Commentary: High Level Data Filtration

Commentary: High Level Data Filtration

The consensus over the last five or so years has converged on a conclusion regarding data: we're drowning in it. We have more than we can possibly monitor with our own eyeballs, and certainly more than we know what to do with intelligently. The motto for data scientists has been "More is better." Well, ask…

On Server Efficiency

On Server Efficiency

For the full text of the paper, including all proofs and supplementary lemmata, click to download  Abstract Editor's note: This paper comprises the second chapter of the PhD dissertation by Rachel Traylor. Cha and Lee defined a mathematical notion of server performance by measuring efficiency defined as the long run average number of jobs completed per…

Commentary: Returning to Fundamentals in Tech

Commentary: Returning to Fundamentals in Tech

I once heard a great analogy about the difference between mathematicians and engineers in their problem-solving approaches. If an engineer and a mathematician are tasked with crossing a river, the engineer will create a set of stepping stones and get you across quickly, and safely in most cases. The mathematician will spend a month examining…

Reduce the Problem: Permutations and Modulo Arithmetic

Reduce the Problem: Permutations and Modulo Arithmetic

We've all seen permutations before. If you have ten distinct items, and rearrange them on a shelf, you've just performed a permutation. A permutation is actually a function that is performing the arrangement on a set of labeled objects. For simplicity, we can just number the objects and work with permuting the numbers.  (more…)

The Gravity of Mathematics: Summary of Tech Field Day at SDC 2017

The Gravity of Mathematics: Summary of Tech Field Day at SDC 2017

Fair warning - this will likely be one of the least technical posts I write. On September 14, I gave a presentation at Tech Field Day that wasn't actually storage related, but rather a call to rekindle the relationship between pure math and industry. Here I'll post the slides from that talk and summarize some of the…

The Central Limit Theorem isn’t a Statistical Silver Bullet

The Central Limit Theorem isn’t a Statistical Silver Bullet

Chances are, if you took anything away from that high school or college statistics class you were dragged into, you remember some vague notion about the Central Limit Theorem. It's likely the most famous theorem in statistics, and the most widely used. Most introductory statistics textbooks state the theorem in broad terms, that as the…

Cauchy Sequences: the Importance of Getting Close

Cauchy Sequences: the Importance of Getting Close

I am an analyst at heart, despite my recent set of algebra posts. Augustin Louis Cauchy can be argued as one of the most influential mathematicians in history, pioneering rigor in the study of calculus, almost singlehandedly inventing complex analysis and real analysis, though he also made contributions to number theory, algebra, and physics.  One…

Theory of Coding, Episode 2: Maximum-Likelihood Decoding

Theory of Coding, Episode 2: Maximum-Likelihood Decoding

The introduction to coding theory in this post will now allow us to explore some more interesting topics in coding theory, courtesy of Pinter's A Book of Abstract Algebra. We'll introduce the notion of a code, informations, and parity check equations. Most communication channels are noisy to some extent, which means that a transmitted codeword may have…

Group Theory, XOR, and Binary Codes: Introducing Coding Theory

Group Theory, XOR, and Binary Codes: Introducing Coding Theory

Binary codes and bit-wise operations are fundamental in computer science. Whatever device you are running today works because of binary codes, and the bit-wise operations AND, OR, NOT, and XOR. (A fun exercise, prove to yourself that each of these rules meets the definition of an operation. If you need a refresher, check out this…