Topology 4: Hausdorff Topologies and Closed Sets

First, we define what is meant by a closed set. Definition 4.1 Closed Set We say a subset of a Topological space is closed if is open. Now, the intuition behind closed sets is that these sets include their boundary, so that when you remove them from the entire set, they don’t include their boundary […]

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 […]

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 […]