Browsed by
Author: Rachel Traylor

Using Boolean Algebra to Find all Maximal Independent Sets in a Graph

Using Boolean Algebra to Find all Maximal Independent Sets in a Graph

Graph theory may be one of the most widely applicable topics I've seen in mathematics. It's used in chemistry, coding theory, operations research, electrical and network engineering, and so many other places. The subject is mainly credited to have begun with the famous  Seven Bridges of Königsberg problem posed by Leonard Euler in 1736. Frank Harary…

Beyond Cookbook Mathematics, Part 2

Beyond Cookbook Mathematics, Part 2

The previous article discussed the importance of definitions to mathematical thought. We looked at a definition (of an end-vertex in a graph), and picked it apart by finding multiple ways to look at it. We also directly used the definition in a practical manner to find “weak links” in a network. This time, we’ll look…

Beyond Cookbook Mathematics, Part 1

Beyond Cookbook Mathematics, Part 1

This post is due to the requests of several independent engineers and programmers. They expressed disappointment at their mathematics education and its failure to impart a deeper understanding of the formulas and algorithms they were taught to use.  This also reflects my observations of teaching university mathematics over the years. I started as a TA…

The Hathlor Classification System

The Hathlor Classification System

Many researchers have their own libraries, and The Math Citadel is no different. Both Jason and I have spent many hours buried in the shelves of bookstores new and used, the stacks of university library shelves, and the rows of books in public libraries across four states now. During this time, we've amassed our own…

On the Essential Nature of Foundations

On the Essential Nature of Foundations

We get asked frequently a valid question: why fund our research? Why fund mathematics research, when I can't see what the finished product will be, and you can't give me a guaranteed code library next quarter? I'm going to use an analogy of building and stray from my usual temptation to use math analogies. Every…

Paper Review: Active Queue Management with Non-Linear Packet Dropping Function

Paper Review: Active Queue Management with Non-Linear Packet Dropping Function

As promised in the previous article, I plan to review Reference 2, Active Queue Management with Non-Linear Packet Dropping Function, by D. Augustyn, A. Domanski, and J. Domanska, published in HET-NETs 2010, which discusses a change in the structure of the packet drop probability function using the average queue length in a buffer. I mentioned previously that…

Networking Mathematics: Random Early Detection and TCP synchronization

Networking Mathematics: Random Early Detection and TCP synchronization

Computer networks are something most of us take for granted--speed, reliability, availability are expectations. In fact, network problems tend to make us very angry, whether it's dropped packets (yielding jittery Skype calls), congestion (that huge game download eating all the bandwidth), or simply a network outage. There's an awful lot going on underneath the hood…

Little’s Law: For Estimation Only

Little’s Law: For Estimation Only

I had been intending on writing some posts on queuing theory for a while now, as this branch is the closest to my research interests and was the spark that sent me down the road that eventually led to my PhD dissertation. Most are quite familiar with the concepts of queuing theory, at least intuitively,…

Dialogue: What do We Mean by Predictive Analytics?

Dialogue: What do We Mean by Predictive Analytics?

Predictive analytics is a phrase that gets used often as a feature in many tech offerings. Predicting when a problem is likely to occur allows either a human or an automated system to take some action to mitigate a potential issue before it occurs and has potentially catastrophic effects. If we take data storage, for…

Cayley’s Theorem: Powerful Permutations

Cayley’s Theorem: Powerful Permutations

We've discussed before how powerful isomorphisms can be, when we find them. Finding isomorphisms "from scratch" can be quite a challenge. Thankfully, Arthur Cayley proved one of the classic theorems of modern algebra that can help make our lives a bit easier. We'll explore this theorem and note the power of groups of permutations.  (more…)