Browsed by
Month: September 2017

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…