceleration Magnitude

In basic circular motion in physics we are given the following equation for the centripetal acceleration on a body moving in circular motion: However how can this be proved? Well, acceleration is a vector- so what we need to know is it’s magnitude and direction. The second part of which is obvious, it’s in the […]